g1 m4 Full - Module PDF

New York State Common Core
1
GRADE
Mathematics Curriculum
GRADE 1 • MODULE 4
Table of Contents
Place Value, Comparison, Addition and Subtraction to 40
Module Overview ......................................................................................................... i
Topic A: Tens and Ones ......................................................................................... 4.A.1
Topic B: Comparison of Pairs of Two-Digit Numbers .............................................. 4.B.1
Topic C: Addition and Subtraction of Tens ............................................................. 4.C.1
Topic D: Addition of Tens or Ones to a Two-Digit Number .....................................4.D.1
Topic E: Varied Problem Types Within 20 .............................................................. 4.E.1
Topic F: Addition of Tens and Ones to a Two-Digit Number................................... 4.F.1
Module Assessments ............................................................................................. 4.S.1
Module 4: Place Value, Comparison, Addition and Subtraction to 40

Date: 9/20/13 i
© 2013 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM Module Overview Lesson
1
Grade 1 • Module 4
Place Value, Comparison, Addition
and Subtraction to 40
OVERVIEW
Module 4 builds upon Module 2’s work with place value within 20, now focusing on the role of place value in
the addition and subtraction of numbers to 40.
The module opens with Topic A, where students study, organize, and manipulate numbers within 40. Having
worked with creating a ten and some ones in Module 2, students now recognize multiple tens and ones.
Students use fingers, linking cubes, dimes, and pennies to represent numbers to 40 in various ways: from all
ones to tens and ones (1.NBT.2). They use a place value chart to organize units. The topic closes with the
identification of 1 more, 1 less, 10 more, and 10 less, as students learn to add or subtract like units (1.NBT.5).
In Topic B, students compare quantities and begin using the symbols for
greater than (>) and less than (<) (1.NBT.3). Students demonstrate their
understanding of place value when they recognize that 18 is less than 21
since 2 tens already have a greater value than 1 ten 8 ones. To support
understanding, the first lesson in the topic focuses on identifying the
greater or lesser amount. With this understanding, students label each of
the quantities being compared and compare from left to right. Finally,
students are introduced to the mathematical symbols, using the story of
the alligator whose hungry mouth always opens toward the greater
number. The abstract symbols are introduced after the conceptual
foundation has been laid.
Topic C focuses on addition and subtraction of tens (1.NBT.4, 1.NBT.6). Having used concrete models in Topic
A to represent 10 more and 10 less, students now recognize that just as 3 + 1 = 4, 3 tens + 1 ten = 4 tens.
With this understanding, students add and subtract a multiple of 10 from another multiple of 10. The topic
closes with the addition of multiples of 10 to numbers less than 40, e.g., 12 + 30.
In Topic D, students use familiar strategies to add two-digit and single-digit numbers within 40. Students
apply the Level 2 strategy of counting on and use the Level 3 strategy of making ten, this time making the next
ten (1.NBT.4). For instance, when adding 28 + 5, students break 5 into 2 and 3 so that they can make the next
ten, which is 30, or 3 tens, and then add 3 to make 33. The topic closes with students sharing and critiquing
peer strategies.
In Topic E, students consider new ways to represent larger quantities when approaching put together/take
apart with total or addend unknown and add to with result or change unknown word problems. Students
begin labeling drawings with numerals, and eventually move to tape diagrams to represent the problem
pictorially (1.OA.1). Throughout this topic, students will continue developing their skills with adding single-
and double-digit numbers, introduced in Topic D, during fluency activities.

Date: 9/20/13 ii
1
The module closes with Topic F, focusing on adding like place value units as students add two-digit numbers.
The topic begins with interpreting two-digit numbers in varied combinations of tens and ones (e.g., 34 = 34
tens 4 tens 14 ten 24 ones). This flexibility in representing a given number
prepares students for addition with regrouping (e.g., 12 + 8 = 1 ten 10 tens or 18 + 16 = 2 tens 14
tens 4 ones). To close the module, students add pairs of numbers with varied sums in the ones to
support flexibility in thinking.

Date: 9/20/13 iii
1
Focus Grade Level Standards1

Represent and solve problems involving addition and subtraction. 2
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding
to, taking from, putting together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a symbol for the unknown
number to represent the problem. (See CCLS Glossary, Table 1.)
Extend the counting sequence.3

1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals
and represent a number of objects with a written numeral.
Understand place value.4

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.
Understand the following as special cases:
a. 10 can be thought of as a bundle of ten ones – called a “ten.”
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six,
seven, eight, or nine tens (and 0 ones).
1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits, recording the
results of comparisons with the symbols >, =, and <.
Use place value understanding and properties of operations to add and subtract.5
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a
two-digit number and a multiple of 10, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the relationship between addition and
subtraction; relate the strategy to a written method and explain the reasoning used.
Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and
sometimes it is necessary to compose a ten.
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having
to count; explain the reasoning used.
1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive
or zero differences), using concrete models or drawings and strategies based on place value,
properties of operations, and/or relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
1
While the use of pennies and dimes will be used throughout the module, 1.MD.3 is not a focus grade level standard in Module 4.
Instead, this standard will become a focal standard in Module 6, when all coins are introduced and used.
2
The balance of this cluster is addressed in Module 2.
3
Focus on numbers to 40.
4
5

Date: 9/20/13 iv
1
Foundational Standards
K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using
objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3
and 5 = 4 + 1).
K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number,
e.g., by using objects or drawings, and record the answer with a drawing or equation.
K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g.,
by using objects or drawings, and record each composition or decomposition by a drawing or
equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and
one, two, three, four, five, six, seven, eight, or nine ones.
Focus Standards for Mathematical Practice

MP.3 Construct viable arguments and critique the reasoning of others. Students describe and
explain their strategies for adding within 40, and critique and adjust student samples to more
efficiently solve addition problems.
MP.5 Use appropriate tools strategically. After learning varied representations and strategies for
adding and subtracting pairs of two-digit numbers, students choose their preferred methods
for representing and solving problems efficiently. Students may represent their computations
using arrow notation, number bonds, quick ten drawings, and linking cubes. As they share
their strategies, students explain their choice of counting on, making ten, adding tens and
then ones, or adding ones and then tens.
MP.6 Attend to precision. Students recognize and distinguish between units, demonstrating an
understanding of the difference between 3 tens and 3 ones. They use this understanding to
compare numbers and to add like place value units.
MP.7 Look for and make use of structure. Students are introduced to the place value chart,
deepening their understanding of the structure within our number system. Throughout the
module, students use this structure as they add and subtract within 40. They recognize the
similarities between 2 tens + 2 tens = 4 tens and 2 + 2 = 4, and use their understanding of tens
and ones to explain the connection.

Date: 9/20/13 v
1
Overview of Module Topics and Lesson Objectives

Standards Topics and Objectives Days
1.NBT.1 A Tens and Ones 6
1.NBT.2 Lesson 1: Compare the efficiency of counting by ones and counting by
1.NBT.5 tens.
Lesson 2: Use the place value chart to record and name tens and ones
within a two-digit number.
Lesson 3: Interpret two-digit numbers as either tens and some ones or as
all ones.
Lesson 4: Write and interpret two-digit numbers as addition sentences
that combine tens and ones.
Lesson 5: Identify 10 more, 10 less, 1 more, and 1 less than a two-digit
number.
Lesson 6: Use dimes and pennies as representations of tens and ones.
1.NBT.3 B Comparison of Pairs of Two-Digit Numbers 4

1.NBT.1 Lesson 7: Compare two quantities, and identify the greater or lesser of
1.NBT.2 the two given numerals.
Lesson 8: Compare quantities and numerals from left to right.
Lessons 9–10: Use the symbols >, =, and < to compare quantities and
numerals.
1.NBT.2 C Addition and Subtraction of Tens 2

1.NBT.4 Lesson 11: Add and subtract tens from a multiple of 10.
1.NBT.6
Lesson 12: Add tens to a two-digit number.
Mid-Module Assessment: Topics A–C (assessment 1 day, return 1 day, 3

remediation or further applications 1 day)
1.NBT.4 D Addition of Tens or Ones to a Two-Digit Number 6

Lessons 13–14: Use counting on and the make ten strategy when adding across
a ten.
Lesson 15: Use single-digit sums to support solutions for analogous sums
to 40.
Lessons 16–17: Add ones and ones or tens and tens.
Lesson 18: Share and critique peer strategies for adding two-digit
numbers.

Date: 9/20/13 vi
1
Standards Topics and Objectives Days

1.OA.1 E Varied Problem Types Within 20 4
Lesson 19: Use tape diagrams as representations to solve put
together/take apart with total unknown and add to with result
unknown word problems.
Lessons 20–21: Recognize and make use of part–whole relationships within
tape diagrams when solving a variety of problem types.
Lesson 22: Write word problems of varied types.
1.NBT.4 F Addition of Tens and Ones to a Two-Digit Number 7

Lesson 23: Interpret two-digit numbers as tens and ones including cases
with more than 9 ones.
Lessons 24–25: Add a pair of two-digit numbers when the ones digits have a
sum less than or equal to 10.
Lessons 26–27: Add a pair of two-digit numbers when the ones digits have a
sum greater than 10.
Lessons 28–29: Add a pair of two-digit numbers with varied sums in the ones.
End-of-Module Assessment: Topics D–F (assessment 1 day, return 1 day, 3

remediation or further applications 1 day)
Total Number of Instructional Days 35
Terminology
New or Recently Introduced Terms
 > (greater than)
 < (less than)
 Place value (quantity represented by a digit in a particular place within a number)
Familiar Terms and Symbols6

 Equal (=)
 Numerals
 Ones
 Tens
6
These are terms and symbols students have seen previously.

Date: 9/20/13 vii
1
Suggested Tools and Representations

 Arrow notation
 Comparison symbols: >, <, =
 Dime
 Hide Zero cards Arrow Notation
 Hundred chart
 Number bond
 Penny
 Place Value Chart
 Quick Ten
 Rekenrek
Hide Zero Cards
 Tape Diagram
whole
part part
Hundred Chart to 40 Number Bond
tens ones
3 4
Quick Ten
Place Value Chart
Tape Diagram
Rekenrek

Date: 9/20/13 viii
1
Scaffolds7
The scaffolds integrated into A Story of Units give alternatives for how students access information as well as
express and demonstrate their learning. Strategically placed margin notes are provided within each lesson
elaborating on the use of specific scaffolds at applicable times. They address many needs presented by
English language learners, students with disabilities, students performing above grade level, and students
performing below grade level. Many of the suggestions are applicable to more than one population. The
charts included in Module 1 provide a general overview of the lesson-aligned scaffolds, organized by
Universal Design for Learning (UDL) principles. To read more about the approach to differentiated instruction
in A Story of Units, please refer to “How to Implement A Story of Units.”
Assessment Summary
Type Administered Format Standards Addressed
Mid-Module After Topic C Constructed response with rubric 1.NBT.1
Assessment Task 1.NBT.2
1.NBT.3
1.NBT.4
1.NBT.5
1.NBT.6
End-of-Module After Topic F Constructed response with rubric 1.OA.1
Assessment Task 1.NBT.1
1.NBT.2
1.NBT.3
1.NBT.4
1.NBT.5
1.NBT.6
7
Students with disabilities may require Braille, large print, audio, or special digital files. Please visit the website,
www.p12.nysed.gov/specialed/aim, for specific information on how to obtain student materials that satisfy the National Instructional
Materials Accessibility Standard (NIMAS) format.

Date: 9/20/13 ix
1
GRADE
Topic A
Tens and Ones
1.NBT.1, 1.NBT.2, 1.NBT.5
Focus Standard: 1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write
numerals and represent a number of objects with a written numeral.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and
ones. Understand the following as special cases:
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five,
six, seven, eight, or nine tens (and 0 ones).
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without
having to count; explain the reasoning used.
Instructional Days: 6
Coherence -Links from: G1–M2 Introduction to Place Value Through Addition and Subtraction Within 20
-Links to: G2– M3 Place Value, Counting, and Comparison of Numbers to 1,000
Module 4 builds on students’ work with teen numbers to now work within 40. Working within 40 helps
students focus on the units, tens and ones, which can be easily modeled pictorially and concretely with these
smaller numbers. The smaller numbers also allow students to count all while having an important experience
of its inefficiency. Students’ innate ability to subitize to 4 keeps the numbers friendly when both adding and
subtracting tens for the first time and managing the new, complex task of considering both tens and ones
when adding. Through their work within 40, students develop essential skills and
concepts that generalize easily to numbers to 100 in Module 6.
In Lesson 1, students are presented with a collection of 20 to 40 items. They discuss
and decide how to count the items, and then compare the efficiency of counting
individual ones with counting tens and ones. Through this exploration, students
come to understand the utility of ten as a unit: both as a method for counting, and
for efficiently recording a given number (1.NBT.1, 1.NBT.2). Students keep their
own set of 40 linking cubes, organized as a kit of 4 ten-sticks, to use as they
tens ones
progress through the module.
3 4
In Lesson 2, students represent and decompose two-digit numbers as tens and
ones, and record their findings on a place value chart, supported by the familiar
Hide Zero cards. Students share thoughts such as, “The 3 in 34 stands for 3 tens.
And the 4 in 34 is just 4 ones!” Up to this point, students have worked with
representations of ten where 10 ones are clearly visible (e.g., as two 5-groups). Place Value Chart
Topic A: Tens and Ones

Date: 9/20/13 4.A.1
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NYS COMMON CORE MATHEMATICS CURRICULUM Topic A 1
While the digit 3 in 34 may appear smaller than the digit 4, its value is determined by its position. Use of the
place value chart represents the students’ first experience with this additional layer of abstraction.
Lesson 3 allows students to explore two-digit numbers as tens and ones, and as just ones. Students use their
fingers to represent “bundled” tens and “unbundled” ones by clasping and unclasping their fingers. For
example, students model 34 with 3 students showing their hands clasped to make a ten, and a fourth student
showing 4 fingers to represent 4 ones. Taking student understanding of place value a step further, Lesson 4
asks students to decompose and compose two-digit numbers as addition equations. Students develop an
understanding that “34 is the same as 30 + 4,” as they move between writing the number when given the
equations and writing the equations when given a number. Throughout these lessons, students use concrete
objects and/or drawings in order to support their understanding and explain their thinking.
Topic A concludes with Lessons 5 and 6, where students use materials and drawings to find 10 more, 10 less,
1 more, and 1 less than a given number (1.NBT.5). In Lesson 5, students use the familiar linking cubes
(organized into tens) and 5-group columns. They engage in conversation about patterns they observe, “I see
that 10 less than 34 is just 1 less ten, so it must be 24!”
Students represent how the number changed using arrow
notation, or the arrow way, as shown to the right. Lesson
6 then introduces the dime and penny as representations
of ten and one respectively.1 Students make the
connection between the familiar representations of tens
and ones to the dime and the penny, and work to find 10
more, 10 less, 1 more, and 1 less.
A Teaching Sequence Towards Mastery of Tens and Ones

Objective 1: Compare the efficiency of counting by ones and counting by tens.
(Lesson 1)
Objective 2: Use the place value chart to record and name tens and ones within a two-digit number.
(Lesson 2)
Objective 3: Interpret two-digit numbers as either tens and some ones or as all ones.
(Lesson 3)
Objective 4: Write and interpret two-digit numbers as addition sentences that combine tens and ones.
(Lesson 4)
Objective 5: Identify 10 more, 10 less, 1 more, and 1 less than a two-digit number.
(Lesson 5)
Objective 6: Use dimes and pennies as representations of tens and ones.

(Lessons 6)
1
Integrates the 1.MD.3 standard for dime and penny. This standard will become a focal standard in Module 6, when all 4 coins have
been introduced.
Topic A: Tens and Ones

Date: 9/20/13 4.A.2
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 1•4
Lesson 1
Objective: Compare the efficiency of counting by ones and counting by
tens.
Suggested Lesson Structure

Fluency Practice (10 minutes)

Application Problem (5 minutes)

Concept Development (35 minutes)

Student Debrief (10 minutes)
Total Time (60 minutes)
 Break Apart Numbers 1.OA.6 (4 minutes)

 Change 10 Pennies for 1 Dime 1.NBT.2 (4 minutes)
 Happy Counting by Tens 1.NBT.5 (2 minutes)
Break Apart Numbers (4 minutes)

Materials: (S) Personal white boards with break apart numbers template
Note: Reviewing decomposing numbers 5–9 supports Grade 1’s required fluency of adding and subtracting
within 10 and is an essential skill in order to apply the Level 3 addition strategy of making ten. If students
struggle with this activity, consider repeating it in lieu of some of the fluency activities that provide practice
with numbers to 20 and beyond.
Students complete as many different number bonds as they can in one minute. Take a poll of how many
students completed all decompositions for 5, 6, etc., and celebrate accomplishments.
Change 10 Pennies for 1 Dime (4 minutes)

Materials: (T) 10 pennies, 1 dime (S) 10 pennies and 1 dime per pair
Note: This activity helps students to see that 10 cents is equal to 1 dime just as 10 ones are equal to 1 ten.
This fluency activity is necessary to prepare students to utilize coins as abstract units that represent tens and
ones in G1–M1–Lesson 6.
Lay out 10 pennies into 5-groups as students count (1 cent, 2 cents, etc.). Make sure students include the
unit as they count.
Lesson 1: Compare the efficiency of counting by ones and counting by tens.

Date: 9/20/13 4.A.3

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Change the 10 pennies for 1 dime and say, “10 pennies is equal to 10 cents.” Repeat the exact same process
but this time say, “10 pennies is equal to 1 dime.” Students repeat the activity with a partner.
Happy Counting by Tens (2 minutes)

Note: Reviewing Happy Counting by Tens prepares students to recognize the efficiency of counting groups of
10 in today’s lesson.
Happy Count by tens the regular way and Say Ten way from 0–120. To really reinforce place value, try
alternating between counting the regular way and the Say Ten way.
T:
T/S: 0 10 20 (pause) 10 0 (pause) 10 20 30 (etc.)
Joy is holding 10 marbles in one hand and 10 marbles in the other hand.
How many marbles does she have in all?
Note: This problem applies a doubles fact that is familiar to most
students. Circulate and notice students that may need to count on to
add the 2 tens. During the Debrief, students will relate the Application
Problem to the efficiency of counting by tens instead of counting by
ones.

NOTES ON
Materials: (T) 40 linking cubes (2 colors, 20 of each), projector MULITPLE MEANS OF
(S) Resealable plastic bag with 40 separated linking REPRESENTATION:
cubes (2 colors, 20 of each)
As students are counting, circulate and
observe their counting levels. Not all
Note: When preparing these bags, be sure to use the same two students may be able to switch
colors for every partner pair. In the later lessons, partners will between counting ones and tens. Take
be combining their cubes to represent numbers more than 20 some extra time with the students who
with a single color. In this lesson, students may choose to count need to practice counting these
by twos and fives, although this is not a first grade standard. patterns. Play some counting games
with the linking cubes. You may also
Students sit at their tables with their bags of linking cubes.
want to send home some counting
T: You will be making your own math tool kit today! Look activities for these students to play at
in your bag. How many cubes do you think are in your home.
bag?

Date: 9/20/13 4.A.4

S: (Look in bag and make prediction.)

T: Open your bag and count how many linking cubes there are.
T: Wow, there are a lot of cubes in our bags. What do you think is the best way to count them?
S: Count by ones.  Don’t count by ones. There are too many cubes.  Count them by twos.  We
can put them in 5-groups and count by fives.  Put them in 5-groups and count them by tens!
T: Arranging these cubes in 5-groups is a great idea! Arrange your cubes, and then count to see how
many cubes there are.
As students arrange their linking cubes and count, circulate, taking note of students’ methods.
T: How many linking cubes did you count?
S: 40 linking cubes.
T: Many of you did a great job putting your cubes in 5-groups and counting by fives or tens. Let’s count
by ones to make sure we have 40 cubes.
T/S: (Count by ones.)
T: Now let’s count them by tens by making them into sticks of 10 cubes. Use the same color cubes for
each ten-stick.
S: (Make 4 ten-sticks.)
T: Now that we have these ten-sticks, we can count by…
S: Tens!
T: Great! Point or move each ten to the side as you count.
S: 10, 20, 30, 40.
T: Did we still count 40 cubes?
S: Yes!
T: No matter how we count, by ones or by tens, we get to the same number. But which way was more
efficient to count?
S: Organizing our cubes so we could count by tens was more efficient.
T: Also, sometimes when I count by ones and get distracted, I lose count. Then it takes even longer to
count by ones because I have to start from the beginning again. But if I make tens, I wouldn’t have
to start all over again.
T: (Show 12 scattered individual cubes on the projector. Have another scattered set of 12 individual
cubes set aside for later.) How can I make these quicker to count?
S: Organize them into 5-groups.  Organize them into ten-sticks.
T: Let’s use ten-sticks. (Invite a student volunteer to demonstrate.)
T: Show me this same number of cubes using your own set. Organize them efficiently, like the ones on
the board.
S: (Show one stick of 10 and 2 individual cubes.)
T: (Take out second set of scattered cubes.) Look at the 12 scattered cubes that I have and the 12
cubes you have in front of you. Which makes it easier for you to see 12 quickly?
S: The ones on my desk.  The ten-stick and 2 cubes are easier to see 12 quickly. I don’t even need to
count it. I can just see that it’s 12.

Date: 9/20/13 4.A.5

T: Let’s make a number bond to show the cubes we grouped and the extra cubes
that we added to the grouped cubes. 12 is made of 10 and 2 extra ones.
Repeat the process with 22 scattered cubes. Next, simply call out numbers from 11 to 40
and invite students to show the number using their ten-sticks and extra ones in the
suggested sequence: 3 tens 2 ones, 15, 25, 35, 3 tens 7 ones, 1 ten 7 ones, 1 ten 8 ones,
29, and 36.
Each time, have students create a number bond, representing
the cubes that were grouped together as tens and the extra NOTES ON
ones. Ask student volunteers to show how they counted their MULTIPLE MEANS OF
cubes to check their work. For example, for 35, one student REPRESENATION:
may count, “10, 20, 30, 31, 32, 33, 34, 35.” Another student As you are calling out numbers from 11
may count, “10, 20, 30, and 5 is 35.” Accept different ways of to 40 for students to show the number
counting the ones, but always guide the students to count the using their ten-sticks, be sure to write
tens first. the numbers so students can also see
them. This will help any students in
At the end of any lesson using the 40 linking cubes, students the class who are hearing impaired,
should regroup the cubes into 4 ten-sticks and store in the visual learners or those students who
resealable bag for use during future lessons. These will become may get behind while putting one of
a part of their math toolkit for G1–Module 4. their ten-sticks together.
Problem Set (10 minutes)

Students should do their personal best to complete the
Problem Set within the allotted 10 minutes.
For some classes, it may be appropriate to modify the
assignment by specifying which problems students should
work on first. With this option, let the careful sequencing
of the problem set guide your selections so that problems
continue to be scaffolded. Balance word problems with
other problem types to ensure a range of practice. Assign
incomplete problems for homework or at another time
during the day.
Lesson Objective: Compare the efficiency of counting by

ones and counting by tens.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers with a partner before going over answers as a class. Look
for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process the lesson.

Date: 9/20/13 4.A.6

You may choose to use any combination of the questions

below to lead the discussion.
 Compare your answer to Problem 15 with your
partner’s. Did you get the same answer? What
are the parts of your number bond? Explain your
thinking. (Accept any variation that aligns with
the picture. For example, students may correctly
bond as 20 and 10, or 30 and 0.)
 What did you do to solve Problem 16? (Similar to
Problem 15, there may be multiple correct
answers.)
 What are the different ways we can group
objects to make counting easier?
 How does organizing objects in groups of 10 help
us?
 How did the Application Problem connect to
today’s lesson?
Exit Ticket (3 minutes)

After the Student Debrief, instruct students to complete
the Exit Ticket. A review of their work will help you assess the students’ understanding of the concepts that
were presented in the lesson today and plan more effectively for future lessons. You may read the questions
aloud to the students.

Date: 9/20/13 4.A.7

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Fluency
Lesson Set 1•4
Practice
1 Problem
Break Apart Numbers
5 5 5
6 6 6 6
7 7 7 7
8 8 8 8 8
9 9 9 9 9

Date: 9/20/13 4.A.8

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson11Problem
Lesson Set 1•4
ProblemSet
Name Date
Circle groups of 10. Write the number.

1. 2.
There are _____ grapes. There are _____ carrots.

3. 4.
There are _____ apples. There are _____ peanuts.

5. 6.
There are _____ grapes. There are _____ carrots.

7. 8.
There are ____ apples. There are ____ peanuts.

Date: 9/20/13 4.A.9

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson11Problem
Lesson Set 1•4
ProblemSet
Make a number bond to show tens and ones.

9. 10.
20
11. 12.
Make a number bond to show tens and ones. Circle tens to help.
13. 14.
15. 16.

Date: 9/20/13 4.A.10

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Exit Ticket 1•4
Name Date
Complete the number bonds.
1. 2.
3. 4.

Date: 9/20/13 4.A.11

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson
Lesson 1 Problem Set 1•4
1 Homework
Name Date
Circle groups of 10 and write the number. Say the number the Say Ten way as you
count.
1. 2.
There are _______ marbles. There are _______ balloons.
3. 4.
There are _______ straws. There are _______ cubes.
5. 6.
There are _______ juice boxes. There are _______ crayons.

Date: 9/20/13 4.A.12

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson
1 Homework
7. 8.
There are _______ cubes. There are _______ cubes.
9. 10.
There are _______ cubes. There are _______ cubes.
Make or complete a math drawing to show tens and ones. Complete the number bonds.
11. 12.
18
10 30 3

Date: 9/20/13 4.A.13

Lesson 2
Objective: Use the place value chart to record and name tens and ones
within a two-digit number.




 Core Addition Fluency Review 1.OA.6 (5 minutes)

 3, 4, and 5 More 1.OA.6 (4 minutes)
 Change 10 Pennies for 1 Dime 1.NBT.2 (5 minutes)
Core Addition Fluency Review (5 minutes)

Materials: (S) Core Addition Fluency Review
Note: This addition review sheet contains the majority of

addition facts within 10 (excluding some +0 and +1 facts), which
are part of the required core fluency for Grade 1. Students will NOTES ON
likely do well with this activity at this point in the year. If not, MULTIPLE MEANS OF
repeat some addition fluency activities from Module 1 and use ACTION AND
this activity as an assessment tool to monitor progress. EXPRESSION:
Students complete as many problems as they can in three Adjust written fluency games for
students with motor delays. Give
minutes. Choose a counting sequence for early finishers to
written fluency activities orally to
practice on the back of their papers, such as counting by ones
students who may be slowed due to
from 46 or counting by tens from 3. When time runs out, read challenges with motor skills, allowing
the answers aloud so students can correct their work. them to experience success with the
Encourage students to remember how many they completed so math skills being addressed.
they can try to improve their scores on future Core Addition
Fluency Reviews.
Lesson 2: Use the place value chart to record and name tens and ones within a
two-digit number. 4.A.14
Date: 9/20/13
3, 4, and 5 More (4 minutes)

Note: This fluency activity provides practice with the grade level standard of addition within 20, while
reinforcing the relationship between single-digit sums and their analogous teen sums.
T: On my signal, say the number that is 3 more.
T: 3 (snap).
S: 6.
T: 13 (snap).
S: 16.
Continue reviewing 3 more. Then review 4 and 5 more.
Change 10 Pennies for 1 Dime (5 minutes)

Materials: (S) 10 pennies and 2 dimes for each pair of students
Note: This fluency activity is necessary in order to prepare students to utilize coins as abstract
representations of tens and ones in G1–M1–Lesson 6.
Students work in pairs. Partner A begins with 10 pennies. Partner B begins with 2 dimes. Both partners
whisper count as Partner A counts 10 pennies into 5-groups (1 cent, 2 cents, etc.). Partner B changes 10 cents
for 1 dime and says, “10 cents equals 1 dime.” Students count on, “11 cents, 12 cents, 13 cents, etc.,
replacing the second set of 10 pennies with a dime and saying, “20 cents equals 2 dimes.” Then, Partners A
and B switch roles.
Ted has 4 boxes of 10 pencils. How many pencils does he have altogether?
Note: This problem applies the concept development from Lesson 1 of counting by tens. As students depict
this problem with a drawing, circulate and notice students who are counting all, counting on, or counting by
tens. During the Debrief, students will represent the number 40 using a place value chart.
Date: 9/20/13
Materials: (T) Hide Zero cards (from G1–M1–Lesson 38 and NOTES ON MULTIPLE
G1–M3–Lesson 2), chart paper (S) 4 ten-sticks from MEANS OF
personal math toolkit (from G1–M4–Lesson 1),
REPRESENTATION:
personal white board with place value chart insert
The familiarity of the Hide Zero cards
Students sit at their desks with their materials. from Module 3 allows for an easy
transition to the use of the place value
T: (Show 17 using Hide Zero cards.) When I pull apart chart for students. Just as some
these Hide Zero cards, 17 will be in two parts. What students have needed to use various
will they be? tools for more support, allow the Hide
Zero cards and place value chart to be
S: 10 and 7.
used throughout the module as
T: (Pull apart 17 into 10 and 7.) You are right! Show me needed.
17 using your linking cubes.
S: (Show 1 ten-stick and 7 extra cubes. If students count out 17 cubes and break them apart
separately, ask them to try to make as many tens as they can.)
T: How many tens, or ten-sticks, do you have?
S: 1 ten.
T: How many extra ones do you have?
S: 7 extra ones.
Repeat the process following the suggested sequence: 27, 37, 23, and 32.
T: (Show 17 with Hide Zero cards and linking cubes again. Make a blank t-chart on the chart paper.) I
can write 1 ten here in this chart (write 1 on the left side of the t-chart, which will become the tens
place). How many extra ones?
S: 7 ones.
T: Point to where you think I should write 7.
S: (Point to the second column.)
T: (Write 7 in the ones place.)
T: (Point to the 1 in the tens place.) What does this 1 stand for? Show me with
your cubes.
S: (Hold up a ten-stick.) 1 ten!
T: I can write tens here because this 1 stands for 1 ten. (Label the place value
chart with tens.)
T: Point to the set of cubes that tells us what this 7 stands for.
S: (Point to 7 loose cubes.) 7 ones!
T: I can write ones here because this 7 stands for…
S: 7 ones.
T: (Point to the place value chart.) Look at our new chart, which is called a place value chart. What is 1
ten and 7 ones?
Date: 9/20/13
S: 17.
T: The Say Ten way?
S: 1 ten 7.
T: Looking at the cubes in front of you, how many tens and ones are in 17?
S: 1 ten 7 ones.
T: Before we go on to other numbers, let’s make a drawing to show 17.
Repeat the process using the following sequence: 27, 37, 14, 24, 34, 13, 31, 30, 12, 21,
and 20.
For the first two numbers (27 and 37), have students represent the number with their linking cubes, 5-group
MP.7 column drawings, and place value chart. For the remaining numbers, have students use only their linking
cubes and place value chart. Making pictorial representations will be inefficient as the numbers get bigger.

Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some
classes, it may be appropriate to modify the assignment by specifying which problems they work on first.
Lesson Objective: Use the place value chart to record and

name tens and ones within a two-digit number.
Set. They should check work by comparing answers with a
partner before going over answers as a class. Look for
misconceptions or misunderstandings that can be
addressed in the Debrief. Guide students in a conversation
to debrief the Problem Set and process the lesson.
 How many tens and how many ones are in the
number 29? What amount is greater, 2 tens or 9
ones? Explain your thinking. Use your cubes and
your place value chart.
 Look at Problem 18. How did you complete your
place value chart? Explain your thinking.
 What new math tool did we use to show how
many tens and ones in a number? (Place value chart.) How does the place value chart help us? (It
helps us see numbers taken apart into tens and ones.)
Date: 9/20/13

today’s lesson? How would you write the answer
in a place value chart?

the Exit Ticket. A review of their work will help you assess
the students’ understanding of the concepts that were
presented in the lesson today and plan more effectively
for future lessons. You may read the questions aloud to
the students
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 2 Practice Sheet 1•4
Name Date
Core Addition Fluency Review
1. 2 + 0 = ___ 16. 1 + 6 = ___ 31. 5 + 3 = ___
2. 2 + 1 = ___ 17. 6 + 1 = ___ 32. 3 + 5 = ___
3. 2 + 2 = ___ 18. 6 + 2 = ___ 33. 3 + 4 = ___
4. 4 + 0 = ___ 19. 5 + 2 = ___ 34. 3 + 3 = ___
5. 0 + 4 = ___ 20. 4 + 3 = ___ 35. 4 + 4 = ___
6. 0 + 3 = ___ 21. 2 + 3 = ___ 36. 5 + 4 = ___
7. 0 + 0 = ___ 22. 2 + 4 = ___ 37. 4 + 6 = ___
8. 3 + 1 = ___ 23. 4 + 2 = ___ 38. 2 + 7 = ___
9. 1 + 3 = ___ 24. 3 + 2 = ___ 39. 2 + 8 = ___
10. 1 + 4 = ___ 25. 9 + 1 = ___ 40. 2 + 5 = ___
11. 1 + 5 = ___ 26. 8 + 2 = ___ 41. 5 + 5 = ___
12. 5 + 1 = ___ 27. 7 + 2 = ___ 42. 4 + 5 = ___
13. 1 + 7 = ___ 28. 7 + 3 = ___ 43. 2 + 6 = ___
14. 7 + 1 = ___ 29. 6 + 3 = ___ 44. 3 + 6 = ___
15. 1 + 8 = ___ 30. 6 + 4 = ___ 45. 3 + 7 = ___
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 2 Problem Set 1•4
Name Date
Write the tens and ones and say the numbers. Complete the statement.
1. 2.
17 = ____ ten ____ ones 26 = ____ tens ____ ones

3. 4.
28 = ____ tens ____ ones ____ tens ____ >
5. 6.
There are _____ balloons. There are _____ flowers.

7. 8.
There are _____ marbles. There are _____ peanuts.
Date: 9/20/13
Write the tens and ones. Complete the statement.

9. 10.
There are _____ cubes. There are _____ cubes.

11. 12.
Write the missing numbers. Say them the regular way and the Say Ten way.
13. 14.
35
_____
2 7 _____
15. 16.
3 9 _____
29
_____
17. 18.
0 40
_____ _____
9
Date: 9/20/13
Name Date
Match the picture to the place value chart that shows the correct tens and ones.
4 0
1 7
3 3
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 2 Homework 1•4
Name Date
Write the tens and ones and complete the statement.
Date: 9/20/13
Write the tens and ones. Complete the statement.

7. 8.

9. 10.
Write the missing numbers. Say them the regular way and the Say Ten way.
11. 12.
23
_____
3 2 _____
13. 14.
0 9 _____
4 0 _____
15. Choose a number less than 40. Make a math drawing to represent it and fill in the
number bond and place value chart.
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 2 Fluency Template 1•4
tens ones
Date: 9/20/13
Lesson 3
Objective: Interpret two-digit numbers as either tens and some ones or as
all ones.




Sue is writing the number 34 on a place value chart. She can't

remember if she has 4 tens and 3 ones or 3 tens and 4 ones. Use a
place value chart to show how many tens and ones are in 34. Use a
drawing and words to explain this to Sue.
Note: This problem invites children to write or discuss their
understanding of tens and ones, based on their learning from Lesson
2. For students who find it challenging to create written
explanations, have them share orally with a partner and use drawings
to support their thinking. During the Debrief, students will also share
other interpretations of 34.

 Dime Exchange 1.NBT.5 (4 minutes)
 Magic Counting Sticks 1.NBT.2 (3 minutes)

Materials: (S) Core Addition Fluency Review from G1–M4–Lesson 2
Note: This activity assesses students’ progress toward mastery of the required addition fluency for first
graders. Since this is the second day students are doing this activity, encourage students to remember how
many problems they answered yesterday and celebrate improvement.
Lesson 3: Interpret two-digit numbers as either tens and some ones or as all
ones. 4.A.26
Date: 9/20/13
Students complete as many problems as they can in three minutes. Choose a counting sequence for early
finishers to practice on the back of their papers. When time runs out, read the answers aloud so students can
correct their work and celebrate improvement.
Dime Exchange (4 minutes)

Materials: (T) 20 pennies and 2 dimes
Note: This activity provides students practice with recognizing pennies and dimes and identifying their
values. This fluency activity is necessary in order to prepare students to utilize coins as abstract
representations of tens and ones in G1–M1–Lesson 6.
T: (Lay out 2 dimes.) What coins do you see?
S: 2 dimes.
T: Let’s count by tens to see how much money I have. (Students count aloud.) I want to exchange
1 dime for some pennies. What is the correct number of pennies?
S: 10 pennies.
T: (Replace a dime with 10 pennies in 5-group formation.) How much money do I have now?
S: 20 cents.
T: You’re right! I still have 20 cents. Count back with me.
S: (Count from 20 cents to 10 cents removing 1 penny at a time.)
Change the other dime for a penny and students count from 10 cents to 0 cents.
Magic Counting Sticks (3 minutes)

Materials: (T) Hide Zero cards (from G1─M1─Lesson 38)
Note: This activity reviews the concept of ten as a unit and as 10

ones, which will prepare students for today’s lesson.
T:(Divide students into partners and assign Partners A and B.
Show 13 with Hide Zero cards.) How many tens are in 13?
S: 1 ten.
T: (Point to the 1 in 13.) Partner A, show 1 ten with your
magic counting sticks. (Partner A holds up a bundled
ten.) How many ones should Partner B show?
S: 3 ones.
T: (Point to the 3.) Partner B, show 3 ones. 1 ten and 3
ones is 13. Partner A, open up your ten. How many
fingers do you have?
S: 10 fingers.
T: (Take apart the Hide Zero cards to show 10 and 3.) 10 fingers + 3 fingers is?
S: 13 fingers.
Alternate partners and repeat with other teen numbers.
ones. 4.A.27
Date: 9/20/13
Materials: (T) Hide Zero cards (from G1–M1– Lesson 38), personal math toolkit of 4 ten-sticks (S) Personal
math toolkit of 4 ten-sticks
Students gather in the meeting area in a semi-circle formation.

T: Show me your magic counting sticks. Wriggle them in the air. Now show me 1 ten.
S: (Clasp their hands together.)
T: Show me 10 ones.
S: (Unclasp hands and show individual fingers.)
T: How can we show 34 using our magic counting sticks?
S: We can’t. We only have 10 magic sticks.  We need more people to show 34.  We need 4
people—3 people to show 3 tens, 1 more person to show 4 extra ones.
T: Great idea! (Call up four volunteers.) Show us 34.
S: (Three students clasp their hands together while the last student on the right facing the class shows
4 fingers.)
T: How many tens and ones make up 34?
S: 3 tens and 4 ones.
T: How many ones is the number 34 made of?
S: I see 3 tens and 4 ones. So there are just 4 ones.  I see 34 ones. Each ten is made of 10 ones. So I
counted on by tens to get to 30, and I counted by ones to get to 34.
T: I heard some students say that there are 4 ones. Think again. If we only use ones to make 34, how
MP.6
many will it take? Open up your hands to show your fingers, volunteers!
S: (The first three students unclasp their hands and show all fingers.)
T: How many ones make up 34?
S: 34 ones.
T: How many ones is the same as 3 tens 4 ones?
S: 34 ones.
T: Let’s count to check. How should we count?
S: We can count the fingers by ones.  Let’s count them by tens first. That will be much faster.
T: Great idea. Let’s count by grouping the 10 ones. Start with Student A. How many ones are here?
S: 10 ones.
T: Keep counting!
S: 20 ones, 30 ones, 34 ones.
T: Great. Let’s do some more. (Call up three volunteers.) Show me 27 ones.
S: (Show individual fingers.)
T: If you are able to make a ten, clasp your hands.
S: (Two students clasp hands.)
ones. 4.A.28
Date: 9/20/13
T: 27 ones is the same as how many tens and ones?

S: 2 tens and 7 ones.
T: How many ones?
S: 27 ones!
Repeat the process using the following sequence: 37, 14, 24,
34, 13, 31, 10, and 40.
NOTES ON
When students demonstrate solid understanding with the finger
MULTIPLE MEANS OF
work, move on to representing the numbers with Hide Zero
cards. ACTION AND
EXPRESSION:
T: (Show 24 using Hide Zero cards.) How many tens and By introducing each number in a
ones make up 24? different way, students are held
S: 2 tens 4 ones. accountable for understanding place
T: How many ones are in 2 tens? (Pull apart 24 into 20 value no matter how the number is
presented. Doing it this way can be a
and 4.)
challenge for some students, so make
S: 20 ones. sure that students who need
T: How many extra ones are there? information presented a specific way
are still getting the information they
S: 4 ones.
need.
T: How many ones is the same as 2 tens and 4 ones?
S: 24 ones.
T: How many tens and ones is the same as 24 ones?
(Put 24 back together.)
S: 2 tens 4 ones.
Repeat the process using the following sequence: 13, 23,
16, 26, 36, 29, 20 and 30 using Hide Zero cards. For the
first two or three, have students work with a partner to
represent the number with their linking cubes, first with as
many tens as possible, and then decomposed into all ones.
Support students in seeing that there are the same
number of cubes and connecting this with the
mathematical idea that, for instance, 1 ten 3 ones is the
same amount as 13 ones.

Note: For completing today’s Problem Set, have students
say the number and the sentence for each problem. This
will allow students to hear themselves reading numbers in
different ways.
Problem Set within the allotted 10 minutes. For some
classes, it may be appropriate to modify the assignment by
ones. 4.A.29
Date: 9/20/13
specifying which problems they work on first. Some

problems do not specify a method for solving. Students
solve these problems using the RDW approach used for
Application Problems.
Lesson Objective: Interpret two-digit numbers as either

tens and some ones or as all ones.
addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process the
lesson.
 Look at Problem 6. What is your solution? How are both of these answers correct?
 Look at Problem 10. Explain how 4 tens is the same as 40 ones. You may use linking cubes or the
place value chart to support your thinking.
 Look at Problem 12. What are the different ways we can make 29?
 Student A says 2 tens and 9 ones only has 9 ones. Do you agree? Why or why not? How can you
help them understand their mistake?
 Look at your Application Problem. Share your work and explain your thinking with a partner. If we
counted in all ones, how many ones are in 34?

After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you
assess the students’ understanding of the concepts that were presented in the lesson today and plan more
effectively for future lessons. You may read the questions aloud to the students.
ones. 4.A.30
Date: 9/20/13
Name Date
Count as many tens as you can. Complete each statement. Say the numbers and the
sentences.
1. 2.
____ ten ____ ones is the same as ____ tens ____ ones is the same as
_____ones. _____ones.
3. 4.
____ tens ____ ones is the same as ____ tens ____ ones is the same as
_____ones. _____ones.
5. 6.
____ tens ____ ones is the same as ____ ten ____ ones is the same as
_____ones. _____ones.
ones. 4.A.31
Date: 9/20/13
Match.
7.
3 tens 2 ones 29 ones
8.
40 ones
1 7 23 ones
9. 37 ones
32 ones
10. 4 tens
17 ones
11.
12.
9 ones 2 tens
Fill in the missing numbers.
13.
15 _____ ones
14. _____ ____ tens ____ ones 39 ones
ones. 4.A.32
Date: 9/20/13
Name Date
1. 2.
____ tens ____ ones is the same ____ tens ____ ones is the same
as _____ones. as _____ones.
3. 27 _____ ones
ones. 4.A.33
Date: 9/20/13
Name Date
Count as many tens as you can. Complete each statement. Say the numbers and the
sentences.
1. 2.
____ tens ____ ones is the same as ____ tens ____ ones is the same
_____ones. as _____ones.
3. 4.
____ tens ____ ones is the same as ____ tens ____ ones is the same
_____ones. as _____ones.
Fill in the missing numbers.
5. _____
2 9 _____ ones
1 7
ones. 4.A.34
Date: 9/20/13
6. 34 ____ tens ____ ones _____ ones
7. _____
3 8 _____ ones
8. _____ 9 ones 3 tens _____ ones
9. _____ ____ ones ____ tens 40 ones

10. Choose at least one number less than 40. Draw the number in three ways:
As grapes: In a number bond: In the place value chart:
ones. 4.A.35
Date: 9/20/13
Lesson 4
Objective: Write and interpret two-digit numbers as addition sentences
that combine tens and ones.




 Subtraction with Cards 1.OA.6 (5 minutes)

 Dime Exchange 1.NBT.2 (5 minutes)
 10 More 1.NBT.5 (2 minutes)
Subtraction with Cards (5 minutes)

Materials: (S) 1 pack of numeral cards 0─10 per set of partners (from G1–M1–Lesson 36)
Note: This review fluency strengthens students’ abilities to subtract within 10, which is a required core
fluency for Grade 1.
Students combine their numeral cards and place them face down between them. Each partner flips over two
cards and subtracts the smaller number from the larger one. The partner with the smallest difference keeps
the cards played by both players. If the differences are equal, the cards are set aside and the winner of the
next round keeps the cards from both rounds. The player with the most cards at the end of the game wins.
Dime Exchange (5 minutes)

Materials: (S) 10 pennies and 2 dimes per pair
Note: This fluency activity is necessary in order to prepare students to utilize coins as abstract
representations of tens and ones in G1–M1–Lesson 6. If there are not enough coins to do this activity in
pairs, it may be done as a teacher-directed activity.
Students work in pairs. Partner A begins with 2 dimes. Partner B begins with 10 pennies. Partner A whisper-
counts as she lays 2 dimes, “10 cents, 20 cents.” Partner B exchanges 1 dime for 10 pennies, lays them out in
5-groups, and says “1 dime is equal to 10 pennies.” Students whisper-count as Partner A takes away 1 penny
Lesson 4: Write and interpret two-digit numbers as addition sentences that

combine tens and ones. 4.A.36
Date: 9/20/13
at a time (20 cents, 19 cents, etc.). When they get to 10, they exchange the dime for 10 pennies and whisper-
count to 0. Partners A and B switch roles and repeat.
10 More (2 minutes)
Note: This fluency activity reviews adding 10 to a single-digit number, which will prepare students for today’s
lesson.
T: What’s 10 more than 5?
S: 15.
T: Say 15 the Say Ten way.
S: Ten 5.
T: Say it as an addition sentence, starting with 5.
S: 5 + 10 = 15.
T: Say the addition sentence, starting with 10.
S: 10 + 5 = 15.
Repeat, beginning with other numbers between 0 and 10.
Lisa has 3 boxes of 10 crayons and 5 extra crayons. Sally has 19 crayons.
Sally says she has more crayons, but Lisa disagrees. Who is right?
Note: In this problem, students use what they learned in Lesson 3 about
interpreting a two-digit number in terms of tens and ones and apply this to a
problem involving a comparison of two quantities. To decide which is larger,
students really only need to compare how many tens Lisa and Sally each have.
Note: Be sure to note which students understand and which don't understand
that Sally has a larger number of ones than Lisa does but that Lisa still has a
larger amount of crayons because she has more tens.
Materials: (T) 40 linking cubes, chart paper with a place value chart, Hide Zero cards (from G1–M3–Lesson
2), piece of blank paper to cover sections (S) personal math toolkit of 4 ten-sticks (from G1–M4–
Lesson 1), personal white board with the place value chart template insert (from G1–M4–Lesson
2), numeral cards (from G1–M1–Lesson 36)
Students gather in the meeting area in a semi-circle formation with their personal white boards. The toolkits
of 4 ten-sticks are at their individual desks or tables.
T: (Lay out 3 ten-sticks and 7 ones using linking cubes on the floor.) Say this number as tens and ones.
S: 3 tens 7 ones.

Date: 9/20/13
T: Which is the same as the number…

S: 37!
T: (Fill in the place value chart.) 3 is the digit in the tens place. 7 is
the digit in the ones place. (Point to each digit in the chart.)
T: On your board, make a number bond that shows the tens and the
ones.
S: (Take apart 37 into 30 and 7.)
T: (Record the number bond on the chart.) Write as many addition
sentences as you can that use your number bond.
Circulate and ensure that students are only using the three numbers from
this bond: 37, 30, and 7. If students begin writing subtraction sentences,
remind them of the directions. You may choose to challenge some students to consider subtraction
sentences, but these sentences will not be addressed during the course of the lesson.
T: Give me a number sentence that matches this number bond. Start with the part that represents the
tens. (Record on the chart as students answer.)
S: 30 + 7 = 37.
T: Start your number sentence with the ones. (Record on the chart.)
S: 7 + 30 = 37.
T: 37 is the same as? (Write 37 = and complete the number sentence as students answer.)
S: 30 plus 7.
T: This time start with the ones. 37 is the same as? (Write 37 = and complete the number sentence.)
S: 7 plus 30.
T: Talk to your partner. What do you notice about the
addends in all of these number sentences? NOTES ON
S: There is one that tells how many tens there are and MULTIPLE MEANS OF
the other tells how many ones there are.  You can EXPRESSION:
switch the addends around and the total is still the Students may need additional support
same.  That was true with smaller numbers, too!  with the language of “___ is the same
The bigger number also tells how many ones are in the as ___,” “___ is ___ more than ___,”
tens. etc. Insert a sentence frame into their
T: Great. (Point to 7.) 7 more than 30 is? Say the whole personal white board, and allow the
sentence. student to fill in the blanks. Pointing to
each word and number as it is read can
S: 7 more than 30 is 37. (Record on the chart.) provide a bridge between the concrete
T: (Point to 30.) 30 more than 7 is? Say the whole and the abstract.
sentence.
S: 30 more than 7 is 37. (Record on the chart.)
Repeat the process following the suggested sequence: 18, 28, 38, 12, 21, 23, 32, 30 and 40. When
appropriate, switch to modeling with Hide Zero cards and have students write their responses on their
boards. Use different language to elicit a variety of answers for each number: (e.g., 18 is the same as…; 10
plus 8 is…; 8 more than 10 is…; 10 more than 8 is….)

Date: 9/20/13
For the remainder of time, have partners play Combine Tens

and Ones. Leave the chart for 37 up on the board as a
reference to support students. NOTES ON
 Prepare two decks by combining numeral cards 0 MULTIPLE MEANS OF
through 9 from both players. The first deck is ENGAGEMENT:
comprised of 1 set of digits 1 to 3. The rest of the cards When playing games with your
are in the second deck. students modeling how the game is
played is very important. Oral
 Pick a card from the first deck. This number is placed in instructions alone are not going to help
the tens place on the place value chart (e.g., 2 is drawn all of your class understand how the
and placed in the tens place). game is played. Have two students
 Pick a card from the second deck. This number is placed demonstrate Partner A and Partner B
roles so that all students see and hear
in the ones place on the place value chart (e.g., 7 is
the way the game is played.
drawn and placed in the ones place).
 Partner A and B make a number bond decomposing the
number into tens and ones.
 Partner A writes two addition number sentences (e.g.,
20 + 7 = 27; 7 + 20 = 27; 27 = 20 + 7; 27 = 7 + 20).
 Partner B writes 1 more than statement that combines
tens and ones (e.g., 20 more than 7 is 27; 7 more than
20 is 27; 27 is 7 more than 20; 27 is 20 more than 7).
 Switch roles for the next set of cards drawn.

Lesson Objective: Write and interpret two-digit numbers

as addition sentences that combine tens and ones.

Date: 9/20/13

lesson.
 How can solving Problem 1 help you solve
Problem 2?
 How did you solve Problem 5? Is it easier for you
to start with the ones first or tens first?
 Look at Problem 15. Explain why the answer is
not 23. Write the number in a place value chart.
Which digit is in the tens place? Which digit is in
the ones place?
 Based on our work today, what do you think the
word digit means? (Digits are the symbols 0–9
that can be used to create any number. 32 is a
two-digit number. The numeral 3 is the digit in
the tens place, and the numeral 2 is the digit in
the ones place.)
 When you played Combine Tens and Ones, did
you ever pick a 0 card? What did you write for your number sentences and number bond?
 Look at your Application Problem. Share your thinking with a partner. How many crayons does Lisa
have? Write the number of crayons Lisa has using two number sentences, as we did during today’s
lesson.


Date: 9/20/13
Name Date
Fill in the number bond. Complete the sentences.
1. 2.
20
3
20 and 3 make ____. 20 and 8 make ____.
20 + 3 = ____ 20 + 8 = ____
3. 4.
20 + 7 = ____ 30 + 6 = ____
7 more than 20 is ____. 6 more than 30 is ____.

5. 6.
5 + 20 = ____ 8 + 30 = ____

Date: 9/20/13
Write the tens and ones. Then write an addition sentence to add the tens and ones.
7. 8.
1 4
10
____ + ____ = ____ 4 ____ + ____ = ____ 3
.
9. 10.
____ = ____ + ____ 30 ____ = ____ + ____ 20

Match.
11. 4 tens       20 + 7
12. 2 tens 7 ones 

    40
13. 3 more than 20     20 + 3
14. 9 ones 3 tens     30 + 2
15. 2 ones 3 tens     9 + 30

Date: 9/20/13
Name Date
Write the tens and ones. Then write an addition sentence to add the tens and ones.
1. 2.
10
____ + ____ = ____ ____ + ____ = ____ 4
3. 4.
____ = ____ + ____ 30 ____ = ____ + ____ 6

Date: 9/20/13
Name Date
Fill in the number bond or write the tens and ones. Complete the addition sentences.
1. 2.
3 + 20 = ____ 20 + 4 = ____
3. 4.
7 + 20 = ____
____ + 30 = ____
5. 6.
carrots
carrots
____ + ____ = ____

20 + ____ = ____

Date: 9/20/13
Match the pictures with the words.
7.
  1 and 30 make ______.
8.
  8 + 30 = _____.
9.
  2 more than 10 is ______.
10.
  20 + 4 = ______.

Date: 9/20/13
Lesson 5
Objective: Identify 10 more, 10 less, 1 more, and 1 less than a two-digit
number.




 Sprint: 10 More, 10 Less Review 1.OA.6 (10 minutes)
Sprint: 10 More, 10 Less Review (10 minutes)

Materials: (S) 10 More, 10 Less Review Sprint
Note: This review Sprint provides practice with addition and subtraction within 20 and prepares students to
extend this skill for numbers to 40 in today’s lesson.
Lee has 4 pencils and buys 10 more. Kiana has 17 pencils and loses 10 of them. Who has more pencils now?
Use drawings, words, and number sentences to explain your thinking.
Note: This problem gives students a chance to add and subtract 10 using their own methods. At this point in
the year, students should feel quite comfortable adding and subtracting 10 with numbers within 20. Circulate
and notice students’ understanding and link this to today’s lesson, as students notice ways to more quickly
add and subtract 10 to and from larger numbers.
Lesson 5: Identify 10 more, 10 less, 1 more, and 1 less than a two-digit number.
Date: 9/20/13 4.A.46

Materials: (T) 4 Rekenrek bracelets stretched into a straight line (first used in G1–
M1–Lesson 8), 5 additional red beads, 5 additional white beads, 4 ten-
sticks, 2 pieces of chart paper with two pairs of place value charts as
shown (S) Personal math toolkit of 4 ten-sticks of linking cubes, personal
white board with double place value charts template
Students sit at their desks with all materials.

T: (Show the Rekenrek bracelet stretched out as a vertical line.) When we
made drawings to show this Rekenrek bracelet stretched out, we called it a…
S: 5-group column!
T: You’re right! We drew 10 circles showing the beads. We also drew a line through it to show there
are 10 circles or beads. (Draw a 5-group column on the board.)
T: (Place 4 individual beads next to the Rekenrek bracelet.) How many beads are there?
S: 14 beads.
T: Say an addition sentence that represents how many beads there are, starting with 10.
S: 10 + 4 = 14.
T: Draw the number of beads using 5-group columns.
S: (Draw one 5-group column and four beads.)
T: (Add two more Rekenrek bracelets representing 34.) How many beads are here now? Let’s count.
S/T: (Point to each bracelet as you count by tens and then to each bead for the last four beads.) 10, 20,
30. (Pause.) 31, 32, 33, 34.
T: Draw the number of beads using 5-group columns. (Give 10 seconds to draw.) Your time is up!
S: I didn’t have enough time to draw all 34 beads!
T: Wow, drawing 34 beads would take us a long time! Let me show you a
shortcut to drawing tens. Watch how quickly I can represent 34. (Draw 3
quick tens and 4 circles.)
T: Now, you try drawing 34 using quick tens.
S: (Draw.)
T: We call each of these lines a quick ten. How do you think it got its name?
S: It’s a line that holds 10 beads.  It represents a ten, so we don’t have to draw all the beads!  It’s
so quick to draw a ten now!
Have students practice representing numbers with quick tens for two minutes. Show or call out using
numbers from 11 to 40 in varied ways (e.g., using Rekenrek bracelets and extra beads, ten-sticks and extra
linking cubes, place value chart, the Say Ten way, an addition expression, a more than statement, and a
number bond with two parts filled in). For the next minute, the teacher and students switch roles. The
teacher draws quick tens and the students say what number they represent.
Date: 9/20/13 4.A.47

T: Draw 15.
S: (Draw a quick ten and 5 circles.)
T: How many tens and ones are there?
S: 1 ten and 5 ones.
T: (Write 15 on the double place value chart
template.)
T: Show me 1 more than 15.
S: (Draw 1 more circle.) NOTES ON
T: What is 1 more than 15? Say the whole sentence. MULTIPLE MEANS FOR
S: 1 more than 15 is 16. (Write 16 on the place value ENGAGEMENT:
chart.) Some students may not be able to
T: So, from 15 to 16, we added 1 more. (Draw an arrow imagine adding or subtracting a ten at
from the first place value chart to the second and write this point. Support these students with
+ 1 above the arrow.) all of the materials used in the lesson
and give them plenty of practice. Their
T: Look at the place value chart. What changed and what path to abstract thinking may be a little
didn’t? Turn and talk to your partner about why this is longer than those of other students.
so.
S: The tens didn’t change. They both stayed as 1 ten
because we only added 1 more.  The ones changed
from 5 to 6 because we added 1 more. 6 is 1 more
than 5.  To figure out 1 more, I just have to add 1
more to the number in the ones place!
T: Great thinking! Show me 15 with your drawing again.
S: (Show 15.)
T: (Write 15 on a new place value chart.) Now, how can you
show 10 more than 15? (Draw an arrow and write + 10 above
it.) Turn and talk to your partner and then show with your
cubes.
S: Just draw one more quick ten!
T: That’s an efficient way to show 10 more! Let’s have
everyone show 10 more this way, drawing just one NOTES ON
more quick ten. What is 10 more than 15? Say the MULTIPLE MEANS OF
whole sentence. ENGAGEMENT:
S: 10 more than 15 is 25. Other students in your class may be
able to visualize adding and subtracting
T: I’m about to write the new number on the place value
ones and tens. Since these students
chart to show 10 more than 15. Talk to your partner
have moved from concrete to abstract
about what you think will change and what will remain thinking, challenge them by giving
MP.6 the same? problems adding or subtracting 2
S: The tens changed this time from 1 ten to 2 tens because we ones/tens or 3 ones/tens.
added 10 more.  The ones didn’t change because we just
added a ten-stick.  We could add 10 extra ones, but once you get 10 we make them into a ten-
Date: 9/20/13 4.A.48

MP.6 stick, so why bother? We can add a ten quickly.  I just have to add 1 more to the number in the
tens place!
T: We added 10 more to 15 to get 25. (Complete the second place value chart with 2 and 5.)
Repeat the process using 1 less and 10 less with 35 as shown to the right.
Then follow the suggested sequence:
 1 more/10 more than 14
 1 less/10 less than 16
 1 more/1 less than 36
 1 more than 29
 1 less than 30

specifying which problems they work on first.
Lesson Objective: Identify 10 more, 10 less, 1 more, and 1

less than a two-digit number.
lesson.
 Look at Problem 11. What is 10 less than 26? Which digit changed when you went from 26 to 16?
 Look at Problem 12. What is 1 less than 26? Which digit changed when you went from 26 to 25?
Date: 9/20/13 4.A.49

 Look at Problem 9. In what ways did the pictures

change from the starting number to the end
number? Explain why this is so. Which digit
changed? What happened to the digits when you
went from 29 to 30? Why is this so? Is this
similar to and different from our other problems?
 What does the word digit mean?
 Look at your solution to Problem 14. What
changed in the number? Even though we added
1 more in Problem 9 and made 1 less in Problem
14, why did the numbers in both the tens and the
ones change?
 What new math drawing did we use to work
more efficiently? (Quick ten drawings.)
today’s lesson?

the students.
Date: 9/20/13 4.A.50

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 5 Sprint 1•4
A Number correct:
Name Date
*Write the missing number.
1 10 + 3 = ☐ 16 10 + ☐ = 11
2 10 + 2 = ☐ 17 10 + ☐ = 12
3 10 + 1 = ☐ 18 5 + ☐ = 15
4 1 + 10 = ☐ 19 4 + ☐ = 14
5 4 + 10 = ☐ 20 ☐ + 10 = 17
6 6 + 10 = ☐ 21 17 - ☐ = 7
7 10 + 7 = ☐ 22 16 - ☐ = 6
8 8 + 10 = ☐ 23 18 - ☐ = 8
9 12 - 10 = ☐ 24 ☐ - 10 = 8
10 11 - 10 = ☐ 25 ☐ - 10 = 9
11 10 - 10 = ☐ 26 1 + 1 + 10 = ☐
12 13 - 10 = ☐ 27 2 + 2 + 10 = ☐
13 14 - 10 = ☐ 28 2 + 3 + 10 = ☐
14 15 - 10 = ☐ 29 4 + ☐ + 3 = 17
15 18 - 10 = ☐ 30 ☐+ 5 + 10 = 18
Date: 9/20/13 4.A.51

B Number correct:
Name Date
1 10 + 1 = ☐ 16 10 + ☐ = 10
2 10 + 2 = ☐ 17 10 + ☐ = 11
3 10 + 3 = ☐ 18 2 + ☐ = 12
4 4 + 10 = ☐ 19 3 + ☐ = 13
5 5 + 10 = ☐ 20 ☐ + 10 = 13
6 6 + 10 = ☐ 21 13 - ☐ = 3
7 10 + 8 = ☐ 22 14 - ☐ = 4
8 8 + 10 = ☐ 23 16 - ☐ = 6
9 10 - 10 = ☐ 24 ☐ - 10 = 6
10 11 - 10 = ☐ 25 ☐ - 10 = 8
11 12 - 10 = ☐ 26 2 + 1 + 10 = ☐
12 13 - 10 = ☐ 27 3 + 2 + 10 = ☐
13 15 - 10 = ☐ 28 2 + 3 + 10 = ☐
14 17 - 10 = ☐ 29 4 + ☐ + 4 = 18
15 19 - 10 = ☐ 30 ☐+ 6 + 10 = 19
Date: 9/20/13 4.A.52

Name Date
Write the number.

1. 2.
+1 -1
1 more than 30 is _____. 1 less than 30 is _____.

3. 4.
+1 -1

5. 6.
+ 10 - 10
Date: 9/20/13 4.A.53

Draw 1 more or 10 more. You may use a quick ten to show 10 more.
7. 8.
1 more than 28 is _____. 10 more than 28 is _____.

9. 10.
Cross off (x) to show 1 less or 10 less.
11. 12.
10 less than 26 is _____. 1 less than 26 is _____.

13. 14.
Date: 9/20/13 4.A.54

Name Date
Draw 1 more or 10 more. You may use a quick ten to show 10 more.
1. 2.
Cross off (x) to show 1 less or 10 less.
3. 4.
Date: 9/20/13 4.A.55

Name Date
Draw quick tens and ones to show the number. Then draw 1 more or 10 more.
1. 2.
3. 4.
Draw quick tens and ones to show the number. Cross off (x) to show 1 less or 10 less.
5. 6.

7. 8.
Date: 9/20/13 4.A.56

Match the words to the picture that shows the right amount.
9.
  1 less than 30.
10.
  1 more than 23 is 24.
11.
  10 less than 36.
12.
  10 more than 20.
Date: 9/20/13 4.A.57

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 5 Template 1•4
tens ones tens ones
Date: 9/20/13 4.A.58

Lesson 6
Objective: Use dimes and pennies as representations of tens and ones.




 Quick Tens 1.NBT.2 (3 minutes)

 Count Coins 1.NBT.2 (2 minutes)
Quick Tens (3 minutes)

Materials: (T) Variety of materials to show tens and ones (e.g., 100-bead Rekenrek, linking cubes with ten-
sticks and extra cubes, place value chart
Note: This fluency activity reinforces place value, as quick tens are an abstract representation of the unit ten.
Show and say numbers from 11 to 40 in varied ways for two minutes. Students draw the number with quick
tens and circles (in 5-group columns). Use the materials listed above to show numbers. Choose different
ways to say the numbers:
 The Say Ten way
 As an addition expression
 As a more than statement
 As a number bond with two parts filled in
For the next minute, represent numbers using quick tens and ones. Students say the numbers aloud.
Count Coins (2 minutes)

Materials: (T) 10 pennies and 4 dimes
Note: This fluency activity provides practice with recognizing pennies and dimes and counting with abstract
representations of tens and ones, which will prepare them for today’s lesson.
Lay out 2 dimes. Students count up from 20 by ones as you lay out 10 pennies into 5-groups. Repeat, this
Lesson 6: Use dimes and pennies as abstract representations of tens and ones.
Date: 9/20/13 4.A.59

time changing the 10 pennies for another dime when you get to 40.
Sheila has 3 bags of 10 pretzels and 9 extra pretzels. She

gives 1 bag to a friend. How many pretzels does she have
now?
Extension: John has 19 pretzels. How many more pretzels
does he need to have as many as Sheila does now?
Note: Depending on students’ strategies for solving, students
may subtract in quantities larger than the grade level
standard of within 20. Some students may subtract 1 bag
from 3 bags as their method for solving, while others may
recognize that sharing 1 bag of 10 pretzels means that they
have to find what number is 10 less than 39. In the Debrief,
students will model the quantity and use place value charts to
demonstrate their method for solving.
Materials: (T) Personal math toolkit with 4 ten-sticks of linking cubes, 4 dimes and 10 pennies, projector
(S) 4 dimes and 10 pennies, personal white board with coin charts and place value charts
template
Students gather in the meeting area with their personal math toolkits in a semi-circle formation.
T: (Lay down a ten-stick on the floor.) How many ones, or individual cubes, are in a ten-stick?
S: 10 ones.
T: (Lay down 10 individual cubes into 5-groups next to the ten-stick.) What is the same or different
about these two groups of cubes?
S: They are different because one of them is a ten and the other is 10 ones.  They are the same
amount. The ten-stick is made up of 10 cubes. The 10 ones are also made of 10 cubes.  If you put
10 ones together, they’ll become a ten-stick.
T: You are right! They are worth the same amount; they have the
same value. Also, they are both made of 10 cubes. (Lay down a
dime, underneath the ten-stick.) How many pennies have the
same value as one dime?
S: 10 pennies.
T: (Lay down 10 pennies into 5-groups next to the dime, directly
below the 10 individual cubes.) What is the same or different
about these two groups of coins?
S: A dime is 10 cents. 10 pennies are worth 10 cents.  The dime is
Date: 9/20/13 4.A.60

only made of 1 coin. The pennies group is made up of 10 coins.  The coins are different.
T: Great observations! So 1 ten-stick has the same value as 10 individual cubes. And 1 dime has the
same value as?
S: 10 pennies!
T: I can take a ten-stick and break it apart into 10 individual
cubes. Can I do the same with a dime?
S: No. A dime is just 1 coin.
T: That’s another difference. The ten-stick has a value of 10 ones and we can see why. It’s actually
made up of 10 ones, and we can see them. The dime has the same value as 10 pennies but it’s just 1
coin. There are no pennies hiding inside. But it still has the same value as 10 pennies.
T: (Project a ten-stick and 3 single cubes.) How many
tens and ones are there?
S: 1 ten 3 ones.
NOTES ON
T: How can I use my coins to show the same number as MULTIPLE MEANS OF
the cubes? Show 1 ten 3 ones with your coins, then
ENGAGEMENT:
share with your partner.
Remember to adjust lesson structure
Students discuss as the teacher circulates. Be sure to address any to suit specific learning needs. Some of
misconceptions while you circulate. Some students may want to put your students may have more success
down 13 pennies but won’t be able to since each student is only given working with a partner since this
10 pennies. lesson calls for a great deal of counting
and manipulation of materials.
T: I noticed that some students wanted to lay down 13
pennies but found that they didn’t have enough. What
can we do to help?
S: Use 1 dime for 1 ten, then use 3 pennies for 3 ones.
MP.7
T: Great idea! It’s just like using the ten-stick to
represent 1 ten. (Choose a student volunteer to show
1 dime and 3 pennies, directly below the linking
cubes.)
Repeat the process using the suggested sequence: 15, 18, 28,
38, 31, 13, 40, and 39.
NOTES ON
T: (Show 39 cents with 3 dimes and 9 pennies.) MULTIPLE MEANS OF
T: How many dimes? REPRESENTATION:
S: 3 dimes. Dimes are an abstract representation
T: (Fill in the dimes and pennies place value chart.) How many of tens, particularly because they are
pennies? smaller than pennies, rather than ten
times the size of a penny. For students
S: 9 pennies. who are struggling with grasping
T: (Fill in the dimes and pennies place value chart.) How many quantities of tens and ones, continue
tens? to use linking cubes or bundled straws,
which can more visually present the
S: 3 tens.
comparative quantities.
T: (Fill in the tens and ones place value chart.) How many
Date: 9/20/13 4.A.61

ones?
S: 9 ones.
T: (Fill in the tens and ones place value chart.) What is the value of 3 dimes and 9 pennies?
S: 39 cents.
T: Give a number sentence to show the total of 39 cents by adding your dimes and pennies.
S: 30 cents + 9 cents = 39 cents.
Repeat the process using the following sequence: 1 dime and 4 pennies, 1 dime and 5 pennies, 2 dimes and 5
pennies, 3 dimes, 6 pennies and 3 dimes, and 2 dimes and 8 pennies. In addition, have students use the place
value chart on their personal white boards to write down the value of these coins. Be sure to flip the coins in
order for the students to become familiar with both heads and tails.
Give students 1 minute to study their 4 dimes and 10 pennies, noticing
similarities and differences of these coins.
T: Show 15 cents.
S: (Show 1 dime 5 pennies.)
T: Now, show me 1 more penny and write how much you have in the
place value chart.
S: (Add a penny and write 16.)
T: So, what is 1 more than 15? Say in a whole sentence.
S: 1 more than 15 is 16.
Repeat the process using the same number for 10 more,
1 less, and 10 less. For further practice, you may use the
following suggested sequence: 3 tens 5 ones, 27, 1 ten 9
ones, 31, and 1 ten 3 ones. When appropriate, have
students move on to drawing instead of using the coins
as shown.
Note: As students are sharing their work with coins
remind them to use the unit, cents. Have students add
their dimes and pennies to their personal math toolkit.

Lesson Objective: Use dimes and pennies as abstract

representations of tens and ones.
Date: 9/20/13 4.A.62

The Student Debrief is intended to invite reflection and active processing of the total lesson experience.
lesson.
 Look at Problem 2. If you were to show that
amount with dimes and pennies, how many of
each coin would you use?
 Look at Problems 3 and 6. How is Problem 6
different from Problem 3? What is different
about the amount shown in the pictures?
 Look at Problems 13 and 14. What did you cross
off in 13? What did you cross off in 14? Why did
you cross off a different coin in each problem?
 How are the tools that represent 1 ten different
from one another? (Project the ten-stick and the
dime.)
 What are some ways that a dime is different from a penny?
 Look at your Application Problem. Discuss how you solved it with a partner. How could you
represent this amount in a place value chart? How is this problem connected to today’s lesson?

Date: 9/20/13 4.A.63

Name Date
Fill in the place value chart and the blanks.

1. 2.
20 = _____ tens 14 = _____ten and _____ones

3. 4.
_____ = 3 tens 5 ones _____ = 2 tens 6 ones

5. 6.
_____= _____ tens _____ ones _____ = _____ tens _____ ones
7. 8.
_____ = _____ tens _____ ones

_____ tens _____ >
Date: 9/20/13 4.A.64

10 more than 25 is _____

Fill in the blank. Draw or cross off tens or ones as needed.
9. 10.
11. 12.

13. 14.

15. 16.
Date: 9/20/13 4.A.65

Name Date

1. 2.
3. 4.
Date: 9/20/13 4.A.66

Name Date
Fill in the place value chart and the blanks.

1. 2.
30 = _____ tens 17 = _____ten and _____ones

3. 4.
_____ = 2 tens 2 ones _____ = 3 tens 3 ones

5. 6.
_____= _____ tens _____ ones _____ = _____ tens _____ ones
7. 8.
_____ = _____ tens _____ ones _____ tens _____ >
Date: 9/20/13 4.A.67

10 more than 25 is _____

9. 10.
11. 12.

13. 14.

15. 16.
Date: 9/20/13 4.A.68

dimes pennies
tens ones
Date: 9/20/13 4.A.69

1
GRADE
Topic B
Comparison of Pairs of Two-Digit
Numbers
1.NBT.3, 1.NBT.1, 1.NBT.2
Focus Standard: 1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits,
recording the results of comparisons with the symbols >, =, and <.
-Links to: G2–M3 Place Value, Counting, and Comparison of Numbers to 1,000
Topic B begins with Lesson 7, where students identify the greater or lesser of two given numbers. They first
work with concrete materials whereby they build each quantity (1.NBT.2) and find the greater or the lesser
number through direct comparison. They progress to the more abstract comparison of numerals using their
understanding of place value to identify the greater or lesser value. Students begin with comparing numbers
such as 39 and 12, where the number of both units in the greater number is more than in the smaller
number. They then compare numbers such as 18 and 40, where they must realize the place of the 4 explains
the greater value of 40. 4 tens is greater than 8 ones.
In Lesson 8, students continue to practice comparing, with the added layer of
saying the comparison sentence from left to right. First, they order a group
of numerals, so that they are reading the set from least to greatest and then
greatest to least, always reading from left to right. Then, as students
compare two quantities or numerals, they place an L below the lesser
quantity and a G below the greater quantity. When they read, they simply
say the first numeral, the comparison word under the numeral, and then the
second numeral. This prepares students for using the symbols in later
lessons.
The topic closes with Lessons 9 and 10, where students use the comparison
symbols >, =, and < to compare pairs of two-digit numbers (1.NBT.3). In
Lesson 9, students focus on the quantity that is greater, as they use the
alligator analogy to “eat” and identify the amount that’s greater. Within this
same lesson, students use the alligator analogy to then identify the amount that is
less. Lastly, in Lesson 10, students write the appropriate mathematical symbol to
Topic B: Comparison of Pairs of Two-Digit Numbers

Date: 9/20/13 4.B.1
NYS COMMON CORE MATHEMATICS CURRICULUM Topic B 1•4
compare two numerals and then apply their knowledge of reading from left to right. For example, 18 < 40 is
read as “18 is less than 40.”
A Teaching Sequence Towards Mastery of Comparison of Pairs of Two-Digit Numbers

Objective 1: Compare two quantities, and identify the greater or lesser of the two given numerals.
(Lesson 7)
Objective 2: Compare quantities and numerals from left to right.

(Lesson 8)
Objective 3: Use the symbols >, =, and < to compare quantities and numerals.
(Lessons 9–10)
Topic B: Comparison of Pairs of Two-Digit Numbers

Date: 9/20/13 4.B.2
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 7 1
Lesson 7
Objective: Compare two quantities, and identify the greater or lesser of
the two given numerals.




 1 More/Less, 10 More/Less 1.NBT.5 (6 minutes)

 Sprint: +1, –1, +10, –10 1.NBT.5 (10 minutes)
1 More/Less, 10 More/Less (6 minutes)

Materials: (S) Kit with 40 linking cubes, 4 dimes, 10 pennies, personal white board with large place value
chart insert
Note: This activity provides practice with both proportional (linking cubes) and non-proportional (coins)
representations of tens and ones. Students review the connection between place value and adding or
subtracting ten or one.
T: Show 20 cubes. Add 1. Say the addition sentence, starting with 20.
S: 20 + 1 = 21.
T: Add 10. Say the addition sentence, starting with 21.
S: 21 + 10 = 31.
T: Subtract 1. Say the subtraction sentence, starting with 31.
S: 31 – 1 = 30.
T: Show 39. Add 1. Say the addition sentence, starting with 39.
S: 39 + 1 = 40.
Continue adding or subtracting 10 or 1, choosing different start numbers within 40 as appropriate. After
three minutes, use coins instead of linking cubes. When using coins, be careful not to ask students to
subtract 1 from a multiple of 10, as students have not yet learned to subtract by decomposing a dime into 10
pennies.
Lesson 7: Compare two quantities, and identify the greater or lesser of the two
given numerals. 4.B.3
Date: 9/20/13
Sprint: +1, –1, +10, –10 (10 minutes)

Materials: (S) +1, –1, +10, –10 Sprint
Note: This Sprint reviews the concepts taught in G1–M1–Lesson 5 and

supports students’ understanding of place value.
Benny has 4 dimes. Marcus has 4 pennies. Benny said, "We have the
same amount of money!" Is he correct? Use drawings or words to
explain your thinking.
Note: This problem enables a teacher to identify which students
understand, or are beginning to understand, the importance of the value
of a unit. The most essential understanding for this problem is for
students to differentiate between the two types of coins and their
values.
Materials: (T) Enlarged dimes and pennies for display, place

value chart (S) 5-group cards, dimes and pennies NOTES ON
from personal math toolkit MULITPLE MEANS OF
ENGAGEMENT:
Students gather in the meeting area with their materials.
Challenge advanced students with
T: Look at the Application Problem. Whose coins have a more questions about the 4 pennies
greater total value? and 4 dimes such as:
S: Benny’s do!  40 cents is more than 4 cents.  How much money do the boys have
(Teacher writes greater under the 4 dimes and circles together?
this side of the work.)  How many more cents does Benny
T: Correct. The word greater means more. 40 is more have than Marcus?
than 4. 40 is greater than 4.  Do you know of any other
combinations of coins that could
T: How could you describe 4 (circle Marcus’ pennies with
make 40 cents?
your finger) compared to 40? 4 is...?
S: Smaller than 40.  Less than 40.  Fewer than 40.
T: Yes, we would say 4 is less than 40. Let’s compare some more numbers. Let’s find the greater
number in each pair of numbers.
Date: 9/20/13
Display the following suggested sequence of number pairs one at a time:

 5 and 12
 39 and 21
 23 and 32
 17 and 15 NOTES ON
 14 and 40 MULITPLE MEANS OF
ENGAGEMENT:
 30 and 13
Some students may have difficulty
 1 ten 9 ones and 2 tens 1 one comparing numbers that have similar
 3 tens 1 one and 1 ten 3 ones digits such as 12 and 21, or numbers
that sound similar, such as 14 and 40
Note: 17 and 15 above is first example in which the ones place or 13 and 30. Use linking cubes along
must be considered to compare the numbers; it will be with the place value chart so students
discussed in the Debrief. can see the comparison with
Use ten-sticks or quick ten drawings. Each time, ask students to manipulatives.
explain how they know which number is greater. Encourage
students to use the language of tens and ones as they compare
the tens and the ones in each number.
Repeat the process, next finding the number that is less in each pair.
T: (Display 28 and 38 in place value charts.) Which number is greater?
S: 38!
T: Look at the place value charts. Do you look at the tens place or the ones place to help you find the
greater number? Turn and talk with a partner.
S: There is an 8 in the ones place for both numbers.  You look at the tens place first though.
T: (Point to each digit while explaining.) Yes, 3 tens is greater than 2 tens. 38 is greater than 28.
T: (Display 29 and 32 in place value charts.) Which number is greater?
S: 32!
T: Look at the place value charts. 9 is a lot bigger than either of the digits in 32. Does that mean 29 is
greater than 32? Turn and talk to your partner.
S: We still have to look at the tens place first. Tens are bigger than ones.  There are only 2 tens in 29
and there are 3 tens in 32. The tens place is where you have to look.
T: (Point to each digit while explaining.) Yes, 3 tens is greater than 2 tens. Let’s remember the value of
the digits when comparing!
Comparison with Cards Game

Partner A and Partner B
1. Each partner turns over two cards.
2. Add the two numbers together and find the total.
3. Partner A says a sentence to compare the totals using the words greater than or equal to.
Date: 9/20/13
4. The partner with the greater total wins the

cards. (If the totals are equal, leave the cards
until the next round when one student does
have a greater total.)
5. Repeat with Partner B making the comparison
statement.
After the first minute of play, change the rules so that the
person with the total that is less wins the cards. Partners
should use the words less than when comparing the cards
during this round. Alternate between the two rules for
four minutes. At the five-minute mark, change the rules
so that if the totals are equal, the game is over. Have
students save one pair of cards to compare with a partner
during the debrief using a place value chart.

Lesson Objective: Compare two quantities, and identify

the greater or lesser of the two given numerals.
Set. They should check work by comparing answers with
a partner before going over answers as a class. Look for
lesson.
 In Problem 3 did you look at the tens or the ones
to compare? Why?
 Look at your Problem Set with a partner and find
an example where you needed to look at the
ones place to compare.
Date: 9/20/13
 How are dimes and pennies similar to tens and ones?

 Look at Problem 4. Was this pair more difficult for you to compare? Why?
 The numeral in the tens place we can call a digit. The numeral in the ones place can also be called a
digit. Look at the pair of numbers in Problem 5(d) and identify the digit in the tens place and the
digit in the ones place for both numbers.
 Take out the cards you kept from today’s Comparison with Cards Game. What is the total of each
pair of cards? Write your total in a place value chart on your personal white board and compare
with your partner.
 Share your answer to today’s Application Problem with a partner. Restate your answer using the
words greater or less.

Date: 9/20/13
A Number correct:
Name Date
*Write the missing number. Pay attention to the addition or subtraction sign.
1 5+1=☐ 16 29 + 10 = ☐
2 15 + 1 = ☐ 17 9+1=☐
3 25 + 1 = ☐ 18 19 + 1 = ☐
4 5 + 10 = ☐ 19 29 + 1 = ☐
5 15 + 10 = ☐ 20 39 + 1 = ☐
6 25 + 10 = ☐ 21 40 - 1 = ☐
7 8-1=☐ 22 30 - 1 = ☐
8 18 - 1 = ☐ 23 20 - 1 = ☐
9 28 - 1 = ☐ 24 20 + ☐ = 21
10 38 - 1 = ☐ 25 20 + ☐ = 30
11 38 - 10 = ☐ 26 27 + ☐ = 37
12 28 - 10 = ☐ 27 27 + ☐ = 28
13 18 - 10 = ☐ 28 ☐+ 10 = 34
14 9 + 10 = ☐ 29 ☐ - 10 = 14
15 19 + 10 = ☐ 30 ☐- 10 = 24
Date: 9/20/13
B Number correct:
Name Date
*Write the missing number. Pay attention to the addition or subtraction sign.
1 4+1=☐ 16 28 + 10 = ☐
2 14 + 1 = ☐ 17 9+1=☐
3 24 + 1 = ☐ 18 19 + 1 = ☐
4 6 + 10 = ☐ 19 29 + 1 = ☐
5 16 + 10 = ☐ 20 39 + 1 = ☐
6 26 + 10 = ☐ 21 40 - 1 = ☐
7 7-1=☐ 22 30 - 1 = ☐
8 17 - 1 = ☐ 23 20 - 1 = ☐
9 27 - 1 = ☐ 24 10 + ☐ = 11
10 37 - 1 = ☐ 25 10 + ☐ = 20
11 37 - 10 = ☐ 26 22 + ☐ = 32
12 27 - 10 = ☐ 27 22 + ☐ = 23
13 17 - 10 = ☐ 28 ☐+ 10 = 39
14 8 + 10 = ☐ 29 ☐ - 10 = 19
15 18 + 10 = ☐ 30 ☐- 10 = 29
Date: 9/20/13
Name Date
For each pair, write the number of items in each set. Then circle the set with the
greater number of items.
1. 2.
____ ____ ____ ____

3. 4.
____ ____ ____ ____
5. Circle the number that is greater in each pair.
a. 1 ten 2 ones 3 tens 2 ones
b. 2 tens 8 ones 3 tens 2 ones
c. 19 15
d. 31 26
6. Circle the set of coins that have a greater value.
3 dimes 3 pennies
Date: 9/20/13
For each pair, write the number of items in each set. Circle the set with fewer items.
7. 8.
____ ____ ____ ____

9. 10.
____ ____ ____ ____
11. Circle the number that is less in each pair.
a. 2 tens 5 ones 1 ten 5 ones
b. 28 ones 3 tens 2 ones
c. 18 13
d. 31 26
12. Circle the set of coins that has less value.
1 dime 2 pennies 1 penny 2 dimes
13. Circle the amount that is less. Draw or write to show how you know.
32 17
Date: 9/20/13
Name Date
1. Write the number of items in each set. Then circle the set that is greater in
number. Write a statement to compare the two sets.
_______ _______
______ is greater than ______ ______ is greater than _______
2. Write the number of items in each set. Then circle the set that is less in number.
Say a statement to compare the two sets.
_______ _______
______ is less than ______ ______ is less than _______
3. Circle the set of coins that has a greater value.
Date: 9/20/13
Name Date
Write the number and circle the set that is greater in each pair. Say a statement to
compare the two sets.
1. 2.
____
Circle the number that is greater for each pair.
____ ____ ____
3. 4.
3 tens 8 ones 3 tens 9 ones 25 35
Write the number and circle the set that is less in each pair. Say a statement to
compare the two sets.
5. 6.
____
Circle the ____
number that is less for each pair. ____ ____
7. 8.
2 tens 7 ones 3 tens 7 ones 22 29
10. Circle the set of coins that has greater value.
Date: 9/20/13
Katelyn and Johnny are playing comparison with cards. They have recorded the totals
for each round. For each round, circle the total that won the cards and write the
statement. The first one is done for you.
ROUND 1 - The total that is the greater wins.
Katelyn’s total Johnny’s total
16 19 19 is greater than 16.
ROUND 2 - The total that is less wins.
27 24
ROUND 3- the total that is greater wins.
32 22
ROUND 4- the total that is less wins.
29 26
If Katelyn’s total is 39 and Johnny’s total has 3 tens 9 ones, who would win the game?
Draw a math drawing to explain how you know.
Date: 9/20/13
tens ones
Date: 9/20/13
Lesson 8
Objective: Compare quantities and numerals from left to right.




 Subtraction with Cards 1.OA.6 (5 minutes)

 Core Subtraction Fluency Review 1.OA.6 (5 minutes)
 Beep Counting by Ones and Tens 1.OA.5, 1.NBT.3 (3 minutes)
Subtraction with Cards (5 minutes)

Materials: (S) 1 pack of numeral cards 0─10 per set of partners (from G1─M1─Lesson 36)
Note: This activity reviews yesterday’s lesson and provides practice with subtraction within 10. Students’
fluency with these facts will be assessed after this game.
Students combine their numeral cards and place them face down between them. Each partner flips over two
cards and subtracts the smaller number from the larger one. The partner with the smallest difference says a
less than sentence and keeps the cards played by both players. If both players have the same difference,
each partner flips two more cards and the player with the smaller difference says a less than sentence and
keeps all the cards. The player with the most cards at the end of the game wins.
Core Subtraction Fluency Review (5 minutes)

Materials: (S) Core Subtraction Fluency Review
Note: This subtraction review sheet contains the majority of subtraction facts within 10 (excluding some –0
and –1 facts), which are part of the required core fluency for Grade 1. Consider using this sheet to monitor
progress towards mastery.
finishers to practice on the backs of their papers. When time runs out, read the answers aloud so students

Date: 9/20/13 4.B.16

can correct their work. Encourage students to remember how many they got correct today so they can try to
improve their scores on future Core Subtraction Fluency Reviews.
Beep Counting by Ones and Tens (3 minutes)

Say a series of three numbers but replace one of the numbers with the word beep (e.g., 1, 2, 3, beep). When
signaled, students say the number that was replaced by the word beep in the sequence. Scaffold number
sequences, beginning with easy sequences and moving to more complex ones. Choose sequences that count
forward and backward by ones and tens within 40.
Suggested sequence type: 10, 11, 12, beep; 20, 21, 22, beep; 20, 19, 18, beep; 30, 29, 28 beep; 0, 10, 20,
beep; 1, 11, 21, beep; 40, 30, 20, beep; 39, 29, 19, beep. Continue with similar sequences, changing the
sequential placement of the beep.
Anton picked 25 strawberries. He picked some more strawberries.

Then he had 35 strawberries.
a. Use a place value chart to show how many more strawberries Anton picked.
b. Write a statement comparing the two amounts of strawberries using one of these phrases: greater
than, less than, or equal to.
Note: In this add to with change unknown problem, students are now asked to use their understanding of
place value to identify how many more strawberries Anton picked and to compare the beginning and ending
quantities.
Materials: (T) Comparison cards (S) Comparison cards,

personal white boards, ten-sticks and coins from
NOTES ON
personal math toolkit
MULTIPLE MEANS OF
Note: For this lesson, use the word side of the comparison REPRESENTATION:
cards. The symbol side will be used in future lessons. Be sure your English Language Learners
understand the word compare.
Project the following two sequences on the board, both of Remind students about comparing the
which were used in today’s Beep Counting: 10, 11, 12, 13 and length of objects as they learned about
40, 30, 20, 10 in Module 3 and show some concrete
examples. Help students make the
T: You said these numbers during fluency. What is
connection between comparing length
different about them? and comparing numbers.
S: One set goes up and one set goes down.  One we
count up by ones and one set we count down by tens.
T: What do you mean it goes up?

Date: 9/20/13 4.B.17

S: The numbers get bigger.

T: Let’s use our math language to explain that. Who
remembers the words we used yesterday when we were
comparing two numbers?
S: Greater than.  Less than.  Equal to.
T: Are you saying this number (point to 10) is less than or
greater than 11 (point to 11)?
S: Less than.
T: What about the next numbers? 11 is…
S: Less than 12.
T: Let’s say the whole sequence and use the comparison words
as we compare each number in the set.
S/T: (Continue pointing to each number.) 10 is less than 11. 11
is less than 12. 12 is less than 13.
T: When we compare numbers using words, we read from
left to right, just like when we are reading a sentence in a
book or when we are reading a number sentence.
T: 40, 30, 20, 10 is in a different order. Turn to your partner
and discuss which word we will use when comparing
them. Remember we start with 40.
S: (Discuss.) Greater than!
T: Let’s read the whole sequence, using greater than to
compare the number pairs as we go.
S/T: 40 is greater than 30. 30 is greater than 20. 20 is greater
than 10.
T: Today, we are reading left to right when we compare
numbers. (Distribute comparison cards to students. Write
13 and 23 on the board.) Partner A (seated on the left),
show 13 with your ten-sticks. Partner B, show 23 with your
ten-sticks. Find the card with the comparison words that
show how your number compares to your partner’s number
and put it under your ten-sticks.
S: (Partners place cubes and cards.) NOTES ON
T: I see these cards under your numbers. (Write less than MULTIPLE MEANS Of
under 13 and greater than under 23.) To read this ACTION AND
from left to right, we would say 13 is….? EXPRESSION:
S: Less than 23! Some students may still need concrete
T: Yes, less than. Let’s move the less than card between models after others are ready to move
our numbers. We’ll read together. (Move card on. When moving to using numbers
between 13 and 23.) only, ask the students who need more
concrete supports to be the class
S/T: 13 is less than 23. helper by modeling the numbers with
linking cubes.

Date: 9/20/13 4.B.18

Repeat the process with the following suggested sequence: 15 and 19, 21 and 19, 3 tens 5 ones and 2 tens 8
ones, 21 and 31, 18 and 9, 38 and 12, and 27 and 19. Move quickly to quick ten drawings or no visual
supports as appropriate for the group of students. Grouping students by readiness levels will make this
easier.
T: Does anyone else notice something interesting about which card we have been using when we read
the comparison from left to right?
S: We always use Partner A’s card!
T: Do we even need Partner B’s card to say our comparison sentence?
S: No!
T: Ok, switch spots so that we can use Partner B’s card. (Partners switch spaces so that Partner B is
sitting on the left.)
Repeat the process with the following suggested sequence: 14
and 17, 3 tens and 2 tens, 2 tens 9 ones and 3 tens, 24 and 38, NOTES ON
and 34 and 28. This time, only Partner B should use the MULTIPLE MEANS OF
comparison cards, since it has been determined that only the REPRESENTATION:
comparison card on the left gets moved into the middle to read Highlight the critical vocabulary for
the comparison sentence. English language learners as you teach
the lesson by showing objects as a
T: (Leave 34 and 28 on display.) Which digit in each visual as you say the words.
number did you look at first to compare them? Vocabulary in this lesson that you will
S: We looked at the digit in the tens place! want to highlight is in order, in front of,
before, and between. Without
T: Why do we look at the tens place first when we
understanding these words, English
compare two numbers? Turn and talk to your partner.
language learners will have difficulty
S: The digit 3 in 34 stands for 30. The digit 2 in 24 stands placing numbers into the tens
for 20. 30 is greater than 20. Even if there were 9 sequence.
ones that’s still less than a ten.
T: (Write the multiples of 10 from 0 to 40 across the
board, with space in between the numbers. Write the
following five numbers above the sequence: 29, 38, 7,
14, 24.) If I want to place these numbers into this set
of numbers, in order, where would they go? Where
would I put 29?
S: In front of the 30. It’s less than 30. (Write 29 between 20 and 30.)
T: Where would I put 38?
S: Between 30 and 40. It’s greater than 30 and less than 40. (Write 38 between 30 and 40. Continue
with this process until all the numbers are placed.)
T: (Leave this sequence on the board. Write the numbers 40, 30, 20, 10, 0 on the board with space in
between the numbers.) Let’s put those same numbers in order into this set.
T: Where does 29 go now?
S: Between the 30 and 20. 29 is less than 30. It’s greater than 20. (Continue having students place the
numbers in order in the sequence.)
T: Let’s read the first sequence we made, starting on the...

Date: 9/20/13 4.B.19

S: Left!
S/T: (Point to the numbers as students read the
sequence.) 0 is less than 7. 7 is less than 10.
(Continue on.)
T: What will we say when we are comparing the
numbers in the second set?
S: Greater than!
S/T: (Point to the numbers as students read the
sequence.) 40 is greater than 38. 38 is greater
than 30. (Continue on.)

In this Problem Set, students wil be ordering numbers
from least to greatest and greatest to least, it would be
helpful to review the meaning of the words least and
greatest to prepare students to answer these questions.
Lesson Objective: Compare quantities and numerals from

left to right.
lesson.
 Look at Problem 2. Use math drawings, materials
or place value charts to prove your solution for
36 _______ 3 tens 6 ones.

Date: 9/20/13 4.B.20

 How did Problem 3 help you solve Problem 4? What is the same about these two problems? What
is different?
 Rewrite your statement for the Application Problem using only numbers and the phrase greater than
or less than to compare the two sets of strawberries. Start with Anton’s amount of strawberries.
 Share your solution to Problem 5 with your partner. Did you have the same solution? If your
solutions were different explain how they could both be correct.


Date: 9/20/13 4.B.21

Name Date
Core Subtraction Fluency Review
1. 8 - 0 = ___ 16. 9 - 3 = ___ 31. 5 - 5 = ___
2. 8 – 1 = ___ 17. 10 - 3 = ___ 32. 6 - 5 = ___
3. 7 - 7 = ___ 18. 10 - 4 = ___ 33. 7 - 5 = ___
4. 3 - 3 = ___ 19. 10 - 2 = ___ 34. 8 - 5 = ___
5. 3 - 2 = ___ 20. 10 – 8 = ___ 35. 8 - 4 = ___
6. 4 - 2 = ___ 21. 10 - 7 = ___ 36. 10 - 5 = ___
7. 5 - 2 = ___ 22. 10 - 6 = ___ 37. 9 - 5 = ___
8. 5 - 3 = ___ 23. 6 - 6 = ___ 38. 9 - 4 = ___
9. 9 - 2 = ___ 24. 7 - 7 = ___ 39. 6 - 3 = ___
10. 8 - 2 = ___ 25. 7 - 6 = ___ 40. 6 - 4 = ___
11. 7 - 2 = ___ 26. 8 - 8 = ___ 41. 7 - 3 = ___
12. 4 - 4 = ___ 27. 8 - 7 = ___ 42. 7 - 4 = ___
13. 4 - 3 = ___ 28. 9 - 9 = ___ 43. 8 - 6 = ___
14. 5 - 4 = ___ 28. 9 - 8 = ___ 44. 9 - 6 = ___
15. 8 - 3 = ___ 30. 10 - 9 = ___ 45. 9 - 7 = ___

Date: 9/20/13 4.B.22

Name Date
Word Bank
1. Draw quick tens and ones to show each number. Label the first is greater than
drawing as less (L), greater (G), or equal to (E) the second. is less than
Write a phrase from the word bank to compare the numbers.
is equal to
a. b. 2 tens 3 tens
20 _____________________ 18 2 tens ________________ 3 tens
c. d.
24 15 26 32
24 _____________________ 15 26 _____________________ 32
2. Write a phrase from the word bank to compare the numbers.
36 _____________________ 3 tens 6 ones
1 ten 8 ones _____________________ 3 tens 1 one

Date: 9/20/13 4.B.23

38 _____________________ 26
1 ten 7 ones _____________________ 27
15 _____________________ 1 ten 2 ones
30 _____________________ 28
29 _____________________ 32
3. Put the following numbers in order from least to greatest. Cross off each number
after it has been used.
9 40 32 13 23
4. Put the following numbers in order from greatest to least. Cross off each number
after it has been used.
9 40 32 13 23
5. Use the digits 8, 3, 2, and 7 to make 4 different two-digit 8 3 2 7

numbers less than 40. Write them in order from greatest
to least. Examples: 32, 27….

Date: 9/20/13 4.B.24

Name Date
Write the numbers in order from greatest to least.
40
39 29
30
Complete the sentence frames using the phrases from the word bank to compare the
two numbers.
Word Bank
is greater than
17 __________________________ 24 is less than
is equal to
23 __________________________ 2 tens 3 ones
29 __________________________ 20

Date: 9/20/13 4.B.25

Name Date
Word Bank
is greater than
1. Draw the numbers using quick tens and circles. Use the
phrases from the word bank to complete the sentence frames is less than
to compare the numbers.
is equal to
20 30 14 22
20 ___________________ 30 14 __________________ 22
15 1 ten 5 ones 39 29
15 ________________ 1 ten 5 ones 39 _____________________ 29

31 13 23 33
31 ___________________ 13 23 ____________________ 33
2. Circle the numbers that are greater than 28.
32 29 2 tens 8 ones 4 tens 18
3. Circle the numbers that are less than 31.
29 3 tens 6 ones 3 tens 13 3 tens 9 ones

Date: 9/20/13 4.B.26

4. Write the numbers in order from least to greatest.
23
32 30
29
Where would the number 27 go in this order? Use words or rewrite the numbers to
explain.
5. Write the numbers in order from greatest to least.
40
13 30
31
Where would the number 23 go in this order? Use words or rewrite the numbers to
explain.
6. Use the digits 9, 4, 3, and 2 to make 4 different two-

digit numbers less than 40. Write them in order from
least to greatest. 9 3 4 2
Examples: 34, 29….

Date: 9/20/13 4.B.27

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 Activity Template 1•4
Comparison cards, p. 1. Print double-sided on cardstock. Distribute each of the three cards to students.
> < = <

> < = >
> < = =
> < =
Date: 9/20/13 4.B.28

Comparison cards, p. 2. Print double-sided on cardstock. Distribute each of the three cards to students.
less than equal to less than greater than
greater than equal to less than greater than
equal to equal to less than greater than
equal to less than greater than

Date: 9/20/13 4.B.29

Lesson 9
Objective: Use the symbols >, =, and < to compare quantities and
numerals.




 Core Subtraction Fluency Review 1.OA.6 (5 minutes)

 Digit Detective 1.NBT.2 (4 minutes)
 Sequence Sets of Numbers 1.NBT.3 (5 minutes)
Core Subtraction Fluency Review (5 minutes)

Materials: (S) Core Subtraction Fluency Review from G1–M4–Lesson 8
graders. Since this is the second day students are doing this activity, encourage students to remember how
many problems they answered yesterday and celebrate improvement.
finishers to practice on the back of their papers. When time runs out, read the answers aloud so students can
correct their work and celebrate improvement.
Digit Detective (4 minutes)

Materials: (T/S) Personal white boards with place value chart insert (from G1–M4–Lesson 2)
Note: This activity reviews the term digit and relates it to place value.
Write a number on your personal white board, but do not show students.
T: The digit in the tens place is 2. The digit in the ones place is 3. What’s my number? (Snap.)
S: 23.
T: What’s the value of the 2? (Snap.)
Lesson 9: Use the symbols >, =, and < to compare quantities and numerals.
Date: 9/20/13 4.B.30

S: 20.
S: 3.
Repeat sequence with a ones digit of 2 and a tens digit of 3.
T: The digit in the tens place is 1 more than 2. The digit in the ones place is 1 less than 2. What’s my
number? (Snap.)
S: 31.
T: The digit in the ones place is equal to 8 – 4. The digit in the tens place is equal to 9 – 7. What’s my
number? (Snap.)
S: 24.
As with the above example, begin with easy clues and gradually increase the complexity. Give students the
option to write the digits on their place value chart as you say the clues.
Sequence Sets of Numbers (5 minutes)

Materials: (S) Personal white boards
Note: This activity reviews yesterday’s lesson.

Write sets of four numbers within 40 (e.g., 23, 13, 32, 22). Students write and read the numbers from least to
greatest, then from greatest to least. Ask questions such as the following:
 How could you use the words greater than or less than to compare 32 and 23?
 What number has the same digit in the tens place and ones place?
 Which two numbers have the same digit in the tens place?
 Which two numbers have the same digit in the ones place?
 Which number is less than 23?
Continue with similar questions and different sets of numbers.
Suggested sets: 13, 11, 31, 1; 17, 27, 21, 12; 38, 18, 25, 35; etc.
Carl has a collection of rocks. He collects 10 more rocks. Now he has 31

rocks. How many rocks did he have in the beginning?
a. Use place value charts to show how many rocks Carl had at the
beginning.
b. Write a statement comparing how many rocks Carl started and
ended with, using one of these phrases: greater than, less than,
equal to.
Date: 9/20/13 4.B.31

Note: In this add to with start unknown problem, students are asked to mentally determine what number is
10 less than 31. For struggling students, a place value chart and/or manipulatives would be helpful.
Materials: (T) Alligator A and B pictures (double-sided), NOTES ON

comparison cards (from G1–M4–Lesson 8) MULTIPLE MEANS OF
(S) Comparison cards (from G1–M4–Lesson 8), EXPRESSION:
personal white boards
English language learners may benefit
from having sentence frames on the
Note: When comparing numbers, most students tend to board or in their personal white boards
express the comparison by starting with the greater number, to refer to as they are reading
regardless of the order of the numbers on the page. For comparison statements from left to
instance, if the numbers 3 and 30 were displayed on the board, right.
students may say 30 is greater than 3. The statement is true, _____ is greater than _____.
even though the student was not comparing from left to right.
_____ is less than _____.
The best support we can give students is to affirm their true
remark, and ask them to now compare the numbers starting As they become more familiar with
with the one on the left, pointing to the 3. Examples of this are reading the statement, remove the
embedded in the dialogue below. sentence frame.
Gather students in the meeting area with their materials.

T: (Project or draw a group of 2 frogs and a group of 10 frogs with enough room in between the groups
to place the alligator picture.) Here is an alligator. He is really hungry. Notice his open mouth.
(Trace the shape of the mouth with your finger.) Would this hungry alligator rather eat 2 frogs for
dinner, or eat 10 frogs for dinner?
S: 10 frogs!
T: Why would he rather eat the group of 10 frogs?
S: 10 frogs is more than 2 frogs!  10 is greater than 2!
T: Yes, terrific. What would we say if we started comparing the numbers from the left, starting with
the number 2?
S: 2 is less than 10. (Place Alligator A, between the frogs, showing the alligator facing the group of 10
frogs.)
T: (Project or draw a group of 15 frogs and a group of 10 frogs in the same manner.) Which group of
frogs will the hungry alligator want to eat this time?
S: The group of 15 frogs!
T: Why?
S: 15 frogs is greater than 10 frogs.
T: Show or explain how you know that.
S: 15 is made of 1 ten and 5 ones. That’s more than just 1 ten.  I can show it with my ten-sticks!
See? 1 ten and 5 ones is more than 1 ten.
Date: 9/20/13 4.B.32

T: (Draw bond under 15 to show 10 and 5. Turn the card over to Alligator B to show the alligator
facing the 15 frogs.)
T: Now I will post only numbers. We’ll continue to compare them and decide which number the
alligator would prefer.
Repeat the process from above with the following suggested sequence of numbers:
 1 ten and 1 ten 6 ones
 30 and 20
 4 tens and 3 tens 8 ones
 39 and 32
 14 and 40
 23 and 32
When appropriate, you may want to use the alligator cards and cover up the words greater than and less than
to encourage students to rely on using just the symbols.
With each pair of numbers, encourage students to explain their reasoning. Ask the students to express each
MP.7 number in tens and ones, comparing the tens and the ones in each number as they explain why one number
is greater than or less than the other number.
T: Now it’s your turn to do this with a partner. Take out your comparison cards. Hold up the card that
says less than.
S: (Hold up less than card, showing the words.)
T: Turn the card over. The wavy water lines should be at the bottom of your
card. You will see a part of the alligator’s mouth. If you’d like, use a yellow
colored pencil to add some teeth to your alligator’s mouth. (Demonstrate
by adding teeth on the teacher comparison card. In tomorrow’s lesson
students will erase teeth.)
Repeat this process for the greater than card.
T: Now we’re ready to play Compare It!
NOTES ON
T: Each of you will write a number from 0 to 40 on your MULTIPLE MEANS OF
board, without showing your partner. When you are ACTION AND
both ready, put them down next to each other. For
EXPRESSION:
the first round, Partner A uses her cards to put the
As students are completing their
alligator picture between the boards, always having
Problem Set, encourage them to
the alligator’s mouth open to the greater number.
quietly read each expression as they
Then Partner B will read the expression from left to circle their answer. This will allow you
right. Each round will last one minute. The object of to hear which students are reading the
the game is to see how many different comparisons expressions correctly and support
you can make within each round. You can use tally those who may need it.
marks to keep track.
At the end of the first round, have partners use Partner B’s cards. Alternate for each round until the students
have played for four minutes. During that time, circulate and notice which students are successful and which
students may need more support. Encourage students to make the game more challenging by varying how
Date: 9/20/13 4.B.33

they represent the number, using quick tens, place value

charts, and writing the numbers as tens and ones.
Grouping students by readiness levels will facilitate this
opportunity to differentiate.

Lesson Objective: Use the symbols >, =, and < to compare

quantities and numerals.
 Compare your answer to Problem 4(a) with your
partner’s. Did you and your partner come up with
the same answer? Can there be more than one
answer? Are there other problems that can have
more than one answer? Why?
 Compare your answer to Problem 4(j) with your
partner’s. Did you and your partner come up with
the same answer? Can there be only one answer.
Are there other problems that can only have one
answer? Why?
 What new math symbols did we use today to
compare different numbers? (> for greater than, <
for less than.)
 Look at your statement to today’s Application
Problem. Rewrite your statement using only
numbers and a symbol.
Date: 9/20/13 4.B.34


Date: 9/20/13 4.B.35

Name Date
1. Circle the alligator that is eating the greater number.

a. b. c. d.
40 20 10 30 18 14 19 36
2. Write the numbers in the blanks so that the alligator is eating the greater number.
With a partner, compare the numbers out loud, using is greater than, is less than, or
is equal to. Remember to start with the number on the left.
a. b. c.
24 4 38 36 15 14
______ ______ ______ ______ ______ ______
d. e. f.
20 2 36 35 20 19
______ ______
______ ______ ______ ______
g. h. i.
31 13 23 32 21 12
______ ______ ______ ______ ______ ______
Date: 9/20/13 4.B.36

3. If the alligator is eating the greater number, circle it. If not, redraw the alligator.
a. b.
20 19 32 23
4. Complete the charts so that the alligator is eating the greater number.
a. b.
1 2 1 2 7 2
c. d.
2 5 5 8 3 8
e. f.
2 1 2 2 4 4
g. h.
1 8 5 2 1 9
9
i. j.
7 2 1 1 4 4
Date: 9/20/13 4.B.37

Name Date
Read the number sentence, using is greater than, is less than, or is equal to.
Remember to start with the number on the left.
a. b. c.
12 10 22 24 17 25
______ ______ ______ ______ ______ ______
d. e. f.
13 3 27 28 30 21
______ ______
______ ______ ______ ______
g. h. i.
12 21 31 13 32 23
______ ______ ______ ______ ______ ______
Date: 9/20/13 4.B.38

Name Date
Read the number sentence, using is greater than, is less than, or is equal to.
Remember to start with the number on the left.
a. b. c.
10 20 15 17 24 22
______ ______ ______ ______ ______ ______
d. e. f.
29 30 39 38 39 40
______ ______ ______ ______ ______ ______
2. Complete the charts so that the gator is eating the greater number.
a. b.
1 8 1 2 4 3
c. d.
2 3 2
e. f.
1 7 7
Date: 9/20/13 4.B.39

Compare each set of numbers by matching to the correct alligator or phrase to make a
true number sentence. Check your work by reading the sentence from left to right.
3.
16 17
31 23
35 25 is less than
12 21
22 32
is greater than
29 30 than
39 40
Date: 9/20/13 4.B.40

Alligator template, double-sided on cardstock for the teacher.
greater than
Date: 9/20/13 4.B.41

Alligator template, double-sided on cardstock for the teacher.
less than
Date: 9/20/13 4.B.42

Lesson 10
Objective: Use the symbols >, =, and < to compare quantities and
numerals.




 Sprint: Number Sequences Within 40 1.NBT.3 (10 minutes)

Sprint: Number Sequences Within 40 (10 minutes)

Materials: (S) Number Sequences Within 40 Sprint NOTES ON
MULTIPLE MEANS OF
Note: In this Sprint, students recognize forward and backward ENGAGEMENT:
counting patterns. As with all Common Core Sprints, the Connect learning to areas of interest.
sequence progresses from simple to complex, with the final Students who enjoy writing can be
quadrant being the most challenging. The last four problems of given the challenge to write their own
this particular Sprint involve counting by twos, a second grade Application Problem using tens and
standard. First grade students who complete enough problems ones. Practicing their writing skills
to encounter this challenge may use their understanding of the during math is a great cross-curricular
relationship between counting and addition to solve these activity. Students can also present
problems (1.OA.5). their problem to the class to solve.

Materials: (T/S) Personal boards with place value chart insert (G1–M1–Lesson 2)
Note: This activity was conducted as teacher-directed fluency in the previous lesson. Today, students
practice in partners and compare their numbers using inequality symbols.
Students work in partners. Each student writes a number from 0 to 40 in their place value chart but does not
show their partner. Partners then can either tell which digit is in each place or give addition or subtraction
clues about the digits. Partners guess each other’s numbers and then write and say an inequality sentence
Date: 9/20/13 4.B.43

comparing them. Circulate and ask questions to encourage students to realize that their inequality sentences
may be different, but may both be true (e.g., 14 < 37 and 37 > 14).
Elaine had 19 blueberries and ate 10. Mike had 13 and

picked 7. Compare Elaine and Mike’s blueberries after
Elaine ate some and Mike picked some more.
a. Use words and pictures to show how many
blueberries each person has.
b. Use the term greater than or less than in your
statement.
Note: In this problem, students apply several elements
from their previous learning, such as mentally adding
10 and using comparative language. During the debrief, students will write the number sentence using the
proper comparative symbol. If the challenge of wielding both Elaine and Mike feels too much for your
students, invite them to work in pairs and let one student be Mike, the other Elaine.
Materials: (T) Alligator template (from G1–M4–Lesson 9), comparison cards (from G1–M4–Lesson 8),
projector (S) Comparison cards (from G1–M4–Lesson 8), erasers, personal white boards
Gather students in the meeting area with their materials.

T: (Project 28 and 37 in place value charts.) Which NOTES ON
number would the hungry alligator want to eat? MULTIPLE MEANS OF
S: 37! ENGAGEMENT:
T: (Place the greater than alligator symbol.) Why? A few students should keep the teeth
S: 37 is greater than 28.  There are more tens in 37 on their alligators while the rest of the
than in 28.  The digit 3 in 37 shows there are more class removes their teeth. This will
tens in 37 than there are in 28. help the class see that the symbols are
the same with or without teeth. The
T: Today, we will use math symbols to compare numbers. students who initially keep their teeth
You just said that 37 is greater than 28. (Hold up the can be those who may need additional
greater than card with the symbol side showing.) I will support reading the statements
use this math symbol to make the number sentence 37 correctly. At some point during the
is greater than 28. (Tape card below the alligator and lesson, switch the job to other students
rewrite the numbers on either side of the symbol.) to support movement towards greater
T: What do you notice is similar between the alligator and independence.
the math symbol? Turn and talk with a partner.
Date: 9/20/13 4.B.44

S: The symbol looks like the alligator’s mouth.  The symbol is open on the side that the alligator likes
to eat.
T: We call this symbol the greater than sign.
T: (Project 15 and 18 in place value charts.) Can you figure out the symbol we will use between these
numbers? Talk with a partner.
S: (Share quickly.) The less than sign!
T: We need to place the less than sign, because 15 is less than 18. What does this sign look like? Draw
it in the air. (Students draw in the air.)
T: Yes, it looks like this. (Draw or tape the less than symbol between 15 and 18.) How did you know?
S: It is like the alligator’s mouth. It should be opened toward the greater number.  The smaller end
points at the smaller number.  The open part is toward the greater number.
T: Today, let’s erase the teeth we made on our comparison cards and try to use the math symbol to
make true number sentences like the two we just made.
T: We will play Compare It! again today. We need someone to remind us of the rules.
S: We play with a partner. Each of us writes a number from 0 to 40 on our board, without showing our
partner. When we are both ready, we put them down next to each other. For the first round,
Partner A uses the cards to put the symbol between the boards.
T: Today, Partner B then reads the true number sentence that you made. Remember that we always
read the number sentences from left to right. (Demonstrate with the number sentence on the
board.)
At the end of the first round, have partners use Partner B’s
cards. Alternate for each round until the students have
played for four minutes. During that time, circulate and
notice which students are successful and which students
may need more support. Encourage students to make the
game more challenging by varying how they represent the
number, using quick tens, place value charts, and writing
the numbers as tens and ones.

Lesson Objective: Use the symbols >, =, and < to compare

quantities and numerals.
Date: 9/20/13 4.B.45


lesson.
 Look at Problems 1(a) and 1(b). How was the
way in which you solved 1(a) different from how
you solved 1(b)? Explain your thinking.
 Look at Problem 2(f). How are the numbers the
same? How are they different? Compare the
digit 2 in each number. How does changing the
position of the digit change the value of the
number?
 What are some different ways you can remember
each of the symbols?
 Look at the Application Problem. How did you
find the answer? Use the symbols from today’s
lesson to write a number sentence that matches your statement.

Date: 9/20/13 4.B.46

A Number correct:
Name Date
*Write the missing number in the sequence.
1 0, 1, 2, __ 16 15, __, 13, 12

2 10, 11, 12, __ 17 __, 24, 23, 22
3 20, 21, 22, __ 18 6, 16, __, 36
4 10, 9, 8, __ 19 7, __, 27, 37
5 20, 19, 18, __ 20 __, 19, 29, 39
6 40, 39, 38, __ 21 __, 26, 16, 6
7 0, 10, 20, __ 22 34, __, 14, 4
8 2, 12, 22, __ 23 __, 20, 21, 22
9 5, 15, 25, __ 24 29, __, 31, 32
10 40, 30, 20, __ 25 5, __, 25, 35
11 39, 29, 19, __ 26 __, 25, 15, 5
12 7, 8, 9, __ 27 2, 4, __, 8
13 7, 8, __, 10 28 __, 14, 16, 18
14 17, __, 19, 20 29 8, __, 4, 2
15 15, 14, __, 12 30 __, 18, 16, 14
Date: 9/20/13 4.B.47

B Number correct:
Name Date
*Write the missing number in the sequence.
1 1, 2, 3, __ 16 13, __, 11, 10

2 11, 12, 13 __ 17 __, 22, 21, 20
3 21, 22, 23 __ 18 5, 15, __, 35
4 10, 9, 8, __ 19 4, __, 24, 34
5 20, 19, 18, __ 20 __, 17, 27, 37
6 30, 29, 28, __ 21 __, 29, 19, 9
7 0, 10, 20, __ 22 31, __, 11, 1
8 3, 13, 23, __ 23 __, 30, 31, 32
9 6, 16, 26, __ 24 19, __, 21, 22
10 40, 30, 20, __ 25 5, __, 25, 35
11 38, 28, 18, __ 26 __, 25, 15, 5
12 6, 7, 8, __ 27 2, 4, __, 8
13 6, 7, __, 9 28 __, 12, 14, 16
14 16, __, 18, 19 29 12, __, 8, 6
15 16, __, 14, 13 30 __, 20, 18, 16
Date: 9/20/13 4.B.48

Name Date
1. Use the symbols to compare the numbers. Fill in the blank with <, >, or = to make a
true number sentence. Read the number sentences from left to right.
40 20 18 20
40 > 20 18 < 20
40 is greater than 20. 18 is less than 20.
a. b. c.
27 24 31 28 10 13
27 is ________ than 24. e.

d. 31 is ________ than 28. 13 is ________ than 10.
f.
13 15 31 29 38 18
13 is ________ than 15. 31 is ________ than 29. 38 is ________ than 18.

g. h. i.
27 17 32 21 12 21
Date: 9/20/13 4.B.49

2. Circle the correct words to make the sentence true. Use >, <, or = and numbers to
write a true number sentence. The first one is done for you.
a. is greater than b. is greater than

36 is less than 3 tens 6 ones 1 ten 4 ones is less than 17
is equal to is equal to
36 = 36
c. d.
is greater than is greater than
2 tens 4 ones is less than 34 20 is less than 2 tens 0 ones
e. f.
31 is less than 13 12 is less than 21
g. h.
17 is less than 3 ones 1 ten 30 is less than 0 tens 30 ones
Date: 9/20/13 4.B.50

Name Date
Circle the correct words to make the sentence true. Use >, <, or = and numbers to write
a true number sentence.
a. is greater than b. is greater than

29 is less than 2 tens 6 ones 1 ten 8 ones is less than 19
c. d.
2 tens 9 ones is less than 40 39 is less than 4 tens 0 ones
Date: 9/20/13 4.B.51

Name Date
1. Use the symbols to compare the numbers. Fill in the blank with <, >, or = to make a
true number sentence. Complete the number sentence with a phrase from the word
bank. Word bank
is greater than
40 20 18 20
is less than
is equal to
40 > 20 18 < 20
40 is greater than 20. 18 is less than 20.
a. b.
17 13 23 33
17 ____________ 13 23____________ 33
c. 36 36 d.
25 32
36 ____________ 36 25 ____________ 32
e. f.
38 28 32 23
38 ____________ 28 32 ____________ 23
Date: 9/20/13 4.B.52

g. h.
1 ten 5 ones 14 3 tens 30
33
1 ten 5 ones _______ 14 3 tens __________ 30
i. j.
29 2 tens 7 ones 19 2 tens 3 ones
29 _________ 2 tens 7 ones 19 __________ 2 tens 3 ones
k. l.
3 tens 1 one 13 35 3 tens 5 ones
3 tens 1 one __________ 13 35 _________ 3 tens 5 ones
m. n.
2 tens 3 ones 32 3 tens 36
13 33
2 tens 3 ones __________ 32 3 tens ___________36
o. p.
29 3 tens 9 ones 4 tens 39
29 _________ 3 tens 9 ones 4 tens ___________ 39
Date: 9/20/13 4.B.53

1
GRADE
Topic C
Addition and Subtraction of Tens
1.NBT.2, 1.NBT.4, 1.NBT.6
Focus Standard: 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and
ones. Understand the following as special cases:
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five,
six, seven, eight, or nine tens (and 0 ones).
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and
adding a two-digit number and a multiple of 10, using concrete models or drawings and
strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written method and explain
the reasoning used. Understand that in adding two-digit numbers, one adds tens and
tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90
(positive or zero differences), using concrete models or drawings and strategies based
on place value, properties of operations, and/or relationship between addition and
-Links to: G1–M6 Place Value, Comparison, Addition and Subtraction to 100
G2–M3 Place Value, Counting, and Comparison of Numbers to 1,000
In Topic C, students pick up from their previous work with 10 more and 10 less to extend the concept to
adding and subtracting multiples of 10.
In Lesson 11, students represent the addition of ten more with
concrete objects and number bonds, first using the numeral and
then writing as units of ten, as shown. After creating such number
bonds for several examples, students notice that only the unit has changed (e.g., 3 bananas + 1 banana = 4
bananas, just as 3 tens + 1 ten = 4 tens). As students explore, they see that this relationship is present even
when adding more than 1 ten. They come to realize that 2 tens + 2 tens = 4 tens, just as 2 + 2 = 4 (1.NBT.4).
Students also explore this relationship with subtraction, seeing that 4 tens can be decomposed as 3 tens and
1 ten, and that 4 tens – 3 tens = 1 ten, just as 4 – 3 = 1 (1.NBT.6). Students see that the arrow is used to show
the addition or subtraction of an amount, regardless of whether the number is increasing (adding) or
decreasing (subtracting). This provides an important foundation for applying strategies such as the make ten
strategy, described in Topic D.
Topic C: Addition and Subtraction of Tens

Date: 9/20/13 4.C.1
NYS COMMON CORE MATHEMATICS CURRICULUM Topic C 1•4
In Lesson 12, students add multiples of 10 to two-digit numbers that include both tens and
ones. They recognize that when tens are added to a number, the ones remain the same.
Students use the cubes within their kit of 4 ten-sticks as well as the more abstract
manipulatives of dimes and pennies, to explore the concept. They represent their
computation in familiar ways such as number bonds, quick ten drawings, arrow notation,
and by using the place value chart to organize the quantities as tens and ones.
A Teaching Sequence Towards Mastery of Addition and Subtraction of Tens

Objective 1: Add and subtract tens from a multiple of 10.
(Lesson 11)
Objective 2: Add tens to a two-digit number.

(Lesson 12)
Topic C: Addition and Subtraction of Tens

Date: 9/20/13 4.C.2
Lesson 11
Objective: Add and subtract tens from a multiple of 10.




 Compare Numbers 1.NBT.3, 1.OA.6 (5 minutes)

 Number Bond Addition and Subtraction 1.OA.6 (5 minutes)
 Happy Counting by Tens 1.NBT.5 (2 minutes)
Compare Numbers (5 minutes)

Teacher: Student:
Note: In this fluency activity, students review yesterday’s lesson and use 5 8 5 < 8
their understanding of place value to compare numbers.
Say and write sets of numbers from 0 to 40 in various ways (e.g., as 15 18 15 < 18
numerals, as tens and ones, the Say Ten way). Students write a number
25 28 25 < 28
sentence in the same order it is written on the board. Students then
read their sentences aloud.
Teacher: Student:
Suggested sets:
 5 and 8, 15 and 18, 25 and 28 6 3 6 > 3
 6 and 3, ten 6 and ten 3, 2 tens 6 and 2 tens 3 ten 6 ten 3 16 > 13
 3 and 3, 3 tens and 3 tens, 3 tens and 3 ones
 3 and 4, 3 tens 4 ones and 4 tens 3 ones, 2 tens 6 2 tens 3 26 > 23
3 ones 4 tens and 4 ones 3 tens
Lesson 11: Add and subtract tens from a multiple of 10.

Date: 9/20/13 4.C.3

Number Bond Addition and Subtraction (5 minutes)

Note: By reviewing the relationship between addition and subtraction

within 10, students will be able to approach today’s problem types with
familiar strategies. In today’s lesson, students will make the connection
that differences for multiples of 10 such as 40 – 30 can be viewed as
4 tens – 3 tens.
Write a number bond for a number between 0 and 10 with a missing
part. Students write an addition and subtraction sentence to find the missing part and solve.
Happy Counting by Tens (2 minutes)

Note: Reviewing Happy Counting by Tens prepares students to recognize the efficiency of counting groups of
10 in today’s lesson.
Happy Count by tens the regular way and Say Ten way from 0 to 120 (see G1-M4-Lesson 1). To really
reinforce place value, try alternating between counting the regular way and the Say Ten way.
Sharon has 3 dimes and 1 penny. Mia has 1 dime and 3

pennies. Whose amount of money has a greater value?
Note: Money is used in this problem as a way to extend place
value concepts and to continue to familiarize students with
coins and their value.
Materials: (T) Chart paper (S) Personal white board with triple NOTES ON
number bond/number sentence template MULTIPLE MEANS OF
REPRESENATION:
Students sit in the meeting area in a semi-circle formation. The use of charts in the next few
T: (Write 2 + 1 on the chart. Call up two volunteers.) lessons will provide students with
Using your magic counting sticks, show us 2 + 1. visual guides to use as resources in the
classroom as they are learning more
S: (Student A shows 2 fingers, Student B shows 1 finger.) about place value. Some students may
T: How many fingers are there? Say the number benefit from having a smaller version
sentence. of the charts in their personal white
boards or folders to refer to as needed.
S: 2 + 1 = 3.
T: (Complete the number sentence on the chart.)

Date: 9/20/13 4.C.4

On their boards, have students write the number sentence, use math drawings to show 2 + 1 = 3, and make a
number bond as you record the information in a chart.
T: Let’s pretend these circles stand for bananas! Say the number
sentence using bananas as the unit.
S: 2 bananas + 1 banana = 3 bananas.
T: (Call for an additional volunteer to join the two
volunteers.) Show us 2 tens + 1 ten using your
magic counting sticks.
S: (Clasp hands to show 2 tens and 1 ten.)
T: (Help the first two students stand closer together to show 20.)
T: (Point to the first two students.) How many tens do we have
here?
S: 2 tens.
T: (Point to the third student.) How many tens do we have here?
S: 1 ten.
T: How many tens are there in all? NOTES ON
S: 3 tens. MULTIPLE MEANS OF
T: Say the number sentence using the unit tens. (If REPRESENATION:
students struggle, say, “Say the number sentence Students demonstrate a true
starting with 2 tens.”) understanding of math concepts when
S: 2 tens + 1 ten = 3 tens. they can apply them in a variety of
situations. Some of your students may
T: (Record the number sentence on the chart.)
not be able to make the connection
Have students write the number sentence, use math drawings, between different number bonds as
and make a number bond as you chart their responses as seen in this lesson. Their path to
shown to the right. abstract thinking may be a little longer
than other’s. Support these students
Repeat the process and record the following suggested sequence with use of manipulatives and plenty of
on the chart: 3 tens + 1 ten, 2 tens + 2 tens, and 1 ten + 3 tens. practice on their personal white
Progress through the units from ones to bananas to tens (e.g., 3 + 1 boards.
= 4 → 3 bananas + 1 banana = 4 bananas → 3 tens + 1 ten = 4 tens).
Have students write the number sentence, make math drawings,
and write the number bond (using the same format from the
teacher-generated chart) for each problem. These charts will be
used later in this lesson.
T: (Point to the first problem on the chart.) Hmmm, how can
knowing 2 + 1 = 3 help us with 2 tens + 1 ten? Turn and talk to
your partner.
MP.7 S: 2 tens + 1 ten = 3 tens is just like 2 + 1 = 3!  It’s 2 things and 1
thing make 3 things. 2 circles and 1 circle make 3 circles. 2
bananas and 1 banana make 3 bananas. 2 tens and 1 ten make
3 tens! Chart 1

Date: 9/20/13 4.C.5

T: The numbers stay the same. The numbers, 2 and 1 and 3, stay the same. But the units change.
T: (Call up three volunteers to show 2 tens + 1
ten = 3 tens again.) Now, unbundle your
magic counting sticks.
S: (Students open up their hands to show 10
fingers.)
T: (Point to the first two students.) What did 2 tens become?
S: 20.
T: (Point to the third student.) What did 1 ten become?
S: 10.
T: What is 20 + 10? Say the number sentence.
S: 20 + 10 = 30.
T: (Write the number sentence on the chart.) We’ll call this the
regular way, when we say 20 + 10 = 30. When we say the place
value units, 2 tens plus 1 ten equals 3 tens, we call this the unit
way.
T: Did we change the number of magic counting sticks when we had
2 tens + 1 ten = 3 tens?
Chart 2
S: No.
Elicit responses to make a number bond as the teacher charts their responses as shown on Chart 1. Have
students fill in the last part of the template on their boards.
Repeat the process by revisiting the previous problems written on the charts and write them again using only
numerals. For example 1 ten + 3 tens = 4 tens is now written as 10 + 30 = 40.
Next, repeat the process following the suggested sequence for solving subtraction problems as shown on
Chart 2: 30 – 10, 30 – 20, 40 – 20, 40 – 40, and 40 – 0. Introduce each expression starting with ones and
bananas, then tens, and finally as numerals (e.g., 2 – 1 = 1 → 2 bananas – 1 banana = 1 banana → 2 tens – 1
ten = 1 ten → 20 – 10 = 10).
T: (Write 4 tens – 3 tens on the chart.) What parts of the number bond can we fill in with these
numbers?
S: 4 tens on top, with 3 tens as one of the parts. (Show the number bond with 1 ten still missing.)
T: What addition sentence can we write to match this number bond? Remember, we can say
“unknown” or “mystery number” for the part we don’t know yet.
S: 3 tens + “the mystery number” = 4 tens. (Record on the chart.)
T: What is the missing part?
S: 1 ten!
T: (Add the missing part to each section.) Say the subtraction sentence we created and the related
addition sentence that we created.
S: 4 tens – 3 tens = 1 ten. 3 tens + 1 ten = 4 tens.
T: Let’s say it the regular way too.

Date: 9/20/13 4.C.6

S: 40 – 30 = 10. 30 + 10 = 40.
Repeat the process as needed to support students’
understanding.

Lesson Objective: Add and subtract tens from a multiple

of 10.
lesson. You may choose to use any combination of the
questions below to lead the discussion.
 Look at Problem 3. What simpler problem can
help you solve this problem?
 How are Problems 4 and 5 related?
 Look at Problem 10. Share your solution with
your partner. Did you solve the problem the
same way? (Answers may vary, e.g., 1 ten – 0
tens = 1 ten, or 1 ten – 1 ten = 0 tens. Accept all
possible interpretations of this picture as long as
the students can support their thinking.)
 Look at Problem 12. Can you find an addition
sentence and a subtraction sentence that are
related?
 Use the arrow way to represent the adding and
subtracting of Problem 12(a), 12(b), and 12(c).
 Explain how you solved today’s Application
Problem.

Date: 9/20/13 4.C.7



Date: 9/20/13 4.C.8

1•4
Name Date
Complete the number bonds and number sentences to match the picture. The first one
is done for you.
1. 2.
20
40
30 10
3 tens + 1 ten = 4 tens ____ ten + ____ ten = ____ tens

30 + 10 = 40
_________________________
3. 4.
____ tens = ____ tens + ____ tens ____ tens = ____ tens + ____ ten
_________________________ _________________________
5. 6.
____ tens - ____ ten = ____ tens ____ tens - ____ tens = ____ tens
_________________________ _________________________

Date: 9/20/13 4.C.9

1•4
7. 8.
____ tens - ____ ten = ____ tens

____ tens + ____ ten = ____ tens _________________________
_________________________
9. 10.
____ tens - ____ tens = ____ ten ____ ten - ____ tens = ____ ten
_________________________ _________________________
11. Fill in the missing numbers. Match the related addition and subtraction facts.
a. 4 tens – 2 tens = _____ 2 tens + 1 ten = 3 tens
b. 40 – 30 = _____ 30 + 10 = 40
c. 30 – 20 = _____ 20 + 20 = 40
12. Fill in the missing numbers.
a. 20 + 20 = _____ b. 30 – 20 = _____ c. 10 + _____ = 40
d. 20 - _____ = 0 e. 40 - _____ = 10 f. _____ + ____ = 30

Date: 9/20/13 4.C.10

1•4
Name Date
Complete the number bonds and number sentences.
1. 2.
20
1 ten + 1 ten = _____ tens _____ tens = _____ tens + _____ ten
20
______ + ______ = ______ ______ = ______ + ______
3. 4.
_____ tens - _____ ten = _____ _____ tens - _____ tens = _____ tens
tens
______ - ______ = ______
______ - ______ = ______

Date: 9/20/13 4.C.11

Name Date
Draw a number bond and complete the number sentences to match the pictures.
1. 2.
____ tens + ____ ten = ____ tens ____ tens = ____ ten + ____ tens
20 + 10 = 30 _____________________
3. 4.
____ tens - ____ ten = ____ ten ____ tens - ____ tens = ____ tens
_____________________ _____________________
5. 6.
____ tens - ____ tens = ____ tens ____ tens + ____ tens = ____ tens
_____________________ _____________________

Date: 9/20/13 4.C.12

Draw quick tens and a number bond to help you solve the number sentences.
7. 8.
10 + 20 = _____ 30 – 10 = _____
9. 10.
20 - 10 = _____ 30 + 10 = _____
Add or subtract.
11. 2 tens + 1 ten = _____ 12. 20 + 20 = _____ 13. 40 – 10 = ____
14. _____= 20 + 10 15. 3 tens – 2 tens = _____ 16. 20 – 10 = _____
17. 10 – 10 = _____ 18. _____ = 30 + 10 19. 40 – 30 = _____

Date: 9/20/13 4.C.13

Number Bond/Number Sentence Template
_____ _____ _____
_____ ten _____ ten _____ ten
______ ______ ______

Date: 9/20/13 4.C.14

Lesson 12
Objective: Add tens to a two-digit number.




 Sprint: Related Addition and Subtraction Within 10 1.NBT.3, 1.OA.6 (10 minutes)
 Add and Subtract Tens Within 40 1.OA.6, 1.NBT.2 (3 minutes)
 Count by Tens with Coins 1.NBT.5 (2 minutes)
Sprint: Related Addition and Subtraction Within 10 (10 minutes)

Materials: (S) Related Addition and Subtraction Within 10 Sprint
Note: This Sprint provides practice with first grade’s core fluency standard, while reviewing the relationship
between addition and subtraction.
Add and Subtract Tens Within 40 (3 minutes)

Note: This fluency activity strengthens students’ understanding of the relationship between addition and
subtraction while providing practice with adding and subtracting multiples of 10.
Write two related addition and subtraction sentences using 0–4 tens in unit form (e.g., 4 tens – 3 tens = ☐
tens and 3 tens + ☐tens = 4 tens). Students convert the number sentences to numeral form and solve (e.g.,
40 – 30 = 10 and 30 + 10 = 40).
Count by Tens with Coins (2 minutes)

Materials: (T) 10 enlarged paper dimes and 6 enlarged paper pennies (template at end of lesson)
Note: Reviewing counting by tens prepares students to add multiples of 10 in today’s lesson.

Date: 9/20/13 4.C.15

Sit in a circle with students. Lay out and remove dimes to direct students to count forward and backward by
tens within 100. Then lay out 6 pennies and add and remove dimes to count by tens, starting at 6 (e.g., 6,
16,26…).
Thomas has a box of paper clips. He used 10 of them to measure the

length of his big book. There are 20 paper clips still in the box. Use the
arrow way to show how many paper clips were in the box at first.
Note: This take apart with start unknown problem allows students to
review the concept of mentally adding or subtracting 10 and using
arrow notation to express their understanding. During the Debrief,
students will share their thinking and notation to explain their
solution. Some students may show their solution as 20 + 10 = 30
while others may solve using 30 – 10 = 20. Accept both solutions.
Materials: (T) 4 ten-sticks, 4 dimes, and 10 pennies from personal math toolkit, double place value charts on
chart paper (S) 4 ten-sticks, 4 dimes, and 10 pennies from personal math toolkit, personal white
board, set of Addition and Subtraction with Cards game cards per pair of students
Note: The cards for the game Addition and Subtraction with Cards are labeled with the letter c to indicate
that these cards correspond with the concepts taught in Topic C. Additional cards will be created in future
topics with their corresponding topic letters.
Have students gather in the meeting area in a semi-circle formation with
their materials.
T: Using your linking cubes, show me 13.
S: (Show 1 ten-stick and 3 ones.)
T: (Point to the chart.) Let’s fill out the place value chart. How many
tens and ones are here?
S: 1 ten 3 ones.
T: (Write +10 above the arrow.) Do what the arrow says
NOTES ON
and show how many cubes we’ll have next.
MULTIPLE MEANS OF
S: (Add a stick of 10.) REPRESENTATION:
T: How many cubes are there now? Students may still struggle with coin
S: 23. values. With more frequent
T: Say the number sentence beginning with the number opportunities to engage with these
of cubes we started with. coins and relate them to tens and
ones, students will have more success
S: 13 + 10 = 23. making the connections.

Date: 9/20/13 4.C.16

T: Use the quick ten drawing to show how we got 23.

S: (Draw.)
T: (Draw after the students have shown their work.) Which digit changed and which digit remained the
same? Turn and talk to your partner and explain your thinking.
S: The digit in the tens place changed because we added 1 ten. We didn’t touch the ones.  1 ten
more than 1 ten is 2 tens. That’s why we have 2 in the tens place. We didn’t add anything to the
ones so the ones digit stays at 3.
T: Write the number bond that shows how we changed 13 to make 23.
S: (Write 23 as the whole with 13 and 10 as the parts.)
Continue the process following the suggested sequence where the unknown is in the sum: 16 + 10, 26 + 10,
15 + 20, and 20 + 18. Next, have students use their ten-sticks and drawings to solve problems in which the
unknown appears as the change or the starting number: 13 + ___ = 23, 16 + ___ = 36, ___ + 10 = 35, and
___ + 20 = 37.
T: Show me 24 using your dimes and pennies.
S: (Show 2 dimes and 4 pennies.)
T: How many tens and ones are in 24?
S: 2 tens 4 ones.
T: (Fill in the place value chart. Write + 10 above the arrow.) Do
what the arrow way says.
S: (Add 1 dime.)
T: How many tens are there now?
S: 3 tens.
T: How many ones are there? NOTES ON
S: 4 ones. MULTIPLE MEANS OF
REPRESENTATION:
T: Let’s use coin drawings to show what you did. (Model
by using circles marked with 10 or 1 to show dimes and Moving forward in small steps is what
some of your students need. You may
pennies.)
need to explicitly connect coin
T: Say the number sentence. drawings to quick ten drawings so that
S: 24 + 10 = 34. students start to see the relationship
between coins and quick ten drawings.
Continue the process following the suggested sequence: 15 + 10, Displaying a chart that shows the quick
15 + 20, 17 + 20, 10 + 17, 20 + 14, 18 + ___ = 28, and 18 + ___ = 38. ten and coin relationship may benefit
Have students play a game called Addition and Subtraction with Cards. some students.
1. Students place the deck of cards face down between them.

2. Each partner flips over one card, then solves the problem and says the number sentence.
3. The partner with the greater total wins the cards. (If the totals are equal, leave the cards until
the next round when one student does have a greater total.)
After the first minute of play, change the rules so that the person with the total that is less wins the cards.
Alternate between the two rules for the remaining time.

Date: 9/20/13 4.C.17


Lesson Objective: Add tens to a two-digit number.

lesson.

 How is solving Problem 7 different from solving
Problem 9?
 With your partner, compare the way you solved
Problem 6. Which number did you draw first?
Why?
 Look at Problem 11 or 12. Which coin is
represented in the tens place? Which coin is
represented in the ones place?
 Look at Problem 11. Explain why the ones digit
didn’t change from the starting number to the
ending number.
 Share your answer to today’s Application
Problem. Explain how you found your answer.

presented in the lesson today and plan more effectively for
future lessons. You may read the questions aloud to the students.

Date: 9/20/13 4.C.18

A Number correct:
Name Date
*Write the missing number. Pay attention to the + and – signs.
1 3 + ☐= 4 16 3 + ☐= 7
2 1 + ☐= 4 17 7=4+☐
3 4-1=☐ 18 7-4=☐
4 4-3=☐ 19 7–3=☐
5 3 + ☐= 5 20 3 + ☐= 8
6 2 + ☐= 5 21 8=5+☐
7 5-2=☐ 22 ☐= 8 - 5
8 5-3=☐ 23 ☐= 8 - 3
9 4 + ☐= 6 24 3 + ☐= 9
10 2 + ☐= 6 25 9=6+☐
11 6-2=☐ 26 ☐= 9 - 6
12 6-4=☐ 27 ☐= 9 - 3
13 6-3=☐ 28 9 - 4 = ☐+ 2
14 3 + ☐= 6 29 ☐+ 3 = 9 - 3
15 6 - ☐= 3 30 ☐- 7 = 8 - 6

Date: 9/20/13 4.C.19

B Number correct:
Name Date
1 4 + ☐= 4 16 2 + ☐= 7
2 0 + ☐= 4 17 7=5+☐
3 4-0=☐ 18 7-5=☐
4 4-4=☐ 19 7–2=☐
5 4 + ☐= 5 20 2 + ☐= 8
6 1 + ☐= 5 21 8=6+☐
7 5-1=☐ 22 ☐= 8 - 6
8 5-4=☐ 23 ☐= 8 - 2
9 5 + ☐= 6 24 2 + ☐= 9
10 1 + ☐= 6 25 9=7+☐
11 6-1=☐ 26 ☐= 9 - 7
12 6-5=☐ 27 ☐= 9 - 2
13 2 + ☐= 6 28 9 - 3 = ☐+ 3
14 4 + ☐= 6 29 ☐+ 2 = 9 - 4
15 6-4=☐ 30 ☐- 6 = 8 - 3

Date: 9/20/13 4.C.20

! !
NYS&COMMON&CORE&MATHEMATICS&CURRICULUM&
! NYS COMMON CORE MATHEMATICS CURRICULUM Lesson&X& X !
Name
Name Date
Date
Fill in the missing numbers to match the picture. Write the matching number bond.
1. 2.
32
22
12 + 20 = _____ 12 20 15 + _____ = _____

2
3. 4.
____ + ____ = ____ ____ + ____ = ____
Draw using quick tens and ones. Complete the number bond and write the sum in the
place value chart and the number sentence.
5. 6.
19 + 10 = ____ 20 + 14 = ____

Date: 9/20/13 4.C.21
!
Lesson&#:& Lesson!Name!EXACTLY!Blank!Worksheet!Template.docx!
Use arrow notation to solve.

7. 8.
+10 +
13 19 39
9. 10.
+20
26 38
Use the dimes and pennies to complete the place value charts and the number
sentences.
11.
+ =
12.
+ =

Date: 9/20/13 4.C.22

Name Date
Complete the number sentences. Use quick tens, the arrow way, or coins to show your
thinking.
28 + 10 = _____
14 + 20 = _____

Date: 9/20/13 4.C.23

Name Date
Fill in the missing numbers to match the picture. Complete the number bond to match.
1. 2.
20 + 13 = ____
17 + ____ = ____
3. 4.
____ + ____ = ____ ____ + ____ = ____

Date: 9/20/13 4.C.24

Draw using quick tens and ones. Complete the number bond and the number sentence.
5. 6.
+ +
1 7 1 0 1 9
=
39
____ + ____ = ____ + ____ = ____
____
Use arrow notation to solve.

7. 8.
+10 +30
19 9
9. 10.
+10 +20
38 31

Date: 9/20/13 4.C.25

Use the dimes and pennies to complete the place value charts.
11.
+ =

Date: 9/20/13 4.C.26


Date: 9/20/13 4.C.27


Date: 9/20/13 4.C.28

G1-M4-Topic C Flashcards
39 + 1 C
30 - 1 C
20 + 20 10 + 30 C C
40 - 20 40 - 30 C C
30 - 20 30 - 10 C C

Date: 9/20/13 4.C.29

40 - 40 30 - 30 C C
10 + 14 15 + 20 C C
12 + 20 27 + 10 C C
29 + 10 20 + 19 C C
20 + 16 12 + 20 C C

Date: 9/20/13 4.C.30

1
GRADE
Topic D
Addition of Tens or Ones to a Two-
Digit Number
1.NBT.4
Focus Standard: 1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding
a two-digit number and a multiple of 10, using concrete models or drawings and
G2–M4 Addition and Subtraction Within 200 with Word Problems to 100
Topic D begins with students applying the Module 2 strategies of counting on and
making ten to larger numbers, this time making a ten that is built on a structure of
other tens. In Lesson 13, students use linking cubes as a concrete representation of the
numbers, write a matching number sentence, and write the total in a place value chart.
As they add cubes, students will see that sometimes you make a new ten, for example,
33 + 7 = 40, or 4 tens.
In Lesson 14, students use arrow notation to get to the next ten and then add the
remaining amount when adding across ten. For example, when adding 28 + 6, students
recognize that they started with 2 tens 8 ones and after adding 6, had 3 tens 4 ones.
Students also use the bond notation from Module 2 to represent how they are
breaking apart the second addend to make the ten (1.NBT.4).
Lesson 15 provides the chance to notice the ways smaller addition problems can help
with larger ones. Students add 8 + 4, 18 + 4, and 28 + 4 and notice that 8 + 4 is
embedded in all three problems, which connects to their earlier work in Topic C.
Lessons 16, 17, and 18 focus on adding ones with ones or adding tens with tens.
During Lesson 16, students recognize single-digit addition facts as they solve
15 + 2, 25 + 2, and 35 + 2. When adding 33 + 4, students see that they are
Topic D: Addition of Tens or Ones to a Two-Digit Number

Date: 9/20/13 4.D.1
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported.License.
NYS COMMON CORE MATHEMATICS CURRICULUM Topic D
adding 4 ones to 3 ones, while the tens remain unchanged, to make 3 tens 7
ones or 37. When adding 12 + 20, students see that they are adding 2 tens to 1
ten to make 3 tens 2 ones or 32. In both cases, one unit remains unchanged.
Students work at a more abstract level by using dimes and pennies to model
each addend. For instance, students model 14 cents using 1 dime and 4
pennies, and add 2 additional dimes or 2 additional pennies.
In Lesson 17, students continue working with addition of like units, and making
ten as a strategy for addition. They use quick tens and number bonds as
methods for representing their work.
During Lesson 18, students share and critique strategies for adding two-digit
numbers. They bring to bear all of the strategies used thus far in the module,
Adding ones with ones
including arrow notation, quick tens, and number bonds. Projecting two correct
work samples, students compare for clarity, discussing questions such as: Which
drawing best shows the tens? Which drawings best help you not count all? Which number sentence is
easiest to relate to the drawing? What is a compliment you would like to give [the student]? What is a way
that [the student] might improve their work? How are [Student A]'s methods different from or the same as
your partner’s?
A Teaching Sequence Towards Mastery of Addition of Tens or Ones to a Two-Digit Number

Objective 1: Use counting on and the make ten strategy when adding across a ten.
(Lessons 13–14)
Objective 2: Use single-digit sums to support solutions for analogous sums to 40.
(Lesson 15)
Objective 3: Add ones and ones or tens and tens.

(Lessons 16–17)
Objective 4: Share and critique peer strategies for adding two-digit numbers.
(Lesson 18)
Topic D: Addition of Tens or Ones to a Two-Digit Number

Date: 9/20/13 4.D.2
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported.License.
Lesson 13
Objective: Use counting on and the make ten strategy when adding across
a ten.
 Application Problems (5 minutes)

 Fluency Practice (12 minutes)
 Concept Development (33 minutes)
 Student Debrief (10 minutes)
Application Problems (5 minutes)
Use linking cubes as you read, draw, and write (RDW) to solve
the problems.
a. Emi had a linking cube train with 4 blue cubes and 2
red cubes. How many cubes were in her train?
b. Emi made another train with 6 yellow cubes and some
green cubes. The train was made of 9 linking cubes.
How many green cubes did she use?
c. Emi wants to make her train of 9 linking cubes into a
train of 15 cubes. How many cubes does Emi need?
Note: Throughout Topic D, the Application Problem comes
before the Fluency Practice. Each day, there are three
problems, sequenced from simple to complex. Limit students’
work time to five minutes. The problems are designed to
pinpoint student strengths and challenges prior to Topic E,
which focuses on word problems.
Take note of students who typically struggle to solve the
Application Problem but who are successful with today's
problems. They may need support moving from concrete to
pictorial problem solving strategies. Also notice which
students struggle when the position of the unknown changes.
Students should keep all Application Problems from Topic D for use during the Debriefs in Topic E.
Lesson 13: Use counting on and the make ten strategy when adding across a
ten. 4.D.3
Date: 9/20/13
 Adding and Subtracting with Cards 1.NBT.4 (4 minutes)

 Race and Roll Addition 1.OA.6 (3 minutes)
Addition and Subtraction with Cards (4 minutes)

Materials: (S) Addition and Subtraction with Cards game cards (from G1─M4─Lesson 12)
Note: This fluency game was played during the previous lesson’s Concept Development. It reviews adding
and subtracting multiples of 10 within 40.
Follow the directions in G1─M4─Lesson 12’s Concept Development.
Race and Roll Addition (3 minutes)

Materials: (S) 1 die for each set of partners
Note: This fluency activity reviews the grade level standard of adding within 20. Circulate as students play
and informally assess which of your students are using the Level 2 strategy of counting on and which are
using the Level 3 strategy of converting to an easier problem (e.g., mentally decomposing 13 and using 3 + 4
to solve 13 + 4).
All students start at 0. Partners take turns rolling a die, saying a number sentence, and adding the number
rolled to the total. For example, Partner A rolls 6 and says, “0 + 6 = 6,” then Partner B rolls 3 and says, “6 + 3
= 9.” They continue rapidly rolling and saying number sentences until they get to 20, without going over.
Partners stand when they reach 20. For example, if the partners are at 18 and roll 5, they take turns rolling
until one of them rolls a 2 or rolls 1 twice, then both stand.

Materials: (S) Core Addition Fluency Review from G1─M4─Lesson 2
graders. Differentiated Practice Sets can be found in G1–M4–Lesson 23, which may be helpful in supporting
students towards these goals.
finishers to practice on the back of their papers. When time runs out, read the answers aloud so students
can correct their work and celebrate improvement.
ten. 4.D.4
Date: 9/20/13

NOTES ON
Materials: (T) 4 ten-sticks from the personal math toolkit, MULTIPLE MEANS FOR
chart paper (S) 4 ten-sticks from the personal ACTION AND
math toolkit, personal white board EXPRESSION:
Students love listening and learning
Have students sit in a meeting area in a semi-circle formation from music. Find a song on iTunes
with their personal math toolkits. about place value. One suggestion is
“The Place Value Song” by Math Fiesta.
T: (Show 13 as 1 ten and 3 ones using linking cubes.)
How many linking cubes are there?
S: 13 linking cubes.
T: (Add 4 more linking cubes of a different color.) How many linking cubes are there now? Turn and
talk to you partner about how you know.
S: There are 17 cubes. I started with 13 and counted on. Thirteeeen, 14, 15, 16, 17.  I added 3
ones and 4 ones. That makes 7 ones. 1 ten and 7 ones is 17.  4 more than 13 is 17.
T: Nice thinking! Let’s try counting on to find our solution.
S: (Point as students count.) Thirteeeen, 14, 15, 16, 17.
T: Now add the ones first. How many are in the ones place in 13?
S: 3 ones.
T: (Point to 3 cubes.) 3 ones and 4 ones is?
S: 7 ones.
T: (Snap the ones cubes together to make 7. Write 7 in the ones
place in the place value chart.) How many tens do we have?
S: 1 ten.
T: (Write 1 in the tens place in the place value chart.)
T: 1 ten 7 ones is?
S: 17.
Note: Since there were no changes in tens, another option is to write 1 in the tens place first, then 7 in the
ones place.
T: What are some different addition sentences we could use to put
together 13 cubes and 4 cubes.
S: 13 + 4 = 17.  10 + 7 = 17.  10 + 3 + 4 = 17.
T: Use quick tens to draw the number of linking cubes we started
with.
S/T: (Draw 1 quick ten and 3 dots for 3 ones.)
T: Draw to show the number of cubes we added to 13 using X’s in 5-
group column formation.
S/T: (Draw 4 X’s above the 3 circles.)
ten. 4.D.5
Date: 9/20/13
T: Say the number sentence using your drawing.

S: 13 + 4 = 17.
T: Let’s use a number bond. (Write 13 + 4.) 13 cubes is 1 ten and 3
ones. (Break 13 apart into 10 and 3.) We next added 3 ones and 4
ones. Use this number bond to solve the problem on your board.
Turn and talk to your partner about what you did.
S: First I added 3 and 4 and got 7. Then I added 10 and 7 and got 17.
T: Let’s record how we added as two number sentences. (Write 3 + 4
= 7 and 10 + 7 = 17.) Let’s solve another problem. Use your cubes
to show 13.
S: (Show 1 ten-stick and 3 individual cubes in a 5-group column.)
T: Using a different color, add 7 more.
S: (Add 7 more cubes using a different color.)
T: How many cubes do you have now? Show what you did to your
partner and talk about how you got the answer.
S: I put the 7 cubes next to 13 cubes. I know 3 and 7 is 10. And 10
and 10 is 20.  I stacked 7 cubes on top of the other 3. It made
another ten-stick!  Now I see 2 ten-sticks. That’s 20!
T: (Model with cubes.) You are right! 3 ones and 7 ones
is?
S: 10 ones.
T: 10 ones is the same as?
S: 1 ten.
T: How many tens are there now? (Hold up each ten.)
S: 2 tens.
T: Where does the digit 2 go in our place value chart?
S: In the tens place.
NOTES ON
T: (Write 2 in the tens place.) Since 3 ones and 7 ones
make 1 ten, which we recorded in the tens place (point MULTIPLE MEANS OF
to place value chart), how many ones do we have now? REPRESENTATION:
Often students learn math concepts in
S: 0.
an isolated fashion; although they may
T: So we write 0 in the? be able to use them with familiar
S: Ones place. problems, they do not see how to
transfer their application to new
T: (Write 0 in the ones place.) Say the number
situations. Be sure to incorporate
sentence.
math at other times in the students’
S: 13 + 7 = 20. day.
T: Draw quick tens to show the addition. Explain your
drawing to your partner.
S: I framed my 7 crosses and 3 circles to show that I made a ten.  I drew a long line through my 10
ones to make it look like a quick ten.
ten. 4.D.6
Date: 9/20/13
T: I love the idea of drawing a line through the new ten to make it look
more like a quick ten! (Model.)
T: Make a number bond to show how you added the ones together.
S: (Write 13 + 7 = 20 by taking apart 13 into 10 and 3.)
T: How does making the number bond help you solve the problem?
S: I can see easily that I can add 3 and 7. That’s 10. Then I add 10 and 10
and get 20.
T: (Write two number sentences.) Great! Now let’s try some more!
Repeat the process using the following sequence: 17 + 2, 18 + 2, 28 + 2, 23 + 6,
33 + 6, 23 + 7, and 33 + 7. As soon as possible, write the addition expression on
the board and have students use quick ten math drawings and number bonds to
solve rather than working with linking cubes. Some students may count on when
adding 1 and 2. Counting on becomes less efficient as the second addend
increases. When the second addend is larger than 3, encourage students to use
Level 3 strategies such as thinking of doubles or using the make ten strategy.

Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For
some classes, it may be appropriate to modify the assignment by specifying which problems they work on
first.
Lesson Objective: Use counting on and the make ten

strategy when adding across a ten.
Set. They should check work by comparing answers with
a partner before going over answers as a class. Look for
lesson.
 How can solving Problem 1 help you solve
Problem 3?
 In Problem 9, explain why there is a 0 in the ones place in the answer when there are some ones in
both addends.
ten. 4.D.7
Date: 9/20/13
 For Problem 10, a student said he has 2 tens and

10 ones. Is he right? Explain your thinking.
 What strategies did we use today to solve
addition problems?
 How does your fluency work with the sums to ten
help you in today’s lesson?

the students.
ten. 4.D.8
Date: 9/20/13
Name Date
Use the pictures to complete the place value chart and number sentence. For problems
5 and 6, make a quick ten drawing to help you solve.
1. 2.
22 + 6 = _____ _____ + 3 = _____

3. 4.



 





12 + _____ = _____ _____ + _____ = _____

5. 6.
24 + 6 = _____ 24 + 3 = _____
ten. 4.D.9
Date: 9/20/13
Draw quick tens, ones, and number bonds to solve. Complete the place value chart.
7. 8.
21 + 9 = _____ 21 + 7 = _____









9. 10.
13 + 7 = _____ 26 + 4 = _____
11. 12.
32 + 3 = _____ 38 + 2 = _____
ten. 4.D.10
Date: 9/20/13
Name Date
Fill in the place value chart and write a number sentence to match the picture.
1. 2.




_____ + _____ = _____ + _____ =

_____ _____
3. 4.
33 + 6 = _____ 23 + 7 = _____
ten. 4.D.11
Date: 9/20/13
Name Date
Use quick tens and ones to complete the place value chart and number sentence.
1. 2.




21 + 4 = _____ 21 + 8 = _____
3. 4.
25 + 4 = _____ 25 + 5 = _____
5. 6.
33 + 3 = _____ 33 + 7 = _____
ten. 4.D.12
Date: 9/20/13
7. 8.
26 + 2 = _____ 36 + 3 = _____
9. 10.
26 + 4 = _____ 24 + 6 = _____
Solve. You may draw quick tens and ones or number bonds to help.
11. a. 22 + 7 = _____ b. 22 + 8 = _____ c. 32 + 8 = _____
ten. 4.D.13
Date: 9/20/13
Lesson 14
Objective: Use counting on and the make ten strategy when adding across
a ten.

Use linking cubes and the RDW process to solve one or more of the problems.
a. Emi had a linking cube train of 7 cubes. She added 4 cubes to
the train. How many cubes are in her linking cube train?
b. Emi made another train of linking cubes. She started with 7
cubes and added some more cubes until her train was 9 cubes
long. How many cubes did Emi add?
c. Emi made one more train of linking cubes. It was made of 8
linking cubes. She took some cubes off and then her train was
4 linking cubes long. How many cubes to Emi take off?
Note: Each problem is successively more challenging. Remind children
that they are not expected to complete all three, but instead to do
their best during the five-minute time frame.
Notice which students are successful with the first problem, where the
unknown number is the result, or total, but who struggle with later
problems where the unknown number is in a different position. Keep
track of this analysis in preparation for Topic E instruction, where you
may want to select or emphasize particular problem types.
The similarity to yesterday’s problems is intended to promote
perseverance and confidence for students who may be struggling with
Application Problems at this point in the year. For students who are
successful with all problems, challenge them to find the total of all the cubes used, ask how many more cubes
the first train has than the last, or encourage them to write their own additional linking cube train story.
ten. 4.D.14
Date: 9/20/13
 Addition Within 40: Counting On 1.NBT.4 (3 minutes)

 Get to 10 1.NBT.4 (3 minutes)
 Make Ten Addition with Partners 1.OA.6 (6 minutes)
Addition Within 40: Counting On (3 minutes)

Note: This fluency activity reviews yesterday’s lesson. Some students may count on, as they learned to do
yesterday. Others may already make the connection between the single-digit addition facts and their
analogous addition sentences. As always, pause to provide thinking time.
T: 5 + 2 is? (Snap.) Give me the number sentence.
S: 5 + 2 = 7.
T: 10 + 7 is? (Snap.)
S: 10 + 7 = 17.
T: 15 + 2 is? (Snap.)
S: 15 + 2 = 17.
Continue with 25 + 2 and 35 + 2. Repeat, beginning with other single-digit addition facts with sums to 10.
Make sure one addend is conducive to counting on (e.g., 1, 2, or 3).
Get to 10 (3 minutes)
Materials: (T) Rekenrek
Note: In this fluency activity, students apply their knowledge of partners to ten to find analogous partners to
20, 30, and 40, which will prepare them for today’s lesson.
For the first minute, say numbers from 0–10. Students say partners to ten on your snap. Then take out the
Rekenrek.
T: (Show 9.) Say the number.
S: 9.
T: Give me the number sentence to make ten.
S: 9 + 1 = 10
T: (Move 1 bead to make 10. Show 19.)
T: Say the number.
S: 19.
T: Give me the number sentence to make 20.
S: 19 + 1 = 20
Suggested sequence: 29, 39; 5, 15, 25, 35; 8, 18, 28, 38; 7, 17, 27, 37; etc.
ten. 4.D.15
Date: 9/20/13
Make Ten Addition with Partners (6 minutes)

Note: This fluency activity reviews how to use the Level 3 strategy of making ten to add two single-digit
numbers. Students will learn how to apply this strategy when adding a one-digit number to a two-digit
number in today’s lesson.
 Assign partners of equal ability.
 Partners choose an addend from 1 to 10 for each NOTES ON
other. MULTIPLE MEANS OF
 On their personal boards, students add their number ENGAGEMENT:
to 9, 8, and 7. Remind students to write the two Careful selection of pairs for
addition sentences they learned in Module 2. collaborative work is essential to
achieving expected outcomes. Some
lessons lend themselves to groupings
of students with similar skill sets while
others work better when students are
heterogeneously grouped. Some
students would benefit from the
opportunity to work independently and
share with the teacher or another pair
after they have completed the task.
 Partners then exchange boards and check each other’s
work.
Materials: (T) 4 ten-sticks, chart paper (S) 4 ten-sticks from the math toolkit, personal white board
Note: During today’s lesson we will be using the make ten strategy which
requires students to break apart the single-digit addend, as in Module 2,
whereas yesterday they broke apart the double-digit addend. This is part of
how students gain confidence in flexibly using number bonds.
Have students sit in the meeting area in a semi-circle formation with their
materials.
T: (Write 19 + 3 on the chart.) How many cubes do I start with?
S: 19 cubes.  1 ten-stick and 9 ones.  You also need 3 ones.
T: (Show 19 + 3 with cubes.) Turn and talk to your partner about how
you can solve 19 + 3.
While students discuss, circulate and listen for sharing of both counting on
and make ten strategies.
T: (Ask student volunteers to come and share their strategies.)
ten. 4.D.16
Date: 9/20/13
S: I can count on. Nineteen, 20, 21, 22.  You can make another ten. 9 plus 1 more makes 10. 2 tens
and then you still have 2 ones left.  19 and 1 is 20. 20 + 2 is 22.
T: Just like we did yesterday, we can make a new ten-stick! How many more ones to make 19 get to
the next ten, 20?
S: 1.
T: From where can we get the 1?
NOTES ON
S: From the 3. MULTIPLE MEANS OF
T: (Hold up 3 cubes. Break off 1 cube and complete a ten- ACTION AND
stick.) How many tens are there now? EXPRESSION:
S: 2 tens. Giving students an opportunity to share
T: How many ones are left? their thinking allows students to
evaluate their process and practice.
S: 2 ones.
English language learners also benefit
T: What is 2 tens and 2 ones? from hearing other students explain
S: 22. their thinking.
T: 19 + 3 is?
S: 22.
T: Excellent work! Let’s try some more!
Have students collaborate with their partners and combine their linking cubes to find the
sum for each addition expression following the suggested sequence: 18 + 4, 28 + 4, 26 +
5, 26 + 7, and 15 + 8. When appropriate, have students also draw quick tens to show how
they solved the problems. (See image to the right.)
T: (Write 19 + 3 on the board again and represent the expression using linking
cubes.) Let’s record what we did to solve 19 + 3 using a number bond. Can we
make a ten?
S: Yes.
T: How many more do we need to get to the next ten from 19? Where can
we get that amount?
S: Take 1 from the 3.
T: (Ask a student volunteer to take 1 from 3 using the linking cubes.) Look at
what we did with 3 in order to make the next ten. We broke 3 into…
S: 1 and 2.
T: (Make a number bond as shown to the right.) What is
19 and 1?
S: 20.
T: (Write 19 + 1 = 20.) 20 and 2 is…?
S: 22.
T: (Write 20 + 2 = 22.) Let’s use the arrow way to record what we did.
(Write 19 and model the arrow way as you talk through the notation.)
We started with 19, then added 1 to make the next ten, which is 20.
Then we had 2 left over. So we added 2 to 20 to get to 22.
ten. 4.D.17
Date: 9/20/13
T: So 19 + 3 =?
S: 22.
Repeat the process following the suggested sequence:
29 + 3, 19 + 5, 18 + 3, 17 + 3 (use 1 arrow), 26 + 3 (use 1
arrow), 26 + 7, and 28 + 7.
When appropriate, have students choose and use only
number bonds with two number sentences or the arrow
MP.5 way to solve instead of using the linking cubes. When
sharing solutions, students should show their notations
and explain their choice.

Lesson Objective: Use counting on and the make ten

strategy when adding across a ten.
 How could Problem 8 help you solve Problem 9?
What smaller problem is in both Problems 8 and
9?
 With your partner, compare your work for
Problem 9. Which method did you use to solve
and why? How are the different methods of using
quick ten drawings, the number bond, and the
arrow way similar?
 How did we record the ways we added today?
ten. 4.D.18
Date: 9/20/13
 (Post the chart using a number bond and the arrow way to solve 19 + 3.) Do you notice any
similarities in our number bond and the arrow way?
 How did your fluency work in Get to Ten help you during today’s lesson?

ten. 4.D.19
Date: 9/20/13
Name Date
Use the pictures or draw quick tens and ones. Complete the number sentence and place
value chart.
1. 2. 3.
18 + 1 = _____ 18 + 2 = _____ 18 + 5 = _____
 

 



4. 5. 6.
29 + 1 = _____ 29 + 3 = _____ 29 + 6 = _____
7. 8. 9.
16 + 4 = _____ 16 + 6 = _____ 26 + 6 = _____
ten. 4.D.20
Date: 9/20/13
Make a number bond to solve. Show your thinking with number sentences or the arrow
way. Complete the place value chart.
10. 11.
17 + 2 = _____ 17 + 5 = _____
12. 13.
25 + 4 = _____ 25 + 6 = _____
14. 15.
34 + 4 = _____ 34 + 8 = _____
ten. 4.D.21
Date: 9/20/13
Name Date
Draw quick tens and ones. Complete number sentence and place value chart.
1. 2. 3.
17 + 1 = _____ 17 + 3 = _____ 17 + 6 = _____
4. 5.
32 + 7 = _____ 26 + 9 = _____
ten. 4.D.22
Date: 9/20/13
Name Date
Use the pictures or draw quick tens and ones. Complete the number sentence and place
value chart.
1. 2. 3.
15 + 3 = _____ 15 + 5 = _____ 15 + 6 = _____


 

 


 



4. 5. 6.
28 + 2 = _____ 28 + 4 = _____ 28 + 7 = _____
7. 8. 9.
17 + 3 = _____ 17 + 7 = _____ 27 + 7 = _____
ten. 4.D.23
Date: 9/20/13
6. 7.
13 + 6 = _____ 13 + 7 = _____
8. 9.
25 + 5 = _____ 25 + 8 = _____
10. 11.
24 + 8 = _____ 23 + 9 = _____
ten. 4.D.24
Date: 9/20/13
Lesson 15
Objective: Use single-digit sums to support solutions for analogous sums to
40.

Today, students should focus on pictorial representations. They

should solve without using linking cubes. They read, draw, and write
(RDW) to solve one or more of the problems.
a. Emi had a linking cube train of 6 cubes. She added 3 cubes to
the train. How many cubes are in her linking cube train?
b. Emi made another train of linking cubes. She started with 7
cubes and added some more cubes until her train was 12
cubes long. How many cubes did Emi add?
c. Emi made one more train of linking cubes. It was made of 12
linking cubes. She took some cubes off and her train became
4 linking cubes long. How many cubes did Emi take off?
Note: Continue to notice students’ strengths and challenges with
each problem type presented. Encourage students who seem to
struggle when the linking cubes have been removed to visualize,
imagine, or draw the cubes as shown in the student work to the right.

 Make Ten Addition with Partners 1.OA.6 (6 minutes)
 Add Tens 1.NBT.4 (4 minutes)
Lesson 15: Use single-digit sums to support solutions for analogous sums to 40.
Date: 9/20/13 4.D.25


Note: This fluency activity builds a student’s ability to add and subtract within
10 while reinforcing the relationship between addition and subtraction.
Write a number bond for a number between 0 and 10, with a missing part or
whole. Students write an addition and a subtraction sentence with a box for
the missing number in each equation. They then solve for the missing number.
Make Ten Addition with Partners (6 minutes)

Note: This fluency activity reviews how to use the Level 3 strategy of making ten to add two single-digit
numbers. Reviewing the make ten strategy will prepare students for today’s lesson, in which they
systematically connect these problem types to analogous problems within 40 (e.g., students will make ten to
solve 9 + 5 and then apply the same strategy to solve 19 + 5 and 29 + 5).
Repeat the activity from G1─M4─Lesson 14.
Add Tens (4 minutes)

Note: This fluency activity reviews adding multiples of 10, which will help prepare students for today’s lesson.
T: (Flash 3 on fingers. Pause.) Add ten. The total is?
S: 13.
T: (Flash 3 again.) Add 2 tens. The total is?
S: 23.
Continue flashing numbers from 0 to 10 and instructing students to add multiples of 10. After a minute, say
the multiples of 10 the regular way (e.g., 20 instead of 2 tens). For the last minute, say teen numbers and
instruct students to add 10 or 2 tens or 20.
Materials: (T) 5 ten-sticks (e.g., 4 red and 1 yellow), chart paper (S) 4 ten-sticks from the math toolkit,
personal white board
Students gather in the meeting area with their materials.

T: (Show 4 red and 2 yellow cubes in a stick.) What is the addition sentence that
matches the cubes?
S: 4 + 2 = 6.
T: (Record on the chart. Place a red ten-stick to the left of 4 and 2 cubes, showing 14 +
2.) How many linking cubes are there now?
Date: 9/20/13 4.D.26

S: 16.
T: What is the number sentence to add these red and NOTES ON
yellow cubes? MULTIPLE MEANS OF
S: 14 + 2 = 16. REPRESENTATION:
Provide opportunities for students to
T: (Record on the chart. Add another red ten-stick,
practice their math facts within 10
showing 24 + 2.) How many linking cubes are there
throughout the day. Students
now? Say the number sentence. (Give wait time.) struggling with mastery of the grade
S: 24 + 2 = 26. level fluency goal benefit from focused
T: (Record on the chart.) What do you think I’ll do next? extra practice. Elicit from them which
Turn and talk to your partner. facts they find harder in order to
determine that focus. Keep parents
S: You’ll add another ten-stick.  The next problem will informed of these details and offer
be 34 + 2. effective ways they can support the
T: You’re right. (Add another red ten-stick, showing student.
34 + 2.) How many linking cubes are there now? Say
the number sentence. (Give wait time.)
S: 34 + 2 = 36.
T: (Record on the chart.) Many of you got the answer to
these questions very quickly. Why? Turn and talk to
you partner.
S: The digit in the tens place in the first addend keeps
going up. The same thing is happening to the answers,
too.  This reminds me of when we added only tens
to a number. The ones digit stayed the same but the
tens digit changed.  We’re always adding 4 and 2. In
every problem, the tens are changing but the ones are
not because we are not touching the ones.
T: Great observations! Let’s try another problem.
T: (Write and show 9 + 5 with 9 red and 5 yellow linking
cubes.) Talk to your partner about how you can solve
9 + 5.
S: I can count every cube.  I can count on from 9.  I
can make ten first. 10 + 4 = 14.
T: (Call up a volunteer to show 10 and 4 with linking cubes
as shown to the right. Record the answer. )
T: (Add another red ten-stick and show 19 + 5.) What is
the new addition problem starting with 19?
S: 19 + 5.
T: (Record on the chart.) Turn and talk to you partner
about how you can figure out how many cubes there
are now.
Date: 9/20/13 4.D.27

S: I can see the cubes. There are 2 tens and 4 ones. That’s 24.  I knew that 9 + 5 was 14. That’s the
simpler problem. We added 10 more to 14. That’s 24.
T: The strategy of using what we already know is a very important math strategy for solving problems.
(Cover 1 ten-stick with a hand.) We know that 9 + 5 = 14. 19 + 5 is just 10 more than 9 + 5. (Reveal
the ten-stick.) 10 more than 14 is?
S: 24.
T: When you show 19 as tens and ones, you can easily see the simpler problem, 9 + 5. (Write the
number bond for 19 as 10 and 9.) 9 + 5 is?
S: 14.
T: (Create a chart like the one shown to the right. 9 + 5 = 14.) 10 more
than 14 is?
S: 24.
MP.7 T: (Write 14 + 10 = 24. Add another red ten-stick and show 29 + 5.)
Write down the new addition problem on your board starting with 29.
S: (Write 29 + 5.)
T: (Record on the chart.) Break apart 29 into tens and ones. What is
the simpler problem?
S: (Make number bond with 29.) 9 + 5.
T: 9 + 5 is?
S: 14.
T: 20 more than 14 is?
S: 34.
T: 29 + 5 is?
S: 34.
T: Using your number bond, let’s write the two number sentences that helped us solve this problem.
T/S: Write 9 + 5 = 14, 14 + 20 = 34.
T: (Create a chart as shown to the right.) Turn and talk to your partner
about the patterns you notice.
S: The ones stayed the same. But the tens changed because we kept
adding more tens.  Every time we add 10 more, the answer also
shows 10 more.  9 + 5 = 14 is always the simpler problem. We
solved 9 + 5 which is 14 first. When we added 1 more ten, then the
answer went up by 1 more ten.
Repeat the process and have student pairs work with their
linking cubes and record their work using the following NOTES ON
sequence: MULTIPLE MEANS FOR
 5 + 4, 15 + 4, 25 + 4, 35 + 4 ENGAGEMENT:
Chose just right numbers in order to
 4 + 6, 14 + 6, 24 + 6, 34 + 6 provide ample opportunities for
 2 + 7, 12 + 7, 22 + 7, 32 + 7 students to experience success in order
to build confidence in their math skills.
Date: 9/20/13 4.D.28

 9 + 3, 19 + 3, 29 + 3
 8 + 6, 18 + 6, 28 + 6
 8 + 8, 18 + 8, 28 + 8
 5 + 7, 5 + 17, 5 + 27
Next, follow the suggested sequence and have students
identify the simpler problem before solving the given
problem: 17 + 2, 19 + 2, 28 + 2, 28 + 4, 27 + 6, and 25 + 7.

classes, it may be appropriate to modify the assignment
by specifying which problems they work on first.
Lesson Objective: Use single-digit sums to support

solutions for analogous sums to 40.
lesson.
 How did looking for patterns help you solve the
problems on the second page of your Problem
Set?
 Look at Problems 8(a–d) and 8(i–k). In (a–d), the
tens in the answers are the same as the tens in
the first addend of each problem, but in (i–k), the
tens in the answers do not match the tens in the
first addends. Explain why this is so.
Date: 9/20/13 4.D.29

 You solved 36 + 2 easily in Problem 8(d). How can this problem help you solve 36 + 3? How can
knowing 36 + 3 then help us solve 26 + 3?
 What new strategy did you learn to solve addition problems when one addend is a two-digit
number?
 Look at the Application Problems and the answers from the Problem Set. Find the related addition
sentence that could have helped you solve the subtraction problem.

Date: 9/20/13 4.D.30

Name Date
Solve the problems.
1.
5 + 3 = _____
2.
15 + 3 = _____
3.
25 + 3 = _____
4.
35 + 3 = _____
5.
8 + 4 = _____
6.
18 + 4 = _____
7.
28 + 4 = _____
Date: 9/20/13 4.D.31

8. Solve the problems.
a. b. c. d.
6 + 2 = ____ 16 + 2 = ____ 26 + 2 = ____ 36 + 2 = ____
e. f. g. h.
6 + 4 = ____ 16 + 4 = ____ 26 + 4 = ____ 36 + 4 = ____
i. j. k.
9 + 2 = ____ 19 + 2 = ____ 29 + 2 = ____
l. m. n.
8 + 6 = ____ 18 + 6 = ____ 28 + 6 = ____
Solve the problems. Show the 1-digit addition sentence that helped you solve.
9. 23 + 6 = _____ ___________________________
10. 27 + 6 = _____ ___________________________
Date: 9/20/13 4.D.32

Name Date
1. Solve the problems.
a.
7 + 5 = ____
b.
17 + 5 = ____
c.
27 + 5 = ____
Solve the problems.
2. a. 5 + 3 = _____ 3. a. 5 + 8 = _____
b. 15 + 3 = _____ b. 15 + 8 = ____
c. 25 + 3 = _____ c. 25 + 8 = ____
d. 35 + 3 = _____
Date: 9/20/13 4.D.33

Name Date
Solve the problems.
1.
5 + 4 = ____
2.
15 + 4 = ____
3.
25 + 4 = ____
4.
35 + 4 = ____
5.
8 + 4 = ____
6.
18 + 4 = ____
7.
28 + 4 = ____
Date: 9/20/13 4.D.34

Use the first number sentence in each set to help you solve the other problems.
8. 9.
a. 5 + 2 = ____ a. 5 + 5 = ____
b. 15 + 2 = ____ b. 15 + 5 = ____
c. 25 + 2 = ____ c. 25 + 5 = ____
d. 35 + 2 = ____ d. 35 + 5 = ____
10. 11.
a. 2 + 7 = ____ a. 7 + 4 = ____
b. 12 + 7 = ____ b. 17 + 4 = ____
c. 22 + 7 = ____ c. 27 + 4 = ____
12. 13.
a. 8 + 7 = ____ a. 3 + 9 = ____
b. 18 + 7 = ____ b. 13 + 9 = ____
c. 28 + 7 = ____ c. 23 + 9 = ____
Solve the problems. Show the 1-digit addition sentence that helped you solve.
14. 24 + 5 = _____ ___________________________
15. 24 + 7 = _____ ___________________________
Date: 9/20/13 4.D.35

Lesson 16
Objective: Add ones and ones or tens and tens.

Use the RDW process to solve one or more of the problems, without
using linking cubes.
a. Emi had a linking cube train with 14 blue cubes and 2 red cubes.
How many cubes were in her train?
b. Emi made another train with 16 yellow cubes and some green
cubes. The train was made of 19 linking cubes. How many green
cubes did she use?
c. Emi wants to make her train of 8 linking cubes into a train of 17
cubes. How many cubes does Emi need?
Note: Today, students use larger numbers to solve problems that are
similar to the Application Problems used over the past few days. Notice
children who were successful with the earlier set but struggled with the
problem today. These students may have difficulty envisioning the
relationships between the larger quantities. Encourage these students to
change from empty circles to filled-in circles at the ten, as shown in the
image, to help them break down and visualize the larger numbers.
 Analogous Addition Sentences 1.NBT.4 (5 minutes)

Lesson 16: Add ones and ones or tens and tens.

Date: 9/20/13 4.D.36
Analogous Addition Sentences (5 minutes)

Materials: (S) Personal white boards, dice
Note: This fluency activity reviews yesterday’s lesson. Some students may STEP 1
wish to show their work with number bonds, while others may choose to Partner A Partner B
work mentally. 4 3
Students work in partners. For struggling students, consider replacing the 6 14 13
on the die with a 0 so the sums do not cross ten. 24 23
34 33
 Step 1: Students roll a die and write the number rolled. They then
make a list, adding 1 ten to their number on each new line up to 3
tens. (See diagram to the right.) STEP 2
 Step 2: Students write equations, adding the number on their Partner A Partner B
partner’s die to each line. 4+3=7 3+4=7
 Partners exchange boards and check each other’s work. 14 + 3 = 17 13 + 4 = 17
24 + 3 = 27 23 + 4 = 27
As students work, make sure to circulate and monitor students’
34 + 3 = 37 33 + 4 = 37
understanding of recently introduced concepts.

Materials: (T/S) Personal white boards
Note: This activity reviews place value, which prepares students to add ones to ones or tens to tens in today’s
lesson. As always, pause to give students enough time to think and write before snapping.
Write a number on your personal board, but do not show students.
T: The digit in the tens place is 3. The digit in the ones place is 1. What’s my number? (Snap.)
S: 31.
S: 30.
S: 1.
Repeat sequence with a ones digit of 3 and a tens digit of 3.
T: The digit in the tens place is 1 more than 2. The digit in the ones place is equal to 7 – 4. What’s my
number? (Snap.)
S: 33.
T: The digit in the ones place is equal to 2 + 6. The digit in the tens place is equal to 8 – 6. What’s my
number? (Snap.)
S: 28.
As with the above example, begin with easy clues and gradually increase the complexity.

Date: 9/20/13 4.D.37
Materials: (T) 4 ten-sticks, 4 dimes, 10 pennies, chart paper (S) 4 ten-sticks, 4 dimes, and 10 pennies from
the math toolkit, personal white board
Students gather in the meeting area with their partners and materials.
T: (Write 16 + 2 and 16 + 20 on the board.) Using your linking cubes, Partner A, show how you would
solve 16 + 2. Partner B, show how you would solve 16 + 20.
S: (Solve.)
T: Share your work with your partner. How are they similar? How are
they different?
MP.6
S: We both started with the same number, 16.  We added a
different number to 16. I added 2, but my partner added
20.  But we both added 2 more things to 16. I added 2
ones. My partner added 2 tens.  I added my 2 ones to 6
ones. My partner added his 2 tens to 1 ten.
T: Excellent job comparing. Let’s make quick ten drawings to
show how we can solve these problems. Start by drawing
16.
S: (Draw 16 on their personal boards.)
T: Let’s add 2 ones. Should we add to the ones or to the tens?
Why?
S: To the 6 ones because we are adding 6 ones and 2 ones. 
We can add to the tens or the ones. We can do 10 + 2 = 12,
then 12 + 6 = 18.  But it’s much easier to add the ones. 6
and 2 is 8. 10 and 8 is 18.  The ones!
T: You’re right. Adding the ones together is much easier. Add 2 to
your ones. (Wait.) 6 ones and 2 ones is?
S: 8 ones.
T: How many tens are there?
S: 1 ten.
T: 1 ten 8 ones is?
S: 18.
T: (Make a number bond for 16.) Turn and talk to your partner about
why 16 is broken apart into 10 and 6.
S: We added 6 ones and 2 ones, so it’s smart to break apart 16 into 10 and 6.  That makes it easy for
me to see the ones.  I like adding 6 + 2. It’s easy for me. 10 + 6 is easy, too, 16!
T: 6 and 2 is? (Write 6 + 2 = 8 once students have answered.)
S: 8.
T: 10 and 8 is? (Write 10 + 8 = 18 once students have answered.)

Date: 9/20/13 4.D.38
S: 18.
T: (Point to 16 + 20.) This time, what’s different?
S: Instead of adding 2 ones, we are adding 2 tens.
T: In our drawing, should we add 2 tens to the tens or the
ones? Turn to your partner and explain your reason.
S: To the tens!  1 ten + 2 tens = 3 tens. That’s easy. 
We can add it to the ones. But we’ll have to think,
“What’s 16 + 20?” That’s not so easy. But if we add to
the tens, it’s much easier.  When you see 3 ten-
sticks, it’s easy to see that it’s 30. 30 + 6 is easy, too.
T: You are right! Adding tens to tens is much easier.
Show what that looks like in your drawing. Add 20, or
2 tens. (Wait.) How many tens are there?
S: 3 tens.
T: How many ones?
S: 6 ones.
T: 3 tens 6 ones is?
S: 36.
T: Turn and talk to your partner about breaking apart to
add 2 tens to the tens first. NOTES ON
MULTIPLE MEANS OF
S: Break apart 16 into 10 and 6.  It takes out the ten
REPRESENTATION:
that we need to add to the 2 tens. 20 and 10 is 30.
Then we add 6 more to get 36. Students below grade level might
benefit from place value charts as well
T: Write down two number sentences to show how we as concrete models to help them
add the tens first, and then the rest, to solve. determine whether to add to the tens
S: (Write 10 + 20 = 30 and 30 + 6 = 36.) or ones.
T: When we have an addition problem, what is a good
question to ask ourselves before adding the second
addend? (Point to the chart.) Think about how we
solved 16 + 2 and 16 + 20.
S: Ask and decide, “Should we add to the ones or to the
tens.”  When you add ones to ones or tens to tens,
it makes the problem easier to solve.
Repeat the process and have Student A solve 18 + 20 and
Student B solve 18 + 2 using cubes and quick ten drawings and
compare their work.
T: Everyone, show 18 with your cubes. (Wait.) Let’s add
2. But first, we need to ask…
S: Should we add to the ones or to the tens?
T: What should we add the 2 to?

Date: 9/20/13 4.D.39
S: The ones!
T: Add 2 to the ones. (Wait.) 18 + 2 is? NOTES ON
MULTIPLE MEANS OF
S: 20.
ENGAGEMENT:
T: Turn and share with your partner about how you got
Adjust the lesson structure based on
your answer.
the needs of your students. Some
S: I added 2 cubes to the 8 cubes. It made another ten- students may be ready for challenging
stick!  I now have 2 ten-sticks. 10 and 10 is 20. problems while others may need to
 8 plus 2 equals 10, 10 plus 10 equals 20. develop one method of representation
T: Use a quick ten drawing and a number bond to show at a time. Provide challenging
problems for students who are ready,
how you added ones and ones together.
while spending time with students who
S: (Complete drawings and number bonds.) may be struggling with one or more of
Repeat the process as partner work following the suggested the ways to represent their work
(number bonds, quick ten drawings,
sequence:
and coin drawings).
 17 + 20 and 17 + 2
 19 + 1 and 19 + 10
 15 + 20 and 15 + 2
To help students see the relationship between tens and ones
and dimes and pennies, have every student use coins, coin
drawings, and number bonds to solve: 14 + 2, 14 + 20, 26 +
10, and 26 + 4.

Lesson Objective: Add ones and ones or tens and tens.

lesson.

Date: 9/20/13 4.D.40
You may choose to use any combination of the questions below to lead the discussion.
 Share your quick ten drawing for Problem 6 with
your partner. How did you make your math
drawing? Why?
 How was solving Problem 7 helpful in solving
Problem 8?
 How are Problems 11 and 12 related?
 For Problem 5, a student says 3 + 14 = 44. How
can you help him understand his mistake?
 How did you determine whether to add to the
ones place or the tens place?
 How did the Application Problems connect to
today’s lesson?

the students.

Date: 9/20/13 4.D.41
Name Date
Draw quick tens and ones to help you solve the addition problems.
1. 2.
16 + 3 = ____ 17 + 3 = ____
3. 4.
18 + 20 = ____ 31 + 8 = ____
5. 6.
3 + 14 = ____ 6 + 30 = ____
7. 8.
23 + 7 = ____ 17 + 3 = ____

Date: 9/20/13 4.D.42
With a partner, try more problems using quick ten drawings, number bonds, or the
arrow way.
9. 32 + 7 = _____
10. 13 + 20 = _____
11. 6 + 34 = _____
12. 4 + 36 = _____
13. 20 + 18 = _____
14. 14 + 20 = _____
15. Draw dimes and pennies to help you solve the addition problems.
16 + 20 = ____ 22 + 7 = ____

Date: 9/20/13 4.D.43
Name Date
Solve using quick ten drawings to show your work.
24 + 5 14 + 20
Draw number bonds to solve.
19 + 20 36 + 3
Draw dimes and pennies to help you solve the addition problem.
13 + 20

Date: 9/20/13 4.D.44
Name Date
Draw quick tens and ones to help you solve the addition problems.
1. 2.
17 + 2 = _____ 17 + 3 = _____
3. 4.
14 + 3 = _____ 24 + 10 = _____
Make a number bond or use the arrow way to solve the addition problems.
5. 6.
6 + 24 = _____ 14 + 20 = _____

Date: 9/20/13 4.D.45
Solve each addition sentence and match.
22 + 1 = _____
13 + 6 = _____
3 + 26 = _____
+3
26 29
37 + 3 = _____
13 + 6
22 + 10 = _____
10 3

Date: 9/20/13 4.D.46
Lesson 17
Objective: Add ones and ones or tens and tens.

Use the RDW process to solve one or more of the problems.

a. Ben had 7 fish. He bought 4 fish at the store. How many fish does
Ben have?
b. Maria has fish. She had 7 fish in her tank and bought some more
fish until she had 9 fish. How many fish did Maria buy?
c. Anton has 8 fish. A few of the fish died and now Anton has 4 fish.
How many fish died?
Note: Today, students solve similar math stories within a new context.
Notice students who easily solved the problems with cubes but found
today's problems more challenging. These students may need support
visualizing story contexts.
 Core Addition Fluency Review: Missing Addends 1.OA.6 (5 minutes)

 Relating Addition and Subtraction 1.OA.4 (2 minutes)
Core Addition Fluency Review: Missing Addends (5 minutes)

Materials: (S) Missing Addends Core Addition Fluency Review
Note: This review sheet contains the majority of addition facts with sums of 5–10, which is part of the
required core fluency for Grade 1. The focus on missing addends strengthens students’ ability to count on, a

Date: 9/20/13 4.D.47
Level 2 strategy that first graders should master. Keep this activity
out so students can use it in the next fluency activity. NOTES ON
Students complete as many problems as they can in three MULTIPLE MEANS OF
minutes. Choose a counting sequence for early finishers to ENGAGEMENT:
practice on the back of their papers. When time runs out, read Encourage students to set goals for
the answers aloud so students can correct their work. improvement on sprints and fluency
Encourage students to remember how many problems they reviews. Provide scaffolds, strategies,
answered correctly in the allotted time so they can work to and opportunities for practice to help
improve their scores on future Missing Addends Core Addition them reach their personal goals.
Fluency Reviews.
Relating Addition and Subtraction (2 minutes)

Materials: (S) Missing Addends Core Addition Fluency Review from previous activity
Note: This fluency activity targets the first grade’s core fluency requirement. Reviewing the relationship
between addition and subtraction is especially beneficial for students who continue to find subtraction
challenging.
Students choose a column from the review sheet and rewrite each problem as a subtraction equation, seeing
how many they can do in two minutes.

Materials: (S) Personal white boards, dice
Note: This is the second day students are doing this partner activity. As students work, ask if it is easier the
second day.
Follow instructions in G1─M4─Lesson 16.
Materials: (T) Ten-sticks, chart paper (S) Ten-sticks from math

toolkit, personal white boards, game cards for Addition NOTES ON
and Subtraction with Cards MULTIPLE MEANS OF
REPRESENTATION:
Students gather in the meeting area with their partners and Highlight the critical vocabulary such as
materials. quick ten drawings, number bonds,
tens, ones, and addends, and use
T: (Write 19 + 2 on chart paper and show 19 red cubes on
pictorial representations to support
the floor.) What are we adding to 19?
student understanding. Have students
S: 2. use these terms as they share their
T: 2 what? thinking. This will support vocabulary
development.
S: 2 ones.

Date: 9/20/13 4.D.48
T: Where should we add the 2 ones, to the tens or the ones? Turn and talk to your partner about
why?
S: The ones!  To 9 ones!  It’s easier to add ones together.
T: Use your cubes to solve 19 + 2.
T: (Circulate to observe the different strategies students are using and
select students to demonstrate.)
S: We knew that 19 needs 1 more to make the next ten. So we took 1
from the 2 and made a ten. Now we have 20 and 1. That’s 21. 
We saw 10 ones in 9 + 1. We now have 2 tens and 1 one. That’s 21.
 We added the ones together. 9 + 2 = 11. One more ten is 21.
T: Excellent strategies! Just like we did yesterday, let’s add the ones
together. 9 and 2 is?
S: 11.
T: What more do we still have to add?
S: 1 ten.
T: 11 and 10 is?
S: 21.
T: Say the number sentence starting with 19.
S: 19 + 2 = 21.
Have students represent their work in quick ten drawings.
T: Let’s represent our work using a number bond. Which number did
we break apart?
S: We broke apart 19 into 10 and 9. That makes it easier to see the
ones. I can add 9 and 2 first, then add 10.
T: Great. (Chart the number bond and complete the number
sentence.) (Point to each number as you say it.) 9 and 2 is?
S: 11.
T: 11 and 10 is?
S: 21.
T: 19 + 2 is?
S: 21.
T: (Write 19 + 20 on the chart.) Show 19 using your cubes or quick ten
drawings.
S: (Show or draw 1 ten-stick and 9 ones.)
T: Before adding the next addend with your cubes, we should ask…
S: Am I adding tens or am I adding ones?
T: Correct! So which are we adding? Tens or ones?
S: Tens.
T: Yes. Add 2 tens. (Pause.) 1 ten and 2 tens is?

Date: 9/20/13 4.D.49
S: 3 tens.
T: How many ones are there?
S: 9 ones.
S: 39.
Guide students as they make the number bond to represent 19 + 20 and write two addition sentences.
Repeat the process following the suggested sequence:
 16 + 2 and 16 + 20
 2 + 13 and 20 + 13
 10 + 28 and 28 + 1
 8 + 27
Have students practice asking, “Do I add to the ones or add to the tens?” before representing their work with
cubes or quick tens and the number bond with two sentences. When appropriate, have students choose just
MP.5
one method to solve and explain their choice to their partner or to the whole group. For more challenging
examples, have students add dimes and pennies when using the sequence above.
For the remainder of time, have partners play Addition and Subtraction with Cards (follow instructions from
G1─M4─Lesson 12) with the new cards labeled D.

Lesson Objective: Add ones and ones or tens and tens.

lesson.

Date: 9/20/13 4.D.50
 Share the problems you solved using quick tens

and a number bond in the Problem Set with your
partner. Why did you choose to solve these
problems using the quick ten or a number bond?
 How can solving 11(a) help you solve 11(b)?
 Look at Problems 3 and 5. In both problems, we
added ones to ones. In the answer, why did the
tens stay the same in Problem 3 but the tens
changed in Problem 5?
 How can your fluency work with the die
(Analogous Addition Sentences) help you solve
addition problems in today’s lesson?

the students.

Date: 9/20/13 4.D.51
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 Core Addition Fluency 1•4
Name Date
Core Addition Fluency Review: Missing Addends
1. 5 + ___ = 5 16. 6 + ___ = 7 31. 9 + ___ = 9
2. 4 + ___ = 5 17. 1 + ___ = 7 32. 0 + ___ = 9
3. 2 + ___ = 5 18. 0 + ___ = 7 33. 1 + ___ = 9
4. 3 + ___ = 5 19. 7 + ___ = 7 34. 2 + ___ = 9
5. 0 + ___ = 5 20. 3 + ___ = 7 35. 7 + ___ = 9
6. 1 + ___ = 5 21. 4 + ___ = 7 36. 6 + ___ = 9
7. 1 + ___ = 6 22. 4 + ___ = 8 37. 5 + ___ = 9
8. 0 + ___ = 6 23. 5 + ___ = 8 38. 3 + ___ = 9
9. 6 + ___ = 6 24. 6 + ___ = 8 39. 4 + ___ = 9
10. 5 + ___ = 6 25. 2 + ___ = 8 40. 4 + ___ = 10
11. 3 + ___ = 6 26. 3 + ___ = 8 41. 5 + ___ = 10
12. 4 + ___ = 6 27. 0 + ___ = 8 42. 6 + ___ = 10
13. 2 + ___ = 6 28. 8 + ___ = 8 43. 3 + ___ = 10
14. 2 + ___ = 7 28. 7 + ___ = 8 44. 1 + ___ = 10
15. 5 + ___ = 7 30. 1 + ___ = 8 45. 2 + ___ = 10

Date: 9/20/13 4.D.52
Name Date
Solve the problems by drawing quick tens and ones or a number bond.
1. 2.
25 + 1 = ____ 25 + 10 = ____
3. 4.
15 + 4 = ____ 15 + 20 = ____
5. 6.
16 + 7 = ____ 26 + 7 = ____
7. 8.
23 + 7 = ____ 33 + 7 = ____

Date: 9/20/13 4.D.53
9. 10.
16 + 20 = ____ 6 + 24 = ____
11. Try more problems with a partner. Use your personal white board to help you solve.
a. 4 + 26 b. 28 + 4
c. 32 + 7 d. 20 + 18
e. 9 + 23 f. 9 + 27
Choose one problem you solved by drawing quick tens and be ready to
discuss.
Choose one problem you solved using the number bond and be ready to
discuss.

Date: 9/20/13 4.D.54
Name Date
Find the totals using quick ten drawings or number bonds.
1. 17 + 8 2. 28 + 7
3. 24 + 10 4. 19 + 20

Date: 9/20/13 4.D.55
Name Date
Use quick ten drawings or number bonds to make true number sentences.
1. 2.
13 + 20 = _____ 23 + 6 = _____
3. 4.
10 + 23 = _____ 28 + 6 = _____
5. 6.
26 + 7 = _____ 20 + 17 = _____
7. How did you solve Problem 5? Why did you choose to solve it that way?

Date: 9/20/13 4.D.56
Solve using quick ten drawings or number bonds.
8. 9.
23 + 9 = _____ 27 + 7 = _____
10. 11.
24 + 10 = _____ 20 + 18 = _____
12. 13.
28 + 9 = _____ 29 9 = _____
14. How did you solve Problem 11? Why did you choose to solve it that way?

Date: 9/20/13 4.D.57
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 Flashcards 1•4
G1-M4-Topic D Flashcards (and Review Subtraction)
35 + 4 D
24 + 3 D
24 + 6 D
28 + 4 D
35 + 5 D
22 + 8 D
17 + 7 D
31 + 6 D

Date: 9/20/13 4.D.58
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 Flashcards 1•4
24 + 9 D
8 + 28 D
26 + 8 D
3 + 33 D
7 + 32 D
29 + 7 D
3 + 18 D
18 - 3 D
17 - 4 D
19 - 5 D

Date: 9/20/13 4.D.59
Lesson 18
Objective: Share and critique peer strategies for adding two-digit numbers.




Use the RDW process to solve one or both of the problems.

a. Some ducks were in a pond. 4 baby ducks joined them.
Now there are 6 ducks in the pond. How many ducks
were in the pond at first?
b. Some frogs were in the pond. Three jumped out and
now there are 5 frogs in the pond. How many frogs were
in the pond at first?
Note: Today’s Application Problems use add to and take from
problems with the unknown in the starting position. For most
students, this is a difficult problem type, and it is for this reason
that the numbers in the stories are small.
Notice how students attempt the problem. Those who simply
add the two numbers in the first problem or subtract the two
numbers in the last problem may need additional reinforcement
in reading one sentence at a time as they review their drawings
to find the matching story parts.
 Core Addition Fluency Review: Missing Addends 1.OA.6 (5 minutes)

 Relating Addition and Subtraction 1.OA.4 (2 minutes)
Lesson 18: Share and critique peer strategies for adding two-digit numbers.
Date: 9/20/13 4.D.60
Core Addition Fluency Review: Missing Addends (5 minutes)

Materials: (S) Missing Addends Core Addition Fluency Review
(from G1–M4–Lesson 17)
NOTES ON
Note: This review sheet contains the majority of addition facts
MULTIPLE MEANS OF
with sums of 5–10, which is part of the required core fluency for
Grade 1. The focus on missing addends strengthens students’ ENGAGEMENT:
ability to count on, a Level 2 strategy that first graders should Scaffold sprints and fluency reviews for
master. students who may be having a difficult
time remembering basic math facts.
Students complete as many problems as they can in three Privately provide a modified version of
minutes. Choose a counting sequence for early finishers to the sprint or review so students can
practice on the back of their papers. When time runs out, read feel successful while building fluency
the answers aloud so students can correct their work. with math facts.
Celebrate improvement by having students compare
yesterday’s total correct with today’s total correct. Share a
class cheer for the student(s) with the most improved score.
Relating Addition and Subtraction (2 minutes)

Materials: (S) Missing Addends Core Addition Fluency Review from previous activity
Note: This fluency activity targets the first grade’s core fluency requirement and 1.OA.4.
Students choose a column from the review sheet and rewrite each problem as a subtraction equation, seeing
how many they can do in two minutes.

Materials: (S) Personal white boards, dice or numeral cards 0–10.
Note: Today, assign partners of equal ability and give students with a strong understanding of sums and
differences to 12 numeral cards instead of dice. The cards go up to 10, so they will be more of a challenge
since there will be more opportunities to make ten.
Repeat the activity from G1–M2–Lesson 16.
Materials: (T) Student work samples (template at end of lesson), projector (S) Personal white boards
Have students come to the meeting area and sit in a semi-circle.

T: (Write 17 + 4 on the board.) Turn and talk to your partner about how you would solve this problem.
S: (Discuss as teacher circulates and listens.)
Date: 9/20/13 4.D.61
T: (Project Student A work.) Turn and

talk to your partner about how he
showed his solution to 17 + 4 and think
about how we can label his work.
S: Let’s label it the arrow way.  He got
to the next ten by adding 3. Then he
added the 1 that was left and got 21.
 You can see his thinking in the
number sentences, too.
T: Yes! The arrow way and the number
sentences clearly show what he was
thinking. I am going to label this work
The Arrow Way. (Label work A.)
T: (Project Student B work.) How did this
student show how to solve 17 + 4?
S: She drew quick tens.
T: (Label this work Quick Ten Drawing.)
S: (Continue.) It looks like she added the ones together. She showed how she made a ten by drawing a
line through the 10 ones.  She added 2 tens and 2 ones and got 22.  I noticed a mistake! She
drew 18 first instead of 17! She drew an extra circle. She added 4 correctly using X’s, but because
she started out by drawing the wrong number, her answer is wrong.  She should have drawn 17
and 4. She should have gotten 21 as the answer.
T: What are some ways this student can improve her work?
S: She needs to count carefully especially when she’s drawing her ones.  She should check her work
with her partner. Then she might have caught her mistake.
T: Even though drawing is easy for many of you, it’s not always the best way to get the correct answer
because sometimes you have to make so many circles and X’s. Somewhere along the way, you can
lose count and make a mistake.
T: Work carefully and show 17 + 4 using the quick ten drawing on your board. Then check your work
with your partner.
S: (Make a quick ten drawing showing 21 as the sum and check with partner.)
T: (Project Student C and D work.) Let’s compare Student C’s work and Student D’s work. Did they
solve the problem in the same way? What similarities and differences do you notice? Turn and talk
to your partner.
S: They both used number bonds.
T: (Label these works Number Bond.)
S: (Continue.) They used number bonds but broke apart different numbers.  Student C added the
ones first.  Student D made the next ten.
T: Turn and talk to your partner about which student work best shows the tens.
S: I think Student D shows the tens the best because I can see that 17 + 3 = 20 and that is 2 tens.  I
think Student C shows the tens the best because I can see that 17 is 10 and 7. I see the 10 in 17.
Date: 9/20/13 4.D.62
T: Can both students’ work be correct even though they broke apart different numbers?
S: Yes.  You can break apart different numbers and get the correct answer, as long as you add every
part.
T: What is a compliment you can give to each of these
students? NOTES ON
MULTIPLE MEANS OF
S: They drew correct number bonds.  Student C added
the ones together first. She clearly showed her two REPRESENTATION:
MP.3
steps by writing both addition sentences.  Student D Facilitate student discussions to
made the next ten from 17. He did a good job breaking provide options for comprehension.
Guide students to recognize strategies
apart 4 into 3 and 1 so that he could make 20 with 17
that can make math easier, for
and 3.
example, breaking a larger number into
T: What are some ways they could improve their work? number bonds as well as looking for
S: Student D could have written two addition sentences patterns and structures in their work.
to show how he got 21.
T: (Write 19 + 5 on the board.) It’s your turn to solve a problem. You may use any method to solve but
you must show your work. When you are finished, swap your work with your partner and study it.
Give them a compliment and a suggestion about how to improve their work.
Have students swap boards with their partner and discuss the following:
 How did your partner show their solution?
 How was their work different from your work?
 How was your work the same?
 Give your partner a compliment on their work.
 Give a suggestion for how they could improve their work.
T: (Project 3 work samples from the class, showing each of the methods: a quick ten drawing, a
number bond, and the arrow way.) Which student work best helps you not count all?
S: The number bond because I counted on.  The arrow way because I got to the next ten and
counted on.
T: Good thinking! Why does the quick ten allow you to count all?
S: The drawing shows all the numbers so I can count them all instead of counting on.
T: How is the student work shown different from your partner’s work?
S: My partner drew the quick tens.  My partner drew circles and X’s for the ones.  My partner
bonded a different number.  My partner started with a different number to get to 20 using the
arrow way.
If time allows, have students solve 18 + 6 and share another set of student work from the class.

Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some
classes, it may be appropriate to modify the assignment by specifying which problems they work on first.
Some of the problems may have more than one correct student work for each problem.
Date: 9/20/13 4.D.63
Lesson Objective: Share and critique peer strategies for

adding two-digit numbers.
Set. They should check work by comparing answers
with a partner before going over answers as a class.
Look for misconceptions or misunderstandings that can
be addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process
the lesson.
You may choose to use any combination of the
 Look at Problem 2. What did you do to fix the
student work?
 Look at Problem 2(b). What suggestion do you
have for this student so she can improve her
work?
 Look at Problem 3(a). How can you help this
student improve?
 Compare your work on Problem 4 with your
partner. Did you solve the same way? Do you
think their way was an easier or harder way to
solve? Explain why.
 Project Student Work A–D from today’s
Concept Development. Which student work
best helps you not count all?
 How did today’s fluency help you to be
successful with the lesson?

the Exit Ticket. A review of their work will help you
assess the students’ understanding of the concepts that
were presented in the lesson today and plan more
effectively for future lessons. You may read the
questions aloud to the students.
Date: 9/20/13 4.D.64
Name Date
1. Each of the solutions is missing numbers or parts of the drawing. Fix each one so it
is accurate and complete.
13 + 8 = 21
a. b. c.
2. Circle the student work that correctly solves the addition problem.
16 + 5
a. b. c.
d. Fix the work that was incorrect by making new work in the space below with the
matching number sentence.
Date: 9/20/13 4.D.65
3. Circle the student work that correctly solves the addition problem.
13 + 20
a. b. c.
d. Fix the work that was incorrect by making a new drawing in the space below with
the matching number sentence.
Solve using quick tens, the arrow way, or number bonds.
17 + 5 = ___
Share with your partner. Discuss why you chose to solve the way you did.
Date: 9/20/13 4.D.66
Name Date
Circle the work that correctly solves the addition problem.

17 + 9
Fix the work that was incorrect by making a new drawing in the space below with the
matching number sentence.
Date: 9/20/13 4.D.67
Name Date
1. Two students both solved the addition problem below using different methods.
18 + 9
Are they both correct? Why or why not?
2. Another two students solved the same problem using quick tens.
Are they both correct? Why or why not?
Date: 9/20/13 4.D.68
Circle any student work that is correct.

19 + 6
Student A Student B Student C
Fix the student work that was incorrect by making new drawings in the space below.
Choose the correct answers and give a suggestion for improvement.
Date: 9/20/13 4.D.69
Student Work Samples
Date: 9/20/13 4.D.70
1
GRADE
Topic E
Varied Problem Types Within 20
1.OA.1
Focus Standard: 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of
adding to, taking from, putting together, taking apart, and comparing, with unknowns
in all positions, e.g., by using objects, drawings, and equations with a symbol for the
unknown number to represent the problem. (See CCLS Glossary, Table 1.)
As students begin working with larger numbers in word problems, representing each item and drawing it
individually can become cumbersome. In previous work with problem types, the two parts have been almost
exclusively single-digit numbers. For example, students were adding 9 and 6 or subtracting 8 from 14 to
solve. During Topic E, students begin to represent quantities in larger groupings while still visualizing the
relationship between the numbers. For example, students may be adding a
two-digit number and a one-digit number, such as 12 and 4, or subtracting a
two-digit number from a two-digit number, such as 16 – 12, represented in
the tape diagram to the right.
In Lesson 19, students are presented with put together/take apart with total
unknown and add to with result unknown word problems within 20 (1.OA.1).
As they solve, they draw and box the two parts, and then include the numeral label tape diagram
within the box, producing tape diagrams. This enables them to quickly identify where
the quantity can be found within the drawing. Students begin adding a bracket as shown to identify the total.
Lessons 20 and 21 allow students to explore number relationships as they solve put together/take apart with
addend unknown and add to with change unknown word problems within 20. As they do so, they explore
number relationships as they notice and discuss how the size of the boxes relate to the size of each part. For
example, when adding 12 + 4, students notice that the part in their tape diagram that contains 12 is much
longer than the part that contains 4. They also notice that when adding 10 + 10, the two parts are the same
size.
During these lessons, students share their strategies for drawing when a part is unknown. For example, when
given the problem, “Maria has 15 playing cards in her hand. She has 8 black cards. If the rest are red, how
many red cards does she have?” In order to solve this, some students may draw all 15 cards first and then
Topic E: Varied Problem Types Within 20

Date: 9/20/13 4.E.1
NYS COMMON CORE MATHEMATICS CURRICULUM Topic E 1•4
place a box around the 8 black cards Maria already has. Other students will draw the 8 black cards and then
count on as they draw to 15. Still other students will label 15 for the total, draw one part labeled 8, and then
work towards identifying the missing part. Students will continue to work on recognizing what kind of
unknown they are looking for: a part or a total.
During Lesson 22, students use their experiences and understanding to write their own word problems of
varied types based on given tape diagrams.
While the addition and subtraction within the problems for Topic E will be within 20, fluency work will
continue to support students’ skill and understanding from Topics A through D using numbers to 40. This
fluency work will prepare them for the increased complexity of addition in the final topic, Topic F.
A Teaching Sequence Towards Mastery of Varied Problem Types Within 20

Objective 1: Use tape diagrams as representations to solve put together/take apart with total unknown
and add to with result unknown word problems.
(Lesson 19)
Objective 2: Recognize and make use of part–whole relationships within tape diagrams when solving a
variety of problem types.
(Lessons 20–21)
Objective 3: Write word problems of varied types.

(Lesson 22)
Topic E: Varied Problem Types Within 20

Date: 9/20/13 4.E.2
Lesson 19
Objective: Use tape diagrams as representations to solve put
together/take apart with total unknown and add to with result unknown
word problems.

 Sprint: Analogous Addition Within 40 1.OA.6, 1.NBT.4 (10 minutes)
Sprint: Analogous Addition Within 40 (10 minutes)

Materials: (S) Analogous Addition Within 40 Sprint
Note: The progression of this Sprint mirrors the progression of concepts taught in Topic D thus far. It begins
with addition sentences conducive to counting on, transitions into sentences in which the sums of the ones
are less than ten, and ends with problems that cross ten.
Materials: (T) Document camera (S) Problem Set
Note: During this lesson, students will complete the Problem Set as the teacher guides instruction. This
method allows students to alternately practice a problem and then analyze both the process and the solution
before moving on to their next practice problem. Although today’s Problem Set includes both put together
and add to problem types, they all have the result or total unknown. The focus of today’s lesson is to support
the use of the tape diagram within the RDW process:
 Read.
 Draw and label.
 Write a number sentence and a statement.
In Lesson 20, students will grapple with solving both addition and subtraction problem types. Students
should keep their Problem Sets in a folder, along with the Application Problems from Lessons 13–18.
Lesson 19: Use tape diagrams as representations to solve put together/take apart
with total unknown and add to with result unknown word problems. 4.E.3
Date: 9/20/13
Distribute Problem Sets and have students work from their

seats. NOTES ON
T: (Project Problem 1 on the board.) Let’s read the MULTIPLE MEANS
problem together. OF ENGAGEMENT:
S/T: Lee saw 6 yellow squash and 7 pumpkins growing in his Appropriate scaffolds help all students
garden. How many vegetables did he see growing in feel successful. Students may use
his garden? translators, interpreters, or sentence
frames to present their solutions or
T: On your own, work on solving the problem. respond to feedback. Models shared
Remember that we always read the problem, draw and may include concrete manipulatives.
label, and write the number sentence and the
statement that answers the question.
S/T: (Reread the problem as students begin to solve.
Provide a maximum of 2 minutes for students to draw
and label.)
T: How did you use drawing to make sense of the
problem? Talk with a partner and explain your
drawing.
S: (Provide students 30–45 seconds to share with a
partner.) I drew the 6 squash in a straight line and
then 7 pumpkins. I figured out that was 13. (Project
students’ work as they describe their drawings to the Problem 1: Lee saw 6 squash and 7
class. Choose student work that most closely pumpkins growing in his garden. How many
resembles the tape diagram shown to the right.) vegetables did he see growing in his garden?
T: Look at this student’s work. Where in the drawing can

I find the squash?
S: (Point to the picture.) NOTES ON
T: (If the 6 squash are not inside a rectangle or circle to MULTIPLE MEANS OF
show the part, include this next sentence.) The label ENGAGEMENT:
helps find this part of the drawing. Let’s put a If you anticipate students struggling
rectangle around it so I can keep track of this part with the problems due to the size of
more easily. the numbers or the complexity of the
T: How many are there? language, follow up with a similar
problem that uses either smaller
S: 6. quantities or less complex language as
T: How can I tell quickly? (If the number is not labeled in a scaffold step. Be sure to provide at
the drawing, or is not near the picture, reword the least one challenging problem to all
second question to, “What can I do so I can tell students, as we help support them in
quickly?”) building stamina and perseverance in
problem solving.
S: He wrote 6 next to his picture.
Repeat the process asking about the pumpkins, using the same student work sample.
T: (Ask a student to read the question from the story again for the class.) How many vegetables are
there?
Date: 9/20/13
S: 13 vegetables.
T: So from here (pointing to one end of the squash) to
here (pointing to the other end of the pumpkins) we
have 13 vegetables?
S: Yes!
T: Let’s show that above our drawing, so we can keep
track. (Draw as shown, so that the bracket, or arms,
represent that everything from one end to the other
has a total of 13. Label with 13 and T for total.) When Problem 2: Kiana caught 6 lizards. Her
we connect our two parts like this, and show the total, brother caught 6 snakes. How many reptiles
we call it a tape diagram. If you didn’t show this in do they have altogether?
your drawing, add it now.
Repeat the process for each of the next problems. Use the
questions to move students towards placing rectangles around
each part and labeling with the number inside the part, as well
as using a letter label outside the shape. Encourage students to
make their rectangles touch, so that they have one large
rectangle for showing the total, the whole.
When discussing Problem 3 after students have had a chance to
solve it, include the following question.
 How could using a color change at 10 help you keep
track of the number of soccer balls on the field?
Problem 3: Anton’s team has 12 soccer balls
Before moving on to the next problem, ensure that all students on the field and 3 soccer balls in the coach’s
have added labels to each part of their drawing and have bag. How many soccer balls does Anton’s
written the number sentence and completed the statement. team have?
Choose probing questions appropriate to the successes and
challenges of the class. Encourage early finishers to write their
own word problems on another sheet of paper. They can write
the problem on one side and then write the solution using a
drawing, number sentence, and statement on the other side.
Problem 4: Emi had 13 friends over for

dinner. Four more friends came over for
cake. How many friends came over to Emi’s
house?
Date: 9/20/13
Problem 5: Six adults and 12 children were Problem 6: Rose has a vase with 13 flowers.
swimming in the lake. How many people She puts 7 more flowers in the vase. How
were swimming in the lake? many flowers are in the vase?
Lesson Objective: Use tape diagrams as representations to solve put together/take apart with total unknown
and add to with result unknown word problems.
Guide students in a conversation to debrief the Problem
Set and process the lesson. Look for misconceptions or
misunderstandings that can be addressed in the Debrief.
 We called our drawings today tape diagrams.
Think about the diagrams we draw in science
class. Why might we use the word diagram here?
What are the important parts of our tape
diagram?
 Look at Problem 2. What do you notice about
the size of each rectangle around the parts? Why
is that?
 Look at Problem 5. How is the tape diagram
similar to the one you made for Problem 2? How
is it different? Compare the size of the two
rectangles around each part of Problem 5. What
do you notice?
Date: 9/20/13
 What do you notice about the story problems we

completed today? Who created a problem that
puts together two known parts to find an
unknown total? Share your story problem with
the class.
 You know your tape diagram has good labels
when you can tell the story by looking at it. Who
can use the tape diagram to tell the soccer ball
story?
 How can a tape diagram help us share our
thinking?

the students.
Date: 9/20/13
A Number correct:
Name Date
1 6+1=☐ 16 6+3=☐
2 16 + 1 = ☐ 17 16 + 3 = ☐
3 26 + 1 = ☐ 18 26 + 3 = ☐
4 5+2=☐ 19 4+5=☐
5 15 + 2 = ☐ 20 15 + 4 = ☐
6 25 + 2 = ☐ 21 8+2=☐
7 5+3=☐ 22 18 + 2 = ☐
8 15 + 3 = ☐ 23 28 + 2 = ☐
9 25 + 3 = ☐ 24 8+3=☐
10 4+4=☐ 25 8 + 13 = ☐
11 14 + 4 = ☐ 26 8 + 23 = ☐
12 24 + 4 = ☐ 27 8+5=☐
13 5+4=☐ 28 8 + 15 = ☐
14 15 + 4 = ☐ 29 28 + ☐ = 33
15 25 + 4 = ☐ 30 25 + ☐ = 33
Date: 9/20/13
B Number correct:
Name Date
1 5+1=☐ 16 6+3=☐
2 15 + 1 = ☐ 17 16 + 3 = ☐
3 25 + 1 = ☐ 18 26 + 3 = ☐
4 4+2=☐ 19 3+5=☐
5 14 + 2 = ☐ 20 15 + 3 = ☐
6 24 + 2 = ☐ 21 9+1=☐
7 5+3=☐ 22 19 + 1 = ☐
8 15 + 3 = ☐ 23 29 + 1 = ☐
9 25 + 3 = ☐ 24 9+2=☐
10 6+2=☐ 25 9 + 12 = ☐
11 16 + 2 = ☐ 26 9 + 22 = ☐
12 26 + 2 = ☐ 27 9+5=☐
13 4+3=☐ 28 9 + 15 = ☐
14 14 + 3 = ☐ 29 29 + ☐ = 34
15 24 + 3 = ☐ 30 25 + ☐ = 34
Date: 9/20/13
Name Date
Read the word problem.

Draw a tape diagram and label.
Write a number sentence and a statement that matches the story.
1. Lee saw 6 squash and 7 pumpkins growing in his garden. How many vegetables did he
see growing in his garden?
Lee saw __________ vegetables.
2. Kiana caught 6 lizards. Her brother caught 6 snakes. How many reptiles do they
have altogether?
Kiana and her brother have __________ reptiles.
3. Anton’s team has 12 soccer balls on the field and 3 soccer balls in the coach’s bag.
How many soccer balls does Anton’s team have?
Anton’s team has __________ soccer balls.
Date: 9/20/13
4. Emi had 13 friends over for dinner. Four more friends came over for cake. How
many friends came over to Emi’s house?
There were __________friends.
5. Six adults and 12 children were swimming in the lake. How many people were
swimming in the lake?
There were __________ people swimming in the lake.
6. Rose has a vase with 13 flowers. She puts 7 more flowers in the vase. How many
flowers are in the vase?
There are __________ flowers in the vase.
Date: 9/20/13
Name Date
Write a number sentence and a statement that matches
the story.
1. Peter counts the number of lightning bolts during a storm, and Lee counts the
rumbles of thunder. Peter counts 14 lightning bolts, and Lee counts 6 rumbles of
thunder. How many lightning bolts and thunder rumbles did they count in all?
They count _____________ lightning bolts and thunder rumbles.
Date: 9/20/13
Name Date
the story.
1. Darnel is playing with his 4 red robots. Ben joins him with 13 blue robots. How
many robots do they have altogether?
They have ________ robots.
2. Rose and Emi have a jump rope contest. Rose jumps 14 times and Emi jumps 6
times. How many times did Rose and Emi jump?
They jumped ________ times.
Date: 9/20/13
3. Pedro counts the airplanes taking off and landing at the airport. He sees 17
airplanes take off and 6 airplanes land. How many airplanes did he count
altogether?
Pedro counts _______ airplanes.
4. Tamra and Willie score all the points for their team in their basketball game.
Tamra scores 13 points, and Willie scores 8 points. What was their team’s score
for the game?
The team’s score was _______ points.
Date: 9/20/13
Lesson 20
Objective: Recognize and make use of part–whole relationships within

 Beep Counting by Ones and Tens 1.OA.5, 1.NBT.3 (2 minutes)

 Addition and Subtraction with Cards 1.NBT.4 (5 minutes)
Beep Counting by Ones and Tens (2 minutes)

Note: This fluency activity allows students to practice their counting sequences as well as practicing mentally
adding 10 and subtracting 10 from a given number.
Say a series of four numbers but replace one of the numbers with the word “beep” (e.g., “1, 2, 3, beep”).
When signaled, students say the number that was replaced by the word “beep” in the sequence. Scaffold
number sequences, beginning with easy sequences and moving to more complex ones. Choose sequences
that count forward and backward by ones and tens within 40.
Suggested sequence type: 10, 11, 12, beep; 20, 21, 22, beep; 20, 19, 18, beep; 30, 29, 28 beep; 0, 10, 20,
beep; 1, 11, 21, beep; 40, 30, 20, beep; 39, 29, 19, beep. Continue with similar sequences, changing the
sequential placement of the beep.

Note: This fluency activity builds students’ ability to add and subtract within 10
or 20, while reinforcing the relationship between addition and subtraction. The
first two to three minutes should be spent reviewing the core fluency within 10.
In the last one to two minutes, allow students who are very strong with sums and
differences to 10 to work with a partner and choose totals between 10 and 20.
Lesson 20: Recognize and make use of part–whole relationships within tape
diagrams when solving a variety of problem types. 4.E.15
Date: 9/20/13
Write a number bond for a number between 0 and 10, with a missing part or whole. Students write an
addition and subtraction sentence with a box for the missing number in each equation. They then solve for
the missing number.
Addition and Subtraction with Cards (5 minutes)

Materials: (S) Topics A and C Addition and Subtraction with Cards game cards (from G1─M4─Lesson 12) and
additional Topic D cards (from G1─M4─Lesson 17)
Note: This fluency game reviews the problem types presented in Topics A─D, as well as reviews subtraction
from Module 2.
Follow the directions in G1─M4─Lesson 12’s Concept Development.

NOTES ON
Materials: (S) Problem Set, highlighter MULTIPLE MEANS
OF EXPRESSION:
Note: During Lesson 20, the suggested delivery of instruction is Partnering students and asking them to
an integration of student work on the Problem Set with guided explain their work to each other can
instruction interspersed between each problem. Today, the support students’ language
unknown in each problem will vary between a part and the development. Students can ask each
total. The sequence of problems has been designed to support other the same questions that the
students in using the RDW process, particularly to keep track of teacher asks. Be sure to have students
information as they determine if they are looking for a part or switch roles so that all students have
the opportunity to practice verbalizing
the total, and to use the visual representation of the
their thinking and listening.
information to support calculations.
Suggested Delivery of Instruction for Solving Word Problems

1. Model the problem, calculate, and write a statement.
Choose two pairs of students who have been accurately solving NOTES ON
the Application Problems from Topic D and who have been MULTIPLE MEANS
using simple shapes in a straight line when drawing. Invite OF ENGAGEMENT:
these two pairs of students to work on chart paper while the Appropriate scaffolds help all students
others work independently or in pairs at their seats. Vary the feel successful. Students may use
selected students as the problems become more complex. translators, interpreters, or sentence
Review the following questions before beginning the first frames to present their solutions or
problem: respond to feedback. Models shared
may include concrete manipulatives.
 Can you draw something?
 What can you draw?
 What can you tell from looking at your drawing?
As students work, circulate. Reread Problem 1 and reiterate the questions above. After a maximum of two
minutes, have the pairs of students share their labeled diagrams. Give everyone two to three minutes to
Date: 9/20/13
finish work on that question, sharing their work and thinking with a peer. All should write their equations
and statements of the answer.
2. Assess the solution for reasonableness.

Give students one to two minutes to assess and explain the reasonableness of their solution. For about one
minute, have the demonstrating students receive and respond to feedback and questions from their peers.
3. As a class, notice the ways the drawing depicts the story and the solution.
Ask questions to help students recognize how each part of their drawing matches the story and solution. This
will help students begin to see how the same process can help them solve varying word problems. Keep at
least one chart paper sample of each solution for reference later in the lesson.
Problem 1
Nine dogs were playing at the park. Some more dogs came to
the park. Then there were 11 dogs. How many more dogs came
to the park?
To support students’ methods for keeping track of their
information, ask some of the following questions:
 What labels did the student use to show the part
consisting of the dogs that were playing at first?
 How did she separate them from the part consisting of
the dogs that came later?
 What label did she use for the total number of dogs?
Problem 1: Nine dogs were playing at the
 Where did she put the label for the total number of park. Some more dogs came to the park.
dogs? How did that help? Then there were 11 dogs. How many more
Be sure to discuss the solution and the number sentence, noting dogs came to the park?
which number from the number sentence is the solution
number. This number should have a rectangle around it, as
shown.
Problem 2
Sixteen strawberries are in a basket for Peter and Julio. Peter ate 8 of them. How many are there for Julio to
eat?
Problem 2: Sixteen strawberries are in a basket for Peter and Julio.

Peter ate 8 of them. How many are there for Julio to eat?
Date: 9/20/13
Problem 3
Thirteen children are on the roller coaster. Three adults are on
the roller coaster. How many people are on the roller coaster?
Have the class read one sentence of the problem at a time,
while the students at the board show where the information is
within their drawing, pointing out the number and letter labels.
Discuss where the solution can be found within the number
sentence, and ensure that everyone has placed a rectangle
around this number.
Problem 3: Thirteen children are on the
Some students will initially assume this problem requires roller coaster. Three adults are on the roller
subtraction. Walking through each sentence to ask, “Is this a coaster. How many people are on the roller
new part, or does this include the part I already drew?” can coaster?
support students internalizing a process for making sense of
word problems.
Problem 4
Thirteen people are on the roller coaster now. Three adults are
on the roller coaster, and the rest are children. How many
children are on the roller coaster?
While this problem uses the same context as Problem 3, the
problem type is different. As students consider the question, “Is
this a new part, or is this a part of what I already drew?” they
will recognize that in this problem, the unknown number is a Problem 4: Thirteen people are on the roller
part of the total 13. coaster now. Three adults are on the roller
coaster, and the rest are children. How
During the Debrief, Problems 3 and 4 will be compared.
many children are on the roller coaster?
Problem 5
Ben has 6 baseball practices in the morning this month. If Ben also has 6 practices in the afternoon, how
many baseball practices does Ben have?
Choose probing questions appropriate to the successes and challenges of the class. Notice students who are
improving, and ask them to share their increasing understanding.
Problem 5: Ben has 6 baseball practices in the morning this month. If Ben also
has 6 practices in the afternoon, how many baseball practices does Ben have?
Date: 9/20/13
Problem 6
Some yellow beads were on Tamra’s bracelet. After she put 14
purple beads on the bracelet, there were 18 beads. How many
yellow beads did Tamra’s bracelet have at first?
As an add to with start unknown problem type, this will most
likely be the most challenging problem of the set.
In this example, the student approaches the problem by first
drawing an empty box for the yellow beads and putting the
question mark in it. Next, the 14 are drawn and the total of 18
is labeled. Finally, the student counts up from 14 to 18 while
drawing in the additional 4 beads to find the missing part.
Problem 5: Some yellow beads were on
The number sentences are written. The most probable solution Tamra’s bracelet. After she put 14 purple
equation would be the center one, 14 + ___ = 18. Not many beads on the bracelet, there were 18 beads.
first graders will opt to start with a part unknown or subtract 14 How many yellow beads did Tamra’s bracelet
from 18. have at first?
Lesson Objective: Recognize and make use of part–whole relationships within tape diagrams when solving a
Guide students in a conversation to debrief the Problem
Set and process the lesson. Look for misconceptions or
misunderstandings that can be addressed in the Debrief.
 How are Problems 3 and 4 alike? How are they
different? How did your drawings help you to
solve each problem?
 In which problems could making ten help you?
Explain your thinking.
 Look at Problem 2 and Problem 3. What is similar
and what is different between the two problems?
What do you notice about the size of the
rectangles around each part in Problem 2? What
do you notice in Problem 3?
 Look at Problem 6. How did you solve this
problem? What did you draw first? Next? Did
anyone do it a different way?
Date: 9/20/13
 Using a highlighter, underline the question in

each problem. Highlight the part of the tape
diagram that shows the answer to the question.
What do you notice?
 Some people only write numbers and not circles
inside the parts of a tape diagram. Why do we
draw the circles sometimes? Why do we just use
numbers at times?

the students.
Date: 9/20/13
Name Date

Write a number sentence and a statement that matches the story.
1. Nine dogs were playing at the park. Some more dogs came to the park. Then there
were 11 dogs. How many more dogs came to the park?
__________ more dogs came to the park.
2. Sixteen strawberries are in a basket for Peter and Julio. Peter ate 8 of them. How
many are there for Julio to eat?
Julio has __________ strawberries to eat.
3. Thirteen children are on the roller coaster. Three adults are on the roller coaster.
How many people are on the roller coaster?
There are __________ people on the roller coaster.
Date: 9/20/13
4. Thirteen people are on the roller coaster now. Three adults are on the roller
coaster, and the rest are children. How many children are on the roller coaster?
There are __________ children on the roller coaster.
5. Ben has 6 baseball practices in the morning this month. If Ben also has 6 practices
in the afternoon, how many baseball practices does Ben have?
Ben has __________ baseball practices.
6. Some yellow beads were on Tamra’s bracelet. After she put 14 purple beads on the
bracelet, there were 18 beads. How many yellow beads did Tamra’s bracelet have at
first?
Tamra’s bracelet had __________ yellow beads.
Date: 9/20/13
Name Date
the story.
There were 6 turtles in the tank. Dad bought some more turtles. Now there are 12
turtles. How many turtles did Dad buy?
Dad bought __________ turtles.
Date: 9/20/13
Name Date
the story.
1. Rose has 12 soccer practices this month. Six practices are in the afternoon, but
the rest are in the morning. How many practices will be in the morning?
Rose has ______ practices in the morning.
2. Ben catches 16 fish. He puts some back in the lake. He brings home 7 fish. How
many fish did he put back in the lake?
Ben put ______ fish back in the lake.
Date: 9/20/13
3. Nikil solved 9 problems on the first sprint. He solved 12 problems on the second
sprint. How many problems did he solve on the two sprints?
Nikil solved ______ problems on the sprints.
4. Shanika returned some books to the library. She had 16 books at first, and she still
has 13 books left. How many books did she return to the library?
Shanika returned ______ books to the library.
Date: 9/20/13
Lesson 21
Objective: Recognize and make use of part–whole relationships within


 Take Out 1 or 10 1.OA.6 (2 minutes)
 Longer/Shorter K.CC.7 (2 minutes)

Materials: 1 die per set of partners
Note: In this fluency activity, students practice adding and subtracting within 20. The competitive nature of
Race and Roll Addition and Subtraction promotes students’ engagement while increasing their brains’ ability
to retain information (since the partners are trying to stand quickly).
All students start at 0. Partners take turns rolling a die, saying a number sentence, and adding the number
rolled to the total. For example, Partner A rolls 6 and says, “0 + 6 = 6,” then Partner B rolls 3 and says, “6 + 3 =
9.” They continue rapidly rolling and saying number sentences until they get to 20 without going over.
Partners stand when they reach 20. For example, if they are at 18 and roll 5, they would take turns rolling
until one of them rolls a 2. Then they would both stand.

Note: This fluency activity builds a student’s ability to add

and subtract within 10. Reviewing the relationship between
addition and subtraction is especially beneficial for students
who continue to find subtraction challenging.
Date: 9/20/13
Write a number bond for a number between 0 and 10, with a missing part or whole. Today, students write
two addition and two subtraction sentences with a box for the missing number in each equation. They then
solve for the missing number.
Take Out 1 or 10 (2 minutes)

Note: This activity reviews place value in order to prepare students for Topic F.
Choose numbers between 10 and 20 and follow the paradigm below.
T: Say 15 the Say Ten way.
S: Ten 5.
T: Take out 1.
S: Ten 4.
Repeat for 25 and 35. Then, take out 10 from 15, 25, and 35, respectively.
Longer/Shorter (2 minutes)
Materials: (T) Board or document camera
Note: Working with visualizing proportional

relationships between numbers can support
students’ number sense development. By using tape
diagram models, students can recognize methods for
representing numbers in relation to other numbers.
Write one pair of numbers on the board at a time
(e.g., 5 and 5). Draw a rectangle under the first
number.
T: This rectangle is long enough to hold
this row of 5 dots. (Draw 5 dots so
that they fill the space.)
T: (Point to the second number, which in this first example is also 5.) I’m going to start drawing a
rectangle that is long enough to hold a row of 5 dots of the same size. Tell me when to stop.
T/S: (Begin drawing a rectangle, and give students the chance to say “Stop!” when it is approximately the
same size as the first rectangle.)
T: Why did you say stop there?
S: It is about the same size as the first rectangle.
Repeat this process for the following sequence of numbers: 5 and 4, 5 and 10, 1 and 3, 4 and 6, 10 and 20.
Only draw the dots for the first example. Have students talk about how the first number relates to the
second number using language such as a little longer, a little shorter, much longer, double, etc. Have students
who find this challenging use a number line with their left pointer finger on zero and their right on the
number (endpoint).
Date: 9/20/13
Materials: (S) Problem Set
Note: Like Lessons 19 and 20, the suggested delivery of instruction for Lesson 21 is an integration of student
work on Problem Sets with guided instruction interspersed between each problem. If students have been
highly successful with the past days’ lessons, today, have them try representing the quantities in each part
using the number and label, without including the shapes inside each part. The goal is to support students in
identifying a process for making sense of a problem.
By working with the tape diagrams as drawings related to the varying problem types, students can internalize
an entry point into any problem. Can you draw something? What can you draw? What can you tell from
looking at your drawing? Tape diagrams, even without shapes inside each part, can be considered a type of
drawing. Remember to have students hold on to the Problem Sets so they can be used as a reference later in
the topic.
Suggested Delivery of Instruction for Solving Word Problems

1. Model the problem, calculate, and write a statement.
Choose two pairs of students who have been accurately solving NOTES ON
the Application Problems from Topic D and who have been MULTIPLE MEANS OF
using simple shapes in a straight line when drawing. Invite REPRESENTATION:
these two pairs of students to work on chart paper while the
Encourage students who have difficulty
others work independently or in pairs at their seats. Vary the moving to the tape diagram
selected students as the problems become more complex. representation as the position of the
Review the following questions before beginning the first unknown changes to draw a number
problem: bond as part of their work. Some
students more easily relate to the tape
 Can you draw something?
diagram through its similarities with
 What can you draw? number bonds.
 What can you tell from looking at your drawing?
As students work, circulate and support. After two minutes,
have the two pairs of students share only their labeled
diagrams. Give everyone two to three minutes to finish work NOTES ON
on that question, sharing their work and thinking with a peer. MULTIPLE MEANS
All should write their equations and statements of the answer. OF ACTION AND
EXPRESSION:
2. Assess the solution for reasonableness. If students do not have experience with
a context such as the one used in
Give students one to two minutes to assess and explain the
Problem 2, act out the problem with a
reasonableness of their solution. For about one minute, have
few student volunteers before having
the demonstrating students receive and respond to feedback the class begin to draw and solve the
and questions from their peers. problem.
Date: 9/20/13
3. As a class, notice the ways the drawing depicts the

story and the solution.
Ask questions to help students recognize how each part of
their drawing matches the story and solution. This will
help students begin to see how the same process can help
them solve varying word problems. Keep at least one
chart paper sample of each solution for reference later in
the lesson.
Problem 1
Rose drew 7 pictures, and Will drew 11 pictures. How
many pictures did they draw altogether?
This problem, a put together with total unknown, is one of
the easiest problem types. After the students have
explained their drawing and solution accurately, point to
sections of the tape diagram and ask the class questions
such as, “What does this part represent? How do you
know? What did the student draw or write to help us
remember?”
For the next five problems, move quickly from one to
the next, having only the students at the board share
their work, so that students have time to work through
and discuss all six problems. Choose one or two probing
questions similar to Problems 1 and 2 to support
student development as needed.
Problem 2
Darnel walked 7 minutes to Lee’s house. Then he walked
to the park. Darnel walked for a total of 18 minutes. How
many minutes did he walk to get to the park?
Problem 3
Emi has some goldfish. Tamra has 14 Beta fish. Tamra
and Emi have 19 fish in all. How many goldfish does Emi
have?
Problem 4
Shanika built a block tower using 14 blocks. Then she
added 4 more blocks to the tower. How many blocks are
there in the tower now?
Date: 9/20/13
Problem 5
Nikil’s tower has 15 blocks. He added some more blocks to his tower. His tower is 18 blocks tall now. How
many blocks did Nikil add?
Problem 6
Ben and Peter caught 17 tadpoles. They gave some to Anton. They have 4 tadpoles left. How many tadpoles
did they give to Anton?
Lesson Objective: Recognize and make use of part–whole relationships within tape diagrams when solving a
Guide students in a conversation to debrief the Problem Set and process the lesson. Look for misconceptions
or misunderstandings that can be addressed in the Debrief.
 Look at Problem 1. What did you draw? How did your drawing help you solve the problem?
 Look at Problem 2. What did you draw first? How is your drawing similar or different from the
drawing you made for Problem 1?
 Look at Problem 3. How did you draw this problem? How is your drawing similar to or different
from your partner’s drawing?
 Look at Problem 5. Did you solve this the same way you solved Problem 3, or did you solve it in a
different way? Share your drawing and explain your thinking.
 Last week, we were looking at smaller, single-digit addition facts inside two-digit addition problems.
Can you find any simpler addition facts inside your number sentences? Share your examples. How
can you draw your tape diagrams in ways that help you see simple problems inside the larger ones?
 Using a highlighter, underline the question in each problem. Highlight the part of the tape diagram
that shows the answer to the question. What do you notice?
 Some people only write numbers and not circles inside the parts of a tape diagram. Why might we
want to include the circles in each part? Why might we choose to use only the number and leave
out the circles in each part sometimes?

Date: 9/20/13
Name Date
the story.
1. Rose drew 7 pictures, and Willie drew 11 pictures. How many pictures did they draw
altogether?
They drew _________ pictures.
2. Darnel walked 7 minutes to Lee’s house. Then he walked to the park. Darnel walked
for a total of 18 minutes. How many minutes did he walk to get to the park?
Darnel walked _________ minutes to the park.
3. Emi has some goldfish. Tamra has 14 Beta fish. Tamra and Emi have 19 fish in all.
How many goldfish does Emi have?
Emi has _________ goldfish.
Date: 9/20/13
4. Shanika built a block tower using 14 blocks. Then she added 4 more blocks to the
tower. How many blocks are there in the tower now?
The tower is made of _________ blocks.
5. Nikil’s tower is 15 blocks tall. He added some more blocks to his tower. His tower
is 18 blocks tall now. How many blocks did Nikil add?
Nikil added _________ blocks.
6. Ben and Peter caught 17 tadpoles. They gave some to Anton. They have 4 tadpoles
left. How many tadpoles did they give to Anton?
They gave Anton _________ tadpoles.
Date: 9/20/13
Name Date
the story.
1. Shanika read some pages on Monday. On Tuesday, she read 6 pages. She read 13
pages in the 2 days. How many pages did she read on Monday?
Shanika read _________ pages on Monday.
Date: 9/20/13
Name Date
the story.
1. Fatima has 12 colored pencils in her bag. She has 6 regular pencils, too. How many
pencils does Fatima have?
Fatima has ________ pencils.
2. Julio swam 7 laps in the morning. In the afternoon he swam some more laps. He
swam a total of 14 laps. How many laps did he swim in the afternoon?
Julio swam ______ laps in the afternoon.
Date: 9/20/13
3. Peter built 18 models. He built 13 airplanes and some cars. How many car models
did he build?
Peter built ________ car models.
4. Kiana found some shells at the beach. She gave 8 shells to her brother. Now she
has 9 shells left. How many shells did Kiana find at the beach?
Kiana found ______ shells.
Date: 9/20/13
Lesson 22
Objective: Write word problems of varied types.




 Sprint: Related Addition and Subtraction Within 10 and 20 1.OA.6 (10 minutes)
 Longer/Shorter K.CC.7 (2 minutes)

Materials: 1 die per set of partners
Note: In previous Race and Roll Addition games, students raced to 20. Today, change the target number to
10 and practice both addition and subtraction. As students play, pay attention to their automaticity. When
students demonstrate strong fluency to 10, increase the target number to 12.
Repeat Race and Roll Addition from G1–M4–Lesson 21. Instead of racing to 20 and stopping, students start at
0 and roll and add until they hit 10. Once they do, they roll to get back to 0 by subtracting.
Sprint: Related Addition and Subtraction Within 10 and 20 (10 minutes)

Materials: (S) Related Addition and Subtraction Within 10 and 20 Sprint
Note: During the last few days of fluency, students have been reviewing the relationship between addition
and subtraction using the context of a number bond. In this Sprint, students apply this knowledge to solve
equations, first within 10, and then within 20. Students who reach the final two questions of the fourth
quadrants will be challenged to apply their understanding of analogous addition equations to analogous
subtraction equations (2.NBT.5).

Date: 9/20/13 4.E.36

Longer/Shorter (2 minutes)
Materials: (T) Board or document camera
Write one pair of numbers on the board at a time (e.g., 10 and 20). Draw a rectangle under the first number.
T: This rectangle can fit a row of 10 dots.
T: (Point to the second number, which in this example is 20.)
I’m going to start to draw a rectangle that can fit a row of 20
dots of the same size. Tell me when to stop.
T/S: (Begin drawing a rectangle, and give students the chance to say “Stop!” when it is approximately
twice the size of the first rectangle.)
T: Why did you say stop there?
S: It is about double the length of the first rectangle. A rectangle for 20 has to fit 10 + 10.
Repeat this process for the following sequence of numbers: 10 and 5, 4 and 4, 4 and 8, 4 and 2, 8 and 10, 10
and 9. Only draw the actual dots for the first example. With each example, help students talk about how the
first number compares, or relates, to the second number using language such as a little longer, a little shorter,
much longer, double, etc.
Materials: (T) Chart paper (S) Folder with Application Problems from Lessons 13–18 and Problem Sets from
Lessons 19–21, personal white board
Have students place the tape diagram template inside their personal white boards, and bring all materials to
the meeting area.
T: (Display the tape diagram shown in the
image to the right.) I found this drawing on a
piece of paper on the floor. It went with
someone’s word problem from this week.
Does anyone know which one it went to?
Look through your Problem Sets with a
partner and see if you can figure it out. Talk
about how you know.
S: (Look back at Problem Sets with their
partners and discuss what is the same about
the problem and the tape diagram.)
T: Which problem does this tape diagram go
with?
Lesson 21 Problem 4

Date: 9/20/13 4.E.37

S: This tape diagram goes with the problem

about Shanika’s tower (Problem 4 in Lesson
21). (Explains how the referents align with
the problem story.)  I think it goes with
the one about Tamra’s yellow and purple
beaded bracelet. (Problem 6 in Lesson 20).
(Explains how the referents align with the
problem story.)
Lesson 20 Problem 6
T: Hmm. They both sound like they could match this tape
diagram.
T: (Draw tape diagram shown in the image on the right.)
This is a tape diagram for a problem from yesterday’s
lesson. Which problem does this match?
S: (Look back at Problem Set for Lesson 21 with partner
and discuss what is the same about the problem and
the tape diagram.)
T: Which problem does the tape diagram go
with?
S: It’s the one where Nikil builds a tower with
15 blocks and then adds some more. It’s
Problem 5. (Explains how the referents align
with the problem story.)
T: With your partner, try to come up with a
different story that could go with this tape Lesson 21 Problem 5
MP.2
diagram. You can use your tape diagram
template as you discuss your idea.
NOTES ON
T: (While students are discussing, circulate and listen.) MULTIPLE MEANS OF
Listen to the students as they generate their story ideas, and ACTION AND
choose three student math stories to be used as samples for the EXPRESSION:
class. Present the stories in the following order: Giving students an opportunity to share
 A story that parallels the examples using a different their thinking allows them to evaluate
topic. (An add to with a change unknown problem their process and practice. English
language learners also benefit from
type, where the 3 is the unknown number, e.g.,
hearing others explain their thinking.
15 + ? = 18.)
 An add to with a result unknown problem type, e.g.,
15 + 3 = ?.
NOTES ON
 A different add to or take from with a change unknown MULTIPLE MEANS OF
problem or an add to with the start unknown problem, REPRESENTATION:
e.g., 3 + ? = 18, 18 - ? = 15, or ? + 15 = 18.
Highlight the vocabulary used in the
As the students share the problem with the class, redraw the Problem Set to ensure understanding
tape diagram, label appropriately for the given story, and write of all words. This supports vocabulary
the accompanying number sentences and statement. development, especially with English
language learners.

Date: 9/20/13 4.E.38

T: What was similar in all of these problems?

S: All of our problems used the same tape diagram.
T: What was different in each story problem?
S: The topic was different.  Sometimes the
unknown or mystery number was different.
 Sometimes my number sentence was an
addition sentence and sometimes it was a
subtraction sentence.  The statement
answered the question, and the question was
different for each story problem.
T: How could knowing the answer to one story
problem help you with a different story
problem?
S: Sometimes they do use the same number
sentence.  Even when the number
sentences were different, they used a related
fact, like 15 + 3 = 18 can still help you with
18 – 15 = 3, since they use the same number
bond.

by specifying which problems they work on first. Some
Lesson Objective: Write word problems of varied

types.
the lesson.

Date: 9/20/13 4.E.39

 Look at Problem A. What story problem did
you write? Share with the class. Posed to the
rest of the class: What is the unknown number
in their question? What number sentence
would help you solve the question? Invite one
or two more students to share. How did you
decide on your labels for your tape diagrams?
 Which problems were the easiest for you to
think of ideas for? Which were harder? Why?
 Look at your application problems from last
week and your Problem Sets from this week.
What do you notice about your work? What
part of your word problem work has been
improving?


Date: 9/20/13 4.E.40

A Number correct:
Name Date
1 2+2=☐ 16 2 + ☐= 8
2 2 + ☐= 4 17 6 + ☐= 8
3 4-2=☐ 18 8-6=☐
4 3+3=☐ 19 8–2=☐
5 3 + ☐= 6 20 9+2=☐
6 6-3=☐ 21 9 + ☐ = 11
7 4 + ☐= 7 22 11 - 9 = ☐
8 3 + ☐= 7 23 9 + ☐ = 15
9 7-3=☐ 24 15 - 9 = ☐
10 7-4=☐ 25 8 + ☐ = 15
11 5+4=☐ 26 15 - ☐ = 8
12 4 + ☐= 9 27 8 + ☐ = 17
13 9-4=☐ 28 17 - ☐ = 8
14 9-5=☐ 29 27 - ☐ = 8
15 9 - ☐= 4 30 37 - ☐ = 8

Date: 9/20/13 4.E.41

B Number correct:
Name Date
1 3+3=☐ 16 2 + ☐= 9
2 3 + ☐= 6 17 7 + ☐= 9
3 6-3=☐ 18 9-7=☐
4 4+4=☐ 19 9–2=☐
5 4 + ☐= 8 20 9+5=☐
6 8-4=☐ 21 9 + ☐ = 14
7 4 + ☐= 9 22 14 - 9 = ☐
8 5 + ☐= 9 23 9 + ☐ = 16
9 9-5=☐ 24 16 - 9 = ☐
10 9-4=☐ 25 8 + ☐ = 16
11 3+4=☐ 26 16 - ☐ = 8
12 4 + ☐= 7 27 8 + ☐ = 16
13 7-4=☐ 28 16 - ☐ = 8
14 7-3=☐ 29 26 - ☐ = 8
15 7 - ☐= 3 30 36 - ☐ = 8

Date: 9/20/13 4.E.42

Name Date
Use the tape diagrams to write a variety of word problems. Use the word bank if
needed. Remember to label your model after you write the story.
Topics (Nouns) Actions (Verbs)
flowers goldfish lizards hide eat go away
stickers rockets cars give draw get
frogs crackers marbles collect build play
A. 19
14 5

Date: 9/20/13 4.E.43

B.
19
9 10

Date: 9/20/13 4.E.44

C. 16
13 ?
D. 19
? 13

Date: 9/20/13 4.E.45

Name Date
Circle the 2 story problems that match the tape diagram.
17
14 ?
A. There are 14 ants on the picnic blanket. Then some more ants came over. Now
there are 17 ants on the picnic blanket. How many ants came over?
B. Fourteen children are on the playground from one class. Then 17 children from
another class came to the playground. How many children are on the playground
now?
C. Seventeen grapes were on the plate. Willie ate 14 grapes. How many grapes are on
the plate now?

Date: 9/20/13 4.E.46

Name Date
Use the tape diagrams to write a variety of word problems. Use the word bank if
needed. Remember to label your model after you write the story.
Topics (Nouns) Actions (Verbs)
flowers goldfish lizards hide eat go away
stickers rockets cars give draw get
frogs crackers marbles collect build play
A.
17
12 5

Date: 9/20/13 4.E.47

B. 16
? 7

Date: 9/20/13 4.E.48

1
GRADE
Topic F
Addition of Tens and Ones to a Two-
Digit Number
1.NBT.4
Focus Standard: 1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and
adding a two-digit number and a multiple of 10, using concrete models or drawings and
In Topic F, students begin adding like units within pairs of two-digit numbers. Lesson 23
focuses on taking interpretations of two-digit numbers a step further, having students
interpret numbers such as 25 as 1 ten and 15 ones as well as 2 tens and 5 ones and as 25
ones. Working with this concept supports student understanding in the next lessons, when
students add pairs such as 14 + 16 and initially make 2 tens and 10 ones.
During Lessons 24 and 25, students
interchangeably add sets of two-digit numbers where
the ones digits produce a sum less than or equal to 10.
For example, when adding 17 + 13, students
decompose the second addend into 10 and 3. They
then add 10 to 17, making 27, and then add the
remaining ones. In Lesson 25, students also practice
adding ones to the first addend and then adding the
remaining ten.
Lesson 24 Lesson 25
Topic F: Addition of Tens and Ones to a Two-Digit Number

Date: 9/20/13 4.F.1
NYS COMMON CORE MATHEMATICS CURRICULUM Topic F 1•4
In Lesson 26 and 27, students add tens and ones when the
ones digits have a sum greater than 10, such as 19 + 15.
Students continue to decompose the second addend,
alternating between adding on the ten first and making the
next ten, as shown to the right. In Lesson 27, students solve
the same problem using the varying strategies taught
throughout the topic. Students continue to strengthen their
use of Level 3 strategies for adding numbers to 40.
The module closes with Lessons 28 and 29, wherein Adding on ten first Adding to make the next
students solve problem sets of varied types to support ten first
flexibility in thinking as they add any pair of two-digits
whose sum is within 40. In Lesson 29, students again share
methods and representations for finding the sums.
A Teaching Sequence Towards Mastery of Addition of Tens and Ones to a Two-Digit Number
Objective 1: Interpret two-digit numbers as tens and ones including cases with more than 9 ones.
(Lesson 23)
Objective 2: Add a pair of two-digit numbers when the ones digits have a sum less than or equal to 10.
(Lessons 24–25)
Objective 3: Add a pair of two-digit numbers when the ones digits have a sum greater than 10.
(Lessons 26–27)
Objective 4: Add a pair of two-digit numbers with varied sums in the ones.
(Lessons 28–29)
Topic F: Addition of Tens and Ones to a Two-Digit Number

Date: 9/20/13 4.F.2
Lesson 23
Objective: Interpret two-digit numbers as tens and ones, including cases
with more than 9 ones.




Kim picks up 10 loose pencils and puts them in a cup. Ben has 1
package of 10 pencils that he adds to the cup. How many
pencils are now in the cup? Use the RDW process to solve the
problem.
Note: This problem bridges the objectives from Lessons 19 through
to today's lesson. During the Debrief, students complete a place
value chart to match the story and reinterpret the number 20 in
several ways. As in Topic D, throughout Topic F the Application
Problem starts the lesson so that fluency activities flow into the
Concept Development.
 Grade 1 Core Fluency Differentiated Practice Sets 1.OA.6 (5 minutes)

 Count by 10 with Dimes 1.NBT.5, 1.MD.3 (2 minutes)
 Tens and Ones 1.NBT.4 (3 minutes)
Grade 1 Core Fluency Differentiated Practice Sets (5 minutes)

Materials: (S) Core Fluency Practice Sets
Note: Throughout Topic F and for the remainder of the year, each day’s fluency includes an opportunity for
review and mastery of the sums and differences with totals through 10 by means of the Core Fluency Practice
Sets or Sprints. Five options are provided in this lesson for the Core Fluency Practice Set, with Sheet A being
Lesson 23: Interpret two-digit numbers as tens and ones, including cases with
more than 9 ones. 4.F.3
Date: 9/20/13
the simplest addition fluency of the grade and Sheet E being the most complex. Start all students on Sheet A.
Keep a record of student progress so that you can move students to more complex sheets as they are ready.
Students complete as many problems as they can in 90 seconds. We recommend 100% accuracy and
completion before moving to the next level. Collect any Practice Sheets that have been completed within the
90 seconds and check the answers. The next time Core Fluency Practice Sets are used, students who have
successfully completed their set today can be provided with the next level.
For early finishers, you might assign a counting pattern and start number. Celebrate improvement as well as
advancement. Students should be encouraged to compete with themselves rather than their peers.
Interview students on practice strategies. Notify caring adults of each child’s progress.
Count by 10 with Dimes (2 minutes)

Materials: (T) 10 dimes
Note: This fluency activity strengthens students’ ability to recognize a dime and identify its value, while
providing practice with counting forward and back by 10.
Lay out and take away dimes in 5-group formation as students count by 10 both the regular way and the Say
Ten way.
Tens and Ones (3 minutes)

Materials: (T) 100-bead Rekenrek
Note: This fluency activity reviews how to decompose two-digit numbers into tens and ones with the
Rekenrek so that students can see alternate decompositions in today’s lesson.
T: (Show a 16 on the Rekenrek). How many tens do you see?
S: 1 ten.
T: How many ones?
S: 6 ones.
T: Say the number the Say Ten way.
S: Ten 6.
T: Good. 1 ten plus 6 ones is?
S: 16.
T: 16 + 10 is?
S: 26.
Slide over the next row and repeat for 26 and then 36. Continue with the following suggested sequence: 15,
25, 35, 45, 55, 65, 75; 17, 27, 37, 57, 97. Then, follow the same script, but ask students to subtract 10 instead
of add 10, using the following suggested sequence: 39, 29, 19, 9; 51, 41, 31, etc.
Date: 9/20/13
Materials: (T) Chart paper, place value chart template from G1–M4–Lesson 2 (optional) (S) Personal white
boards, ten-sticks from math toolkit
Have students gather in the meeting area in a semi-circle formation.

T: (Ask three student volunteers to come to the front.) Show us 3 tens using your magic counting
sticks.
S: (Each student shows clasped hands.)
T: How many tens do you see?
S: 3 tens.
T: How many loose ones do you see?
S: 0 ones.
T: What is the value of 3 tens?
S: 30.
T: (Write 30 = 3 tens and fill in the place value chart.
Continue to chart student responses as they make
other combinations of 30 using tens and ones.)
T: (Ask one student to unclasp her hands.) How many
tens do you see?
S: 2 tens.
T: How many loose ones do you see?
S: 10 ones.
T: Do we still have 30? Explain how you know.
S: Yes!  We didn’t add anything or take anything away.
 1 ten became 10 ones, but they are the same
amount.  They have the same value. NOTES ON
T: How is 30 made here? (Chart the students’ answer.) MULTIPLE MEANS OF
S: With 2 tens and 10 ones. REPRESENTATION:
Careful selection of pairs for
Repeat the process and ask the remaining students to unbundle
collaborative work is essential to
their tens one at a time to show 1 ten 20 ones and, finally, 30
achieving expected outcomes. This
ones. lesson will work well with hetero-
T: Let’s look at the chart. The number 30 can be geneous groupings of students. Pair
represented in many different ways. 30 can be made one student with a clear understanding
of? of the concept with another student
who might need more practice with
S: 3 tens, 2 tens 10 ones. 1 ten 20 ones, 30 ones! tens and ones. Pair an English
T: Get together with your partner and another pair of language learner with another student
students. Show as many tens as you can using your who expresses their reasoning
magic counting sticks. (Wait.) especially well.
Date: 9/20/13
T: What is the largest amount of tens you can make?

S: 4 tens.
T: What is 4 tens?
S: 40.
T: Show more ways to make 40 and record them on your boards.
S: We made 3 tens 10 ones.  2 tens 20 ones.  1 ten 30 ones.  40 ones.
T: (Ask four volunteers to come to the front.) Show 37 using your magic counting sticks with as many
tens as possible.
S: (Show 3 tens 7 ones.)
T: (Tap the third student on the shoulder.) If Student 3 unbundles his ten, how many tens and ones will
we have?
S: 2 tens 17 ones.
T: Let’s check. Student 3, unbundle your magic counting sticks! Were we correct? Are there 2 tens
and 17 ones?
S: Yes!
T: Explain to your partner how 2 tens 17 ones is the same as 37.
MP.7
S: 17 ones is the same as 1 ten and 7 ones. 2 tens and 1 ten is 3 tens. 7 more ones is 37.
T: Show 37 as 3 tens 7 ones again. If only 1 student shows 1 ten, how many ones will there be to make
37? 37 is the same as 1 ten and how many ones?
S: 1 ten 27 ones.
T: How did you know?
S: (Point to each student with unclasped hands.) 10, 20, 7 is 27.  Two students will have to unbundle
their sticks, so that’s 20. 20 ones and 7 ones is 27 ones.
T: Let’s check. Student 1, keep your hands clasped. The other students with tens, unbundle and show
10 ones. (Wait.) 37 is the same as how many tens and how many ones?
S: 1 ten 27 ones.
Repeat the process, showing 0 tens 37 ones.
Have students work in pairs using linking cubes or working in groups of four using magic counting sticks to
make all combinations of tens and ones to make 13, 23, 27, 34, and 38.
Next, write a number in the tens and ones place using the place value chart template (see image below) and
ask students to determine the total value:
T: (Write 1 ten 15 ones on a place value chart.) What is
the value of 1 ten 15 ones? You may use your cubes or
work with your classmates and their magic counting
sticks to show your thinking.
S: 10 plus 15 is 25.  1 ten is 10 ones. 10 ones and 15
ones is 25 ones. 15 ones is the same as 1 ten 5 ones.
Add another 1 ten and I have 2 tens 5 ones, that’s 25.
T: So the value of 1 ten 15 ones is?
Date: 9/20/13
S: 25!
Repeat the process with the following sequence:
 1 ten 5 ones, 25 ones
 3 tens 5 ones, 2 tens 15 ones, 1 ten 25 ones NOTES ON
 31 ones, 2 ten 11 ones, 1 ten 21 ones, 3 tens 1 one MULTIPLE MEANS OF
 2 ten 16 ones, 3 tens 6 ones REPRESENTATION:
 1 ten 29 ones, 3 tens 9 ones As students complete the Problem Set,
allow those who need more concrete
Students may work in pairs and use their linking cubes or practice to use their ten-sticks and
in groups of 4 using fingers to solve while others visualize ones cubes. Some students may not be
every 10 ones as 1 ten. able to visualize ones as tens especially
when completing Problem 4. Support
Problem Set (10 minutes) these students by having them lay out
the numbers as they are matching.
Students should do their personal best to complete the Their path to abstract thinking may be
Problem Set within the allotted 10 minutes. For some a little longer than those of other
classes, it may be appropriate to modify the assignment students.
Lesson Objective: Interpret two-digit numbers as tens

and ones, including cases with more than 9 ones.
the lesson.
 How did you solve Problem 4? Explain your
thinking.
 Look at Problem 1(d). A student says 2 tens 13
ones can be written as 213. How can you help
this student understand why this is not correct?
Date: 9/20/13
 Look at Problem 2. Circle the place value

charts that have two digits in the ones place.
What do you notice?
 Look at Problem 3. Circle the statement that is
not true. Write down as many combinations of
tens and ones to make the statement true.
 How can using Say Ten counting help you find
your combinations of tens and ones?
today’s lesson? How could we write the total
number of pencils in the place value chart?
What other combinations of tens and ones can
we use to make this number?

Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 Core Fluency Practice Set A 1•4
Name Date
My Addition Practice
1. 6 + 0 = ___ 11. 7 + 1 = ___ 21. 5 + 3 = ___
2. 0 + 6 = ___ 12. ___ = 1 + 7 22. ___ = 5 + 4
3. 5 + 1 = ___ 13. 3 + 3 = ___ 23. 6 + 4 = ___
4. 1 + 5 = ___ 14. 3 + 4 = ___ 24. 4 + 6 = ___
5. 6 + 1 = ___ 15. ___ = 3 + 5 25. ___ = 4 + 4
6. 1 + 6 = ___ 16. 6 + 3 = ___ 26. 3 + 4 = ___
7. 6 + 2 = ___ 17. 7 + 3 = ___ 27. 5 + 5 = ___
8. 5 + 2 = ___ 18. ___ = 7 + 2 28. ___ = 4 + 5
9. 2 + 5 = ___ 19. 2 + 7 = ___ 29. 3 + 7 = ___
10. 2 + 4 = ___ 20. 2 + 8 = ___ 30. ___ = 3 + 6
Today I finished _____ problems.
I solved _____ problems correctly.
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 Core Fluency Practice Set B 1•4
Name Date
My Missing Addend Practice
1. 6 + ___ = 6 11. 3 + ___ = 6 21. 4 + ___ = 7
2. 0 + ___ = 6 12. 4 + ___ = 8 22. 7 = 3 + ___
3. 5 + ___ = 6 13. 10 = 5 + ___ 23. 2 + ___ = 7
4. 4 + ___ = 6 14. 5 + ___ = 9 24. 2 + ___ = 8
5. 0 + ___ = 7 15. 5 + ___ = 7 25. 9 = 2 + ___
6. 6 + ___ = 7 16. 8 = 5 + ___ 26. 2 + ___ = 10
7. 1 + ___ = 7 17. 5 + ___ = 9 27. 10 = 3 + ___
8. 7 + ___ = 8 18. 8 + ___ = 10 28. 3 + ___ = 9
9. 1 + ___ = 8 19. 7 + ___ = 10 29. 4 + ___ = 9
10. 6 + ___ = 8 20. 10 = 6 + ___ 30. 10 = 4 + ___
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 Core Fluency Practice Set C 1•4
Name Date
My Related Addition and Subtraction Practice
1. 5 + ___ = 6 11. 7 + ___ = 10 21. 4 + ___ = 8
2. 1 + ___ = 6 12. 10 – 7 = ___ 22. 8 – 4 = ___
3. 6 - 1 = ___ 13. 5 + ___ = 7 23. 4 + ___ = 7
4. 9 + ___ = 10 14. 7 – 5 = ___ 24. 7 – 4 = ___
5. 1 + ___ = 10 15. 5 + ___ = 8 25. 5 + ___ = 9
6. 10 – 9 = ___ 16. 8 – 5 = ___ 26. 9 – 5 = ___
7. 5 + ___ = 10 17. 4 + ___ = 6 27. 6 + ___ = 9
8. 10 – 5 = ___ 18. 6 – 4 = ___ 28. 9 – 6 = ___
9. 8 + ___ = 10 19. 3 + ___ = 6 29. 4 + ___ = 7
10. 10 – 8 = ___ 20. 6 – 3 = ___ 30. 7 – 4 = ___
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 Core Fluency Practice Set D 1•4
Name Date
My Subtraction Practice
1. 6 - 0 = ___ 11. 6 - 3 = ___ 21. 8 - 4 = ___
2. 6 - 1 = ___ 12. 7 - 3 = ___ 22. 8 - 3 = ___
3. 7 - 1 = ___ 13. 9 – 3 = ___ 23. 8 - 5 = ___
4. 8 - 1 = ___ 14. 10 - 8 = ___ 24. 9 - 5 = ___
5. 6 - 2 = ___ 15. 10 - 6 = ___ 25. 9 - 4 = ___
6. 7 - 2 = ___ 16. 10 – 4 = ___ 26. 7 - 3 = ___
7. 9 - 2 = ___ 17. 10 - 5 = ___ 27. 10 - 7 = ___
8. 10 - 10 = ___ 18. 7 – 6 = ___ 28. 9 - 7 = ___
9. 10 - 9 = ___ 19. 7 - 5 = ___ 29. 9 - 6 = ___
10. 10 - 7 = ___ 20. 6 - 4 = ___ 30. 8 - 6 = ___
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 Core Fluency Practice Set E 1•4
Name Date
My Mixed Practice
1. 4 + 2 = ___ 11. 2 + ___ = 6 21. 8 - 5 = ___
2. 2 + ___ = 6 12. 6 - 2 = ___ 22. 3 + ___ = 8
3. 6 = 3 + ___ 13. 6 - 4 = ___ 23. 8 = ___ + 5
4. 2 + 5 = ___ 14. 5 + ___ = 7 24. ___ + 2 = 9
5. 7 = 5 + ___ 15. 7 - 5 = ___ 25. 9 = ___ + 7
6. 4 + 3 = ___ 16. 7 - 4 = ___ 26. 9 – 2 = ___
7. 7 = ___ + 4 17. 7 - 3 = ___ 27. 9 - 7 = ___
8. 8 = ___ + 4 18. 8 = 6 + ___ 28. 9 - 6 = ___
9. 4 + 5 = ___ 19. 8 - 2 = ___ 29. 9 = ___ + 4
10. 9 = ___ + 4 20. 8 – 6 = ___ 30. 9 - 6 = ___
Date: 9/20/13
Name Date
1. Fill in the blanks and match the pairs that show the same amount.
a.
____ tens ____ ones ____ tens ____ ones
b.
____ tens ____ ones

1 ten ____ ones
c.
2 tens ____ ones 2 tens ____ ones
d.
2 tens ____ ones 2 tens ____ ones
Date: 9/20/13
2. Match the place value charts that show the same amount.
2 2 3 6
2 16 3 4
2 14 1 2
3. Check each sentence that is true.
27 is the same as 1 ten 17 ones. 33 is the same as 2 tens 23 ones.
37 is the same as 2 tens 17. 29 is the same as 1 ten 19 ones.
5
4. Lee says that 35 is the same as 2 tens 15 ones, and Maria says that 35 is the same
as 1 ten 25 ones. Draw quick tens to show if Lee or Maria is correct.
Date: 9/20/13
Name Date
Match the place value charts that show the same amount.
2 12 2 16
2 8 1 18
3 6 3 2
Tamra says that 24 is the same as 1 ten 14 ones, and Willie says that 24 is the same as
2 tens 14 ones. Draw quick tens to show if Tamra or Willie is correct.
Date: 9/20/13
Name Date
1. Fill in the blanks and match the pairs that show the same amount.
a.
____ tens ____ ones 2 tens ____ ones
b.
____ tens ____ ones 1 ten ____ ones
c.
____ tens ____ ones 2 tens ____ ones
d.
____ tens ____ ones 1 ten ____ ones
Date: 9/20/13
2. Match the place value charts that show the same amount.
2 18 3 8
1 16 2 1
0 21 2 6
3. Check each sentence that is true.
35 is the same as 1 ten 25 ones. 28 is the same as 1 ten 18 ones.
36 is the same as 2 tens 16 ones. 39 is the same as 2 tens 29 ones.
4. Emi says that 37 is the same as 1 ten 27 ones, and Ben says that 37 is the same as 2
tens 7 ones. Draw quick tens to show if Emi or Ben is correct.
Date: 9/20/13
Lesson 24
Objective: Add a pair of two-digit numbers when the ones digits have a




A dog hides 11 bones behind his doghouse. Later, his owner gives
him 5 bones. How many bones does the dog have? Use the RDW
process to share your thinking as you solve the problem.
Extension: All the bones are brown or white. The same number of
bones are brown as white. How many brown bones does the dog
have?
Note: This problem reviews the add to with result unknown problem
type so that they can focus on the drawing and labeling of the tape
diagram. In the extension, students are challenged to consider the
relationship between the two parts. Keep at least one student work
sample to use as a comparison during the following day's Debrief.

 Count by 10 or 1 with Dimes and Pennies 1.NBT.5, 1.MD.3 (3 minutes)
 Add Tens 1.NBT.4 (2 minutes)

Materials: (S) Core Fluency Practice Sets from G1–M4–Lesson 23
Lesson 24: Add a pair of two-digit numbers when the ones digits have a sum less
than or equal to 10. 4.F.19
Date: 9/20/13
graders. Give Practice Set B to students who correctly answered all questions on Practice Set A in the
previous lesson. All other students should try to improve their scores on Practice Set A.
Students complete as many problems as they can in 90 seconds. Assign a counting pattern and start number
for early finishers, or tell them to practice make ten addition or subtraction on the backs of their papers.
Collect and correct any Practice Sets completed within the allotted time.

Materials: (S) Personal white boards, die per pair
Note: This fluency activity addresses Grade 1’s core fluency

requirement and strengthens understanding of the
relationship between addition and subtraction.
Repeat the activity from G1–M4–Lesson 21. Today, assign
partners of equal ability and an appropriate range of numbers
for each pair. Allow partners to choose a number for their
whole and roll the die to determine the one of the parts. Both
students write two addition and two subtraction sentences
with a box for the missing number in each equation and solve
for the missing number. They then exchange boards and check
each other’s work.
Count by 10 or 1 with Dimes and Pennies (3 minutes)

Materials: (T) 10 dimes and 10 pennies
Note: This activity uses dimes and pennies as abstract representations of tens and ones to help students
become familiar with coins, while simultaneously providing practice with counting forward and back by 10
or 1.
 Minute 1: Place and take away dimes in a 5-group formation as students count along by 10.
 Minute 2: Begin with 2 pennies. Ask how many ones there are. Instruct students to start at 2 and
add and subtract 10 as you place and take away dimes.
 Minute 3: Begin with 2 dimes. Ask how many tens there are. Instruct students to begin at 20 and
add and subtract 1 as you place and take away pennies.
Add Tens (2 minutes)

Materials: (T) 100-bead Rekenrek
Note: Reviewing how to add multiples of 10 enables students to utilize their understanding of place value to
add 2 two-digit numbers in today’s lesson.
T: (Show 14 on the Rekenrek.) Add 10.
S: 14 + 10 = 24.
Date: 9/20/13
T: Add 20.
S 14 + 20 = 34.
Repeat, displaying other teen numbers and instructing students to add 10 and 20. If students find it
challenging to mentally add 20, scaffold by asking them to add 2 tens and modeling with the Rekenrek before
asking them to add 20.
Materials: (T) 5 ten-sticks (3 red and 2 yellow), chart paper (S) 4 ten-sticks from math toolkit, personal white
board
Students gather in the meeting area with their partners and materials.
T: (Write 24 + 13.) Partner A, show 24 with your cubes. Partner B, show 13 with your cubes.
S: (Show 24 or 13 with cubes.)
T: Combine your cubes to show the easiest way to find the total.
S: (Add cubes.)
T: How did you add 24 and 13?
S: We put the tens together and the ones together. NOTES ON
 We put 2 tens and 1 ten together. We put 4 ones MULTIPLE MEANS
and 3 ones together.  We have 3 ten-sticks and 7 OF EXPRESSION:
ones. We made 37. At this stage of development, students
T: I love the way you combined the tens with tens and will typically start in the highest place,
ones with ones together. 2 tens and 1 ten is? in this case, the tens place. This is an
acceptable strategy for addition at any
S: 3 tens.
level. Starting with the ones place only
T: 4 ones and 3 ones is? makes the standard algorithm easier
S: 7 ones. and is not necessary until students are
adding larger numbers with regrouping
in multiple places.
S: 37.
T: 24 + 13 is?
S: 37.
T: (Complete the number sentence. Then show 24 using red cubes.) You are
experts at working with tens. You know how to add tens to any number
just like we practiced during fluency today. Let’s use that skill to add 24
and 13. Let’s add 10 from 13 to 24 first.
T: (Place the ten-stick next to 2 ten-sticks.) 1 ten more than 2 tens 4 is?
S: 3 tens 4.
T: What do I need to still add?
S: 3 ones.
Date: 9/20/13
T: (Place 3 yellow cubes on top of 4 red cubes.) 34 and 3

is?
S: 37. NOTES ON
T: We just used our expertise on tens by adding 1 ten to MULTIPLE MEANS
24 first. OF ENGAGEMENT:
T: Let’s use a number bond to do the same thing. How Appropriate scaffolds help all students
did we break apart 13? feel successful. Some students may get
S: 10 and 3. the tens and ones confused when
adding. Students may use place value
T: (Draw the number bond.) What did we do first? (Point
charts to write the numbers in that
to the number bond.) they are adding to help them move
S: Add 10. (Write 24 + 10.) towards visualizing. Using their ten-
T: 24 + 10 is? sticks and ones cubes will also help
these students eventually move from
S: 34. concrete to abstract.
T: Next? (Point to the number bond.)
S: Add 3.
T: 34 + 3 is?
S: 37.
T: Now you write the two addition sentences to show
how we added 1 ten first.
S: (Write 24 + 10 = 34 and 34 + 3 = 37.)
T: Let’s try a new problem. (Write 24 + 16.) Partner A, make 24
with your linking cubes. Partner B, make 16. (Wait.) What part
of 16 did we add first before?
S: 10!
T: Add 10 to 24. What do you get?
S: (Lay down a ten-stick next to 2 ten-sticks.) 34.
T: What more do we have to add?
S: 6.
T: How much do you have altogether?
S: 40.
T: Show us what you did.
S: We made another ten-stick with 4 and 6. Now we have 4 ten-
sticks. That’s 40.  4 ones and 6 ones is 10 ones. 3 tens and 10
ones is the same as 40. That’s what we did yesterday!
T: Make a number bond and write two number sentences to record
how you solved 24 + 16. We started with 24. Let’s break apart
16 into?
S: 10 and 6. (Break apart 16 into 10 and 6.)
Date: 9/20/13
If needed, have students represent their process of adding 24

and 16 in quick ten drawings, talking through the steps with NOTES ON
their partners. Ask students to also write two addition MULTIPLE MEANS OF
sentences to record their steps.
ENGAGEMENT:
Repeat the process following the suggested sequence: 22 + 14, Remember to provide challenging
23 + 16, 23 + 17, 19 + 21, 22 + 18, and 12 + 28 (start with 28, the extensions for your advanced students.
bigger addend, then add 10 and 2). Give them one two-digit number and
the sum. Have students find the
Problem Set (10 minutes) mystery two-digit addend.

Lesson Objective: Add a pair of two-digit numbers when

the ones digits have a sum less than or equal to 10.
the lesson.
 How did you solve Problem 1(d)? Which addend did you start with and why?
 How can setting up for Problem 1(e) help you solve Problem 1(f)?
 How can setting up for Problem 2(e) help you solve Problem 2(f)?
 What new strategy did we use to add 2 two-digit addends?
 How did the Application Problem connect to today’s lesson?
Date: 9/20/13

questions aloud to the student
Date: 9/20/13
Name Date
1. Solve using number bonds. Write the two number sentences that show that you
added the ten first. Draw quick tens and ones if that helps you.
a. b.
14 + 13 = ____ 13 + 24 = ____
10 3 10 3
14 + 10 = 24 24 + 10 = _____
24 + 3 = 27 _____ + 3 = _____
c. d.
16 + 13 = ____ 13 + 26 = ____
10 3
10 3
16 + 10 = ____ 26 + 10 = ____
____ + 3 = ____ ____ + ___ = ____
e. f.
15 + 15 = ____ 15 + 25 = ____
10 5
___ + ___ = ____ ___ + ___ = ____
___ + ___ = ____ ___ + ___ = ____
Date: 9/20/13
2. Solve using number bonds or the arrow way. The first row has been started for you.
a. b.
15 + 13 = _____ 14 + 23 = _____
10 3
c. d.
16 + 14 = ____ 14 + 26 = ____
e. f.
21 + 17 = ____ 17 + 23 = ____
g. h.
21 + 18 = ____ 18 + 12 = ____
Date: 9/20/13
Name Date
a. 13 + 26 = _____ b. 19 + 21 = _____
____ + ____ = ____ ____ + ____ = ____
____ + ____ = ____ ____ + ____ = ____
Date: 9/20/13
Name Date
1. Solve using number bonds. Write the two number sentences that show that you
added the ten first. Draw quick tens and ones if that helps you.
a. 13 + 16 = ____ b.
16 + 23 = ____
10 3
10 6
16 + 10 = 26 23 + 10 = _____
26 + 3 = 29 _____ + 6 = _____
c. d.
16 + 14 = ____ 14 + 26 = ____
10 4
10 4
16 + 10 = ____ 26 + 10 = ____
____ + 4 = ____ ____ + ___ = ____
e. f.
17 + 13 = ____ 27 + 13 = ____
10 3
___ + ___ = ____ ___ + ___ = ____
___ + ___ = ____ ___ + ___ = ____
Date: 9/20/13
2. Solve using number bonds. The first row has been started for you.
a. b.
14 + 13 = _____ 24 + 14 = _____
10 3
14 + 10 = _____ ___ + ___ = ____
_____ + 3 = _____ ___ + ___ = ____
c. d.
15 + 14 = ____ 24 + 15 = ____
e. f.
22 + 17 = ____ 27 + 12 = ____
g. h.
18 + 12 = ____ 28 + 12 = ____
Date: 9/20/13
Lesson 25




A chipmunk hides 11 acorns under a tree. Later, he gives 5 acorns to

his friend. How many acorns does the chipmunk have? Use the
RDW process to solve the problem.
Extension: A squirrel has double the number of acorns the chipmunk
had to begin with. How many acorns does the squirrel have?
Note: Today's problem challenges students to pay attention to the
differences in a story problem. During the Debrief, students
compare yesterday's Application Problem with today's, analyzing the
parts and the whole or total in each problem.
 Get to 10 or 20 1.OA.6 (4 minutes)

 Sprint Targeting Core Fluency: Missing Addends for Sums of Ten(s) 1.OA.6 (10 minutes)
Get to 10 or 20 (4 minutes)
Materials: (S) 1 dime and 10 pennies
Note: This activity uses dimes and pennies as abstract representations of tens and ones to help students
become familiar with coins, while simultaneously providing practice with missing addends to ten(s).
Date: 9/20/13
For the first two minutes:

 Step 1: Lay out 0–10 pennies in 5-group formation and ask students to identify the amount shown
(e.g., 9 ones).
 Step 2: Ask for the addition sentence to get to 10 (e.g., 9 ones + 1 ones).
For the next two minutes:
 Repeat Steps 1 and 2, then add a dime and ask students to identify the amount shown (e.g., 1 ten 9
or 9 cents + 10 cents = 19 cents) and a new addition sentence (e.g., 19 cents + 1 cent = 20
cents).
Vary the unit terminology throughout the activity (ones, pennies, cents, tens, dimes).
Sprint Targeting Core Fluency: Missing Addends for Sums of Ten(s) (10 minutes)
Materials: (S) Missing Addends for Sums of Ten(s) Sprint
Note: The first two quadrants of this Sprint focuses on partners to 10, which reviews the core fluency
standard and prepares students for today’s lesson. The third and fourth quadrants relate partners to 10 to
corresponding partners to 20. This adds excitement to the grade level fluency goals as students see how
these equations relate to larger numbers.

Note: This anticipatory fluency practices taking out 1 or 2 from two-digit numbers in order to prepare
students to use this skill when adding 2 two-digit numbers in upcoming lessons.
Choose numbers between 0 and 10 and follow the paradigm below.
T: Take out 1 from each number. 6. (Snap.)
S: 1 and 5.
Continue with other numbers within 10. Then start again at 6.
T: 6.
S: 1 and 5.
T: 16.
S: 1 and 15.
T: 26.
S: 1 and 25.
T: 36.
S: 1 and 35.
After students take out 1 for a minute, start again and take out 2.
Date: 9/20/13
Materials: (T) 5 ten-sticks (4 red and 1 yellow) (S) 4 ten-sticks

from math toolkit, personal white board NOTES ON
MULTIPLE MEANS
Students gather in the meeting area with their materials in a FOR ACTION AND
semi-circle formation. EXPRESSION:
The first 10 minutes of Lesson 25’s Concept Development can More advanced students may choose
be used to solidify the learning that has occurred in Lesson 24. to show how they solved some
Three sets of problems have been provided for students who problems using the arrow way. This
are ready to extend their double-digit addition skills. The shows you that these students are
teaching sequence from Lesson 24 may be used to guide thinking more abstractly while adding
instruction. Students should be encouraged to use their cubes, two-digit numbers.
quick ten drawing, or the number bond to solve their problems.
Note that Problems 10–12 involve numbers greater than 40.
Encourage students to use place value language to describe and
compare strategies for solving. Ask questions such as, “What is
another way this can be solved? Why did you choose your
method?”
Problems 1–4 Problems 5–8 Problems 9–12
15 + 12 24 + 13 37 + 22
15 + 13 26 + 13 46 + 23
15 + 15 27 + 13 46 + 24
16 + 14 12 + 28 53 + 17
After 10 minutes of practice, proceed with the following:

T: (Write 17 + 13.) How could we solve this?
S: 17 + 10 = 27. 27 + 3 = 30. (As students describe, show the number
bond and write two number sentences.)
T: Great job! So far, we have been practicing to add the tens first as an
easy way to add two-digit numbers. What if I wanted to add my tens at
the end? How else might we start?
S: We can add the ones first. 17 + 3 is 20, and then 20 + 10 is 30. (As
students describe, use the number bond and number sentences as
shown.)
T: Great strategies! Earlier today, we were adding on tens first. This
time, we can add the ones first. Let’s try some more!
Date: 9/20/13
Repeat the process following the suggested sequence: 18 + 12,

28 + 12, 18 + 22, 16 + 23, 16 + 24, and 21 + 19. Students may NOTES ON
choose to continue practicing adding on the tens first or try MULTIPLE MEANS
MP.5
adding the ones first using the number bond or the arrow way FOR ACTION AND
and explain their choice.
EXPRESSION:
Encourage students to explain their
thinking about adding or subtracting
Students should do their personal best to complete the Problem tens. Students may learn as much
Set within the allotted 10 minutes. For some classes, it may be from each other’s reasoning as from
the lesson. As the teacher, you will
appropriate to modify the assignment by specifying which
learn more about their level of thinking
problems they work on first.
and ability to express that thinking.
Lesson Objective: Add a pair of two-digit numbers

when the ones digits have a sum less than or equal to
10.
the lesson.
 Look at Problem 1(c) and 1(d). Why can’t we
use the strategy to get to the next ten in 1(c)
while we can in 1(d)?
 In Problem 2(g), which addend did you start
with? Why?
 Share your strategy for solving 2(h) with your
partner. How are your strategies similar or
different?
 Look at Problem 2(h). How might a number bond look different for using the adding the ten strategy
compared to the adding the ones strategy?
 Look at Problem 2(c). How can you use the arrow way to show the different ways to solve this
problem?
Date: 9/20/13
 How is the adding the ten strategy similar and

different compared to the adding the ones
strategy? How does that show in your number
bonds and the two number sentences that
follow the number bond?
today’s lesson?

Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 25 Sprint CF 1•4
Number correct:
Name Date
1 5 + ☐ = 10 16 9 + ☐ = 10
2 9 + ☐ = 10 17 19 + ☐ = 20
3 10 + ☐ = 10 18 5 + ☐ = 10
4 0 + ☐ = 10 19 15 + ☐ = 20
5 8 + ☐ = 10 20 1 + ☐ = 10
6 7 + ☐ = 10 21 11 + ☐ = 20
7 6 + ☐ = 10 22 3 + ☐ = 10
8 4 + ☐ = 10 23 13 + ☐ = 20
9 3 + ☐ = 10 24 4 + ☐ = 10
10 ☐ + 7 = 10 25 14 + ☐ = 20
11 2 + ☐ = 10 26 16 + ☐ = 20
12 ☐ + 8 = 10 27 2 + ☐ = 10
13 1 + ☐ = 10 28 12 + ☐ = 20
14 ☐ + 2 = 10 29 18 + ☐ = 20
15 ☐ + 3 = 10 30 11 + ☐ = 20
Date: 9/20/13
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 25 Sprint CF 1•4
Number correct:
Name Date
1 10 + ☐ = 10 16 5 + ☐ = 10
2 0 + ☐ = 10 17 15 + ☐ = 20
3 9 + ☐ = 10 18 9 + ☐ = 10
4 5 + ☐ = 10 19 19 + ☐ = 20
5 6 + ☐ = 10 20 8 + ☐ = 10
6 7 + ☐ = 10 21 18 + ☐ = 20
7 8 + ☐ = 10 22 2 + ☐ = 10
8 2 + ☐ = 10 23 12 + ☐ = 20
9 3 + ☐ = 10 24 3 + ☐ = 10
10 ☐ + 7 = 10 25 13 + ☐ = 20
11 2 + ☐ = 10 26 17 + ☐ = 20
12 ☐ + 8 = 10 27 4 + ☐ = 10
13 1 + ☐ = 10 28 16 + ☐ = 20
14 ☐ + 9 = 10 29 18 + ☐ = 20
15 ☐ + 2 = 10 30 12 + ☐ = 40
Date: 9/20/13
Name Date
1. Solve using number bonds. This time, add the tens first. Write the 2 number
sentences to show what you did.
a. b.
11 + 14 = ____ 21 + 14 = ____
c. d.
14 + 15 = ____ 26 + 14 = ____
e. f.
26 + 13 = ____ 13 + 24 = ____
Date: 9/20/13
2. Solve using number bonds. This time, add the ones first. Write the 2 number
a. b.
29 + 11 = ____ 17 + 13 = ____
c. d.
14 + 16 = ____ 26 + 13 = ____
e. f.
28 + 11 = ____ 12 + 27 = ____
g. h.
18 + 12 = ____ 22 + 18 = ____
Date: 9/20/13
Name Date
Solve using number bonds. Write the 2 number sentences to record what you did.
a. b.
12 + 27 = ______ 21 + 19 = ______
Date: 9/20/13
Name Date
1. Solve using number bonds. This time, add the tens first. Write the 2 number
a. b.
12 + 14 = ____ 14 + 21 = ____
c. d.
15 + 14 = ____ 25 + 14 = ____
e. f.
23 + 16 = ____ 16 + 24 = ____
Date: 9/20/13
2. Solve using number bonds. This time, add the ones first. Write the 2 number
a. b.
27 + 10 = ____ 27 + 13 = ____
c. d.
13 + 26 = ____ 26 + 14 = ____
e. f.
12 + 18 = ____ 18 + 21 = ____
g. h.
19 + 11 = ____ 21 + 19 = ____
Date: 9/20/13
Lesson 26
sum greater than 10.




It snowed 7 days in February and the same number of days in March.

How many days did it snow in those two months? Use the RDW process
to solve the problem.
Extension: It snowed 3 days in January. How many days did it snow in
all 3 months? How many more days did it snow in February than in
January?
Note: Today's problem gives students the chance to work with equal
parts. Some students may struggle when only one number is given.
Circulate and notice which students are reading and making sense of
the problem. Students who are struggling may need more support as
they read through the problem to draw as they go.
 Sprint Targeting Core Fluency: Missing Addends for Sums of Ten(s) 1.OA.6 (10 minutes)
Sprint Targeting Core Fluency: Missing Addends for Sums of Ten(s) (10 minutes)
Materials: (S) Missing Addends for Sums of Ten(s) Sprint from G1–M4–Lesson 25
Note: Students complete the same Sprint from the prior day’s lesson as an opportunity to build confidence as
they work to master the core fluency of the grade level and to extend this thinking to larger numbers.
Between Sprints, engage the students in jumping jacks or running in place as they count from 40 to 80. This
keeps their math minds going and builds confidence for the second Sprint.
Lesson 26: Add a pair of two-digit numbers when the ones digits have a sum
greater than 10. 4.F.42
Date: 9/20/13
Materials: (T) 5 ten-sticks (3 red and 2 yellow) (S) 4 ten-sticks from math toolkit, personal white board
Students gather at the meeting area with their partner and materials in a semi-circle formation.
T: (Write 19 + 15 on the chart and show with 19 red and 15 yellow linking cubes.) Partner A, make 19
with your cubes. Partner B, make 15 with yours.
S: (Show cubes in a ten-stick and some ones to match their addend.)
T: Let’s add on the tens first to solve.
T/S: (Move the yellow ten-stick next to the red ten-stick.)
T: 19 and 10 is?
S: 29.
T: What do we still have to add?
S: 5.
T: Add 5 to 29. (Wait as students use their cubes to solve.)
T: How did you add 5 to 29?
S: I can count on. Twenty niiiine 30, 31, 32, 33, 34.  29
needs 1 more to make 30, so I got 1 from 5. That gave
us 30 and 4. That’s 34.  9 needs 1 more to make 10.
2 tens and 1 ten is 3 tens. Now we have 3 tens plus 4
ones. That’s 34.
T: Let’s draw a number bond that shows exactly how we
solved 19 + 15. We are starting with 19. Why did we
break apart 15 into 10 and 5?
S: We added on the ten first, so we took out 10 from 15.
5 is the other part of 15.
T: So our first number sentence is?
S: 19 + 10 = 29.
T: (Record.) Next? (Write 29 + 5 = .) How can we NOTES ON
record what we did to add 5? MULTIPLE MEANS
S: Break apart 5 into 1 and 4. We needed the 1 to make OF ENGAGEMENT:
the next ten. Some students may need extra time to
T: (Write the number bond.) 29 + 1 is? solidify their understanding of the
adding on the ten strategy. Give them
S: 30. another sequence of problems for
T: 30 + 4 is? further practice rather than
S: 34. introducing a new strategy.
T: (Complete the number sentence.)
Date: 9/20/13
Repeat the process following the suggested sequence, releasing students to work independently, in pairs, or
small groups, as possible: 19 + 16, 19 + 18, 18 + 17, 17 + 15, 16 + 16, and 15 + 18.
Chart the problems with their number bonds and two number sentences, listing them vertically. During the
next component of the lesson, these solutions will be juxtaposed to solutions completing the ten first.
T: Let’s look at 19 + 15 again. Partner A, make 19 with
your cubes. Partner B, make 15. (Show 19 and 15 with
cubes.) Before, we broke 15 into 10 and 5 because
adding on the tens is easy. What’s another strategy we
know that uses ten?
S: Make the next ten!
T: Yes! Use your cubes to make the next ten and solve
19 + 15.
S: 19 needs 1 more to make 20, so we took 1 from 15 to
make 20. That gave us 3 tens and 4 ones. That’s 34.
 19 plus 1 is 20. 20 plus 14 is 30 and 4. That’s 34.
(As students describe, make a number bond below the
number sentence showing 15 broken apart into 1 and
14.)
T: 19 needs how many more to make the next ten?
(Point to 19 cubes.)
S: 1 more.
T: (Take away 1 cube from the 5 in 15 and place with 19 cubes.) How many tens did we make from 19?
S: 2 tens.
T: We still need to add 14. 20 + 14 is?
S: 34.
T: How did we break apart 15 this time? Why? (Point to how the yellow cubes are decomposed.)
S: We broke it into 1 and 14.  We took 1 from 15 because 19 needs 1 more to make the next ten.
When we took away 1, there was still 14 left from the 15.
T: Work with your partner and write the two number sentences that show how we made the next ten
first to solve.
S: (Write 19 + 1 = 20 and 20 + 14 = 34.)
Repeat the process, modeling with cubes and number bonds using the same sequence from above and chart
the number bonds and two number sentences.
T: (Point to the chart.) Look at the two ways we solved the same addition problem. What do you
notice about the difference in how we broke apart one of the addends?
S: When we want to add on the tens first, we always break apart the number to 10 and some ones.
But when we want to make the next ten, we break apart the addend to get out the number we need
and then add the rest.  If we start with 19, we take out a 1 from the other addend because 19 and
1 makes 20. If we start with 18, we take out a 2 from the other addend because 18 + 2 = 20.
Date: 9/20/13

by specifying which problems they work on first. Some
problems do not specify a method for solving.
Lesson Objective: Add a pair of two-digit numbers

when the ones digits have a sum greater than ten.
the lesson.
 How are Problems 1(a) and 1(b) related? How
can solving 1(a) help you solve 1(b)?
 Which strategy is easier for you to use when
you add? Adding on the ten first or making the
next ten first? Explain why it’s easier for you.
 Using what we learned today, try solving
49 + 11. Which strategy did you use?
 Look at the Application Problem from today
and yesterday. How are they similar? How are
they different?
Date: 9/20/13

Date: 9/20/13
Name Date
1. Solve using a number bond to add ten first. Write the 2 addition sentences that
helped you.
a. b.
18 + 14 = ____ 14 + 17 = ____
10 4 10 4
17 + 10 = 27
18 + 10 = 28
27 + 4 = 31
28 + 4 = 32
c. d.
19 + 15 = ____ 18 + 15 = ____
10 5 10 5
19 + 10 = _____
18 + 10 = _____
____ + 5 = _____
____ + 5 = _____
e. f.
19 + 13 = ____ 19 + 16 = _____
10 3
10 6
19 + 10 = _____ 19 + 10 = _____
____ + ____ = _____ ____ + ___ = _____
Date: 9/20/13
2. Solve using a number bond to make a ten first. Write the 2 number sentences that
helped you.
a. b.
19 + 14 = 18 + 13 =
_____ _____
1 13 2 11
18 + 2 = 20
19 + 1 = 20
20 + 11 = 31
20 + 13 = 33
c. d.
18 + 14 = _____ 18 + 16 = ____
2 12
2 14
18 + 2 = ____ 18 + 2 = ____
20 + 12 = ____ ____ + 14 = ____
e.
15 + 17 = ____
f. 17 + 18 = ____
12 3 15 2
____ + 3 = ____ ____ + ____ = ____

____ + 12 = ____ ____ + ____ = ____
Date: 9/20/13
Name Date
1. Solve using number bonds to add ten first. Write the 2 number sentences that
helped you.
a. 15 + 19 = ____ b. 19 + 17 = ____
____ + ____ = ____ ____ + ____ = ____
____ + ____ = ____ ____ + ____ = ____
2. Solve using number bonds to make a ten. Write the 2 number sentences that helped
you.
c. d.
15 + 19 = ____ 19 + 17 = ____
____ + ____ = ____ ____ + ____ = ____
____ + ____ = ____ ____ + ____ = ____
Date: 9/20/13
Name Date
1. Solve using a number bond to add ten first. Write the 2 addition sentences that
helped you.
a. b.
18 + 13 = ____ 13 + 19 = ____
10 3 10 3
18 + 10 = 28 19 + 10 = 29
28 + 3 = 31 29 + 3 = 32
c. d.
17 + 15 = ____ 17 + 16 = ____
10 5 10 6
17 + 10 = _____
17 + 10 = _____
____ + 5 = _____
____ + 6 = _____
e. f.
17 + 14 = ____ 19 + 17 = _____
10 4 10 7
17 + 10 = _____
19 + 10 = _____
____ + ____ = _____
____ + ___ = _____
Date: 9/20/13
2. Solve using a number bond to make a ten first. Write the 2 number sentences that
helped you.
a. b.
19 + 13 = 19 + 14 =
_____ _____
1 12 1 13
19 + 1 = 20 19 + 1 = 20
20 + 12 = 32 20 + 13 = 33
c. d.
18 + 15 = _____ 18 + 17 = ____
2 13
2 15
18 + 2 = ____ 18 + 2 = ____
20 + 13 = ____ ____ + 15 = ____
e.
18 + 19 = ____
f. 19 + 19 = ____
17 1 18 1
____ + 1 = ____ ____ + ____ = ____

____ + 17 = ____ ____ + ____ = ____
Date: 9/20/13
Lesson 27
sum greater than ten.




It snowed 14 days. Some snowy days, we stayed

home. Nine snowy days we were in school. How
many snowy days did we stay home? Use the RDW
process to solve the problem.
Extension: How many more days did it snow when
we were in school compared to when we were
home?
Note: Today's problem poses a take apart with
addend unknown problem type. Continue to remind
students of the simple questions they can ask
themselves as they attempt the problem: Can I draw
something? What can I draw? What does my
drawing show me that can help me with the
question? The goal is that over time these questions
be internalized by the students.

 Race to the Top 1.OA.6 (5 minutes)
greater than ten. 4.F.52
Date: 9/20/13

graders. Give the appropriate Practice Set to each student. Students who completed all questions correctly
on their most recent Practice Set should be given the next level of difficulty. All other students should try to
improve their scores on their current levels.
Race to the Top (5 minutes)

Materials: (S) Personal white boards with Race to the Top insert
Note: This fluency primarily targets the core fluency for Grade 1.
Students take turns rolling the dice, saying an addition sentence and recording the sums on the graph. The
game ends when time runs out or one of the columns reaches the top of the graph.

Note: This anticipatory fluency practices taking out 1 or 2 from two-digit numbers in order to prepare
students to use this skill when adding two two-digit numbers in upcoming lessons.
Choose numbers between 0 and 10 and follow the script below.
T: Take out 1 from each number. 6. (Snap.)
S: 1 and 5.
Continue with other numbers within 10. Then start again at 6.
T: 6.
S: 1 and 5.
T: 16.
S: 1 and 15.
T: 26.
S: 1 and 25.
T: 36.
S: 1 and 35.
After students take out 1 for a minute. Then start again and take out 2.
Date: 9/20/13

NOTES ON
Materials: (S) Personal white boards, 4 ten-sticks from the MULTIPLE MEANS
math tool kit (optional) FOR ACTION AND
EXPRESSION:
The time allotted for Lesson 27’s Concept Development can be Students may choose how they want to
used to solidify the learning that has occurred in Lesson 26. solve problems—with drawings,
Three sets of problems have been provided for students to number bonds, or the arrow way.
practice and gain accuracy and efficiency when adding a pair of Students should begin to move away
double digit numbers. The teaching sequence from Lesson 26 from drawing to the more abstract
may be used to guide instruction. Students should be method of problem solving. However,
encouraged to use their cubes, quick ten drawings, number not all students will be ready to
bonds with pairs of number sentences to solve (MP.5). Note abstractly solve problems, so support
students wherever they are in their
that Problems 9–12 involve numbers greater than 40. This is
learning and guide them as they
intended to serve as a challenge set for advanced learners.
progress.
Encourage students to use place value language as they
describe how their strategy works. Challenge them to compare
MP.5
strategies with their partners and look for related problems
within the set.
19 + 11 18 + 12 17 + 23
19 + 13 17 + 17 27 + 25
NOTES ON
18 + 15 17 + 16 24 + 29 MULTIPLE MEANS
17 + 16 16 + 15 34 + 27 FOR ACTION AND
EXPRESSION:
Problem Set (10 minutes) Continue to challenge your advanced
students. After they have completed
Students should do their personal best to complete the Problems 9–12, give students some
Problem Set within the allotted 10 minutes. For some word problems to solve with similar
classes, it may be appropriate to modify the assignment numbers.
Lesson Objective: Add a pair of two-digit numbers when the ones digits have a sum greater than ten.
Invite students to review their solutions for the Problem Set. They should check work by comparing answers
with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can
be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the
lesson.
Date: 9/20/13

 How can solving Problem 1(a) help solve 1(b)?
 Look at Problem 1(c) and 1(d). Explain how
they are related. Why do they have the same
answers?
 Look at 2(f). Which addend did you start with
to solve this problem? Why?
 Which ten strategy, make the next ten or add
on the ten, is easier for you to use when
adding? Explain your choice.
 Look at today’s Application Problem. Explain
your drawing and solution to your partner.

Date: 9/20/13
Names Date
Race to the Top!
2 3 4 5 6 7 8 9 10 11 12
Date: 9/20/13
Name Date
1. Solve using number bonds with pairs of number sentences. You may draw quick tens
and some ones to help you.
a. b.
19 + 12 = ____ 18 + 12 = ____
c. d.
19 + 13 = ____ 18 + 14 = ____
e. f.
17 + 14 = ____ 17 + 17 = ____
g. h. 18 + 19 = ____
18 + 17 = ____
Date: 9/20/13
2. Solve. You may draw quick tens and some ones to help you.
a. b.
19 + 12 = ____ 18 + 13 = ____
c. d.
19 + 13 = ____ 18 + 15 = ____
e. f.
19 + 16 = ____ 15 + 17 = ____
g. h.
19 + 19 = ____ 18 + 18 = ____
Date: 9/20/13
Name Date
a. b.
16 + 15 = ____ 17 + 13 = ____
c. d.
16 + 16 = ____ 17 + 15 = ____
Date: 9/20/13
Name Date
a. b.
17 + 14 = ____ 16 + 14 = ____
c. d.
17 + 15 = ____ 18 + 13 = ____
e. f.
18 + 15 = ____ 18 + 16 = ____
g. 19 + 15 = ____ h. 19 + 16 = ____
Date: 9/20/13
2. Solve. You may draw quick tens and some ones to help you.
a. b.
17 + 14 = ____ 16 + 15 = ____
c. d.
17 + 15 = ____ 16 + 16 = ____
e. f.
19 + 16 = ____ 14 + 19 = ____
g. h.
19 + 19 = ____ 18 + 18 = ____
Date: 9/20/13
Lesson 28
Objective: Add a pair of two-digit numbers with varied sums in the ones.




Anton collected some crayons in his pockets. His teacher gave him 2 more. When he counted all of his
crayons, he had 16 crayons. How many crayons did Anton have in his pockets originally? Use the RDW
process to solve the problem.
Note: Today's problem is the challenging add to with start unknown problem type. Although crayons were
added within the story because the start is the unknown number, the problem requires subtraction.
Several images are shown below representing students’ varied approaches.
In Model A, the student draws all 16 crayons to begin with, partitioning the last two in order to find the initial
14.
In Model B, the student may have drawn the part they know, 2, with the total, 16
drawn below. The student then counts up to add more circles until the quantity
matches 16, recounting to find the amount drawn.
In Model C, the student represents the unknown with an empty box and builds the
chunk of two on the end. This student could use a missing addend number sentence
or subtraction number sentence to solve the problem.
Model A Model B Model C
Lesson 28: Add a pair of two-digit numbers with varied sums in the ones.
Date: 9/20/13 4.F.62


 Coin Drop 1.OA.6, 1.NBT.6 (3 minutes)
 Make Ten: 9 Up 1.OA.6 (3 minutes)
 Addition Strategies Review 1.OA.6 (5 minutes)

graders. Students who completed all questions correctly on their most recent Practice Set should be given
the next level of difficulty. All other students should try to improve their scores on their current levels.
Coin Drop (3 minutes)

Materials: (T) 4 dimes, 10 pennies, can
Note: In this activity, students practice adding and subtracting ones and tens.
T: (Hold up a penny.) Name my coin.
S: A penny.
T: How much is it worth?
S: 1 cent.
T: Listen carefully as I drop coins in my can. Count along in your minds.
Drop in some pennies and ask how much money is in the can. Take out some pennies and show them. Ask
how much money is still in the can. Continue adding and subtracting pennies for a minute or so. Then repeat
the activity with dimes.
Make Ten: 9 Up (3 minutes)

Note: This fluency activity reviews how to calculate sums within 20 using the make ten strategy students
learned in Module 2.
T: When I say up, tell me how to get to ten from my number. 9 up.
S 9 + 1 = 10.
Repeat with other numbers within 10.
Date: 9/20/13 4.F.63

In the next section, model the first few problems with a number bond and write the two-step addition
sentences.
T: (Write 9 + 3 = .) 9 up.
S: 9 + 1 = 10.
T (Draw a number bond under the 3 with 1 as a part and write 9 + 1 = 10, then point to the 3). How
much is left to add?
S: 2.
T: (Write 2 as the other part, and the second addition sentence, 10 + 2.) 10 + 2 is?
S: 12.
T: So, 9 + 3 is?
Repeat with the following suggested sequence: 9 + 3, 9 + 5, 9 + 6, 9 + 9, 9 + 8. When students are ready,
consider omitting the number bond and number sentences so students can mentally review the make a ten
strategy.
Addition Strategies Review (5 minutes)

Note: This review fluency helps strengthen students’ understanding of the make ten and add the ones
addition strategies, as well as their ability to recognize appropriate strategies based on problem types.
T: (Partner A, Show me 9 on your Magic Counting Sticks. Partner B, show me 6. If I want to solve 9 + 6,
how can I make a 10?
S: Take one from the 6 and add 1 to 9.
T: Yes. Show me! We changed 9 + 6 into an easier problem. Say our new addition sentence with the
solution.
S: 10 + 5 = 15.
T: If we want to add 3 to 15, should we make a ten to help us?
S: No. We already have a ten!
T: Should we add 3 to our 5 or our 10?
S: Our 5.
T: Yes! Show me! Say the addition sentence.
S: 15 + 3 = 18.

NOTES ON
MULTIPLE MEANS
Materials: (T) Chart paper (S) Personal white board, 4 ten-
OF ENGAGEMENT:
sticks from math toolkit (optional)
Appropriate scaffolds help all students
Have students gather in the meeting area with their materials. feel successful. As students are
working, keep a close eye to see if any
The time allotted for Lesson 28’s Concept Development is set would benefit from some one-on-one
aside to consolidate and solidify the learning that has occurred problem solving with you.
Date: 9/20/13 4.F.64

in Lessons 24–27. Three sets of problems have been provided

for practice so that students gain accuracy and efficiency when NOTES ON
adding a pair of double-digit numbers. MULTIPLE MEANS
The teaching sequence from earlier lessons may be used to FOR ACTION AND
guide remedial instruction. Students should be encouraged to EXPRESSION:
use their number bonds and the arrow way to solve their Continue to challenge your advanced
problems while having full access to drawing materials and students. After they have completed
manipulatives (MP.5). Note that Problems 11–15 involve sums Problems 11–15, encourage them to
greater than 40. This is intended to serve as a challenge set for write a word problem to match one of
advanced learners. the number sentences. Have students
who write a word problem trade
Encourage students to use place value language as they papers and solve each other’s problem.
describe their methods and strategies for solving. Challenge
them to compare strategies with their partners and explain
their own method.
15 + 2 14 + 3 13 + 4
15 + 20 14 + 20 23 + 40
28 + 12 17 + 23 28 + 22
18 + 14 17 + 15 26 + 25
17 + 16 16 + 19 36 + 27

Lesson Objective: Add a pair of two-digit numbers with

varied sums in the ones.
Date: 9/20/13 4.F.65


 Which method did you use the most to solve
today’s addition problems? Explain the reason for
your choice.
 Share how you solved Problem 2(f). How can
solving Problem 2(f) help you solve 2(h)?
 A student says he solved Problem 1(f) by adding 2
tens and 13 ones. Is he correct? Explain his
strategy for adding.
 With your partner, share how you solved your
Application Problem and act out each part of the
story. Explain how each part of your drawing or
tape diagram represents different parts of the
story.

Date: 9/20/13 4.F.66

Name Date
1. Solve using quick ten drawings, number bonds, or the arrow way. Check the
rectangle if you made a new ten.
a. 23 + 12 = ____ b. 15 + 15 = ____
c. d.
19 + 21 = ____ 17 + 12 = ____
e. f. 17 + 16 = ____
27 + 13 = ____
Date: 9/20/13 4.F.67

2. Solve using quick ten drawings, number bonds, or the arrow way.
a. 15 + 13 = _____ b. 25 + 13 = _____
c. d.
24 + 14 = ____ 25 + 15 = ____
e. f.
18 + 14 = ____ 18 + 18 = ____
g. 24 + 16 = ____ h. 17 + 18 = ____
Date: 9/20/13 4.F.68

Name Date
Solve using quick tens and ones, number bonds, or the arrow way.
a. b.
12 + 16 = ____ 26 + 14 = ____
c. d.
18 + 16 = ____ 19 + 17 = ____
Date: 9/20/13 4.F.69

Name Date
Solve using quick tens and ones, number bonds, or the arrow way.
a. b.
13 + 16 = ____ 15 + 16 = ____
c. d.
16 + 16 = ____ 26 + 12 = ____
e. f.
22 + 17 = ____ 17 + 15 = ____
g. h.
17 + 16 = ____ 18 + 17 = ____
Date: 9/20/13 4.F.70

i. j.
24 + 13 = ____ 15 + 24 = ____
k. l.
19 + 16 = ____ 14 + 22 = ____
m. n.
27 + 12 = ____ 28 + 12 = ____
o. p.
18 + 17 = ____ 19 + 18 = ____
Date: 9/20/13 4.F.71

Lesson 29
Objective: Add a pair of two-digit numbers with varied sums in the ones.




Kiana’s friend gave her 3 more stickers. Now Kiana has

16 stickers. How many stickers did Kiana already have?
Use the RDW process to solve the problem.
Note: This problem allows students to continue
practicing the challenging add to with start unknown
problem type. According to the Progressions Document,
students should have exposure to this problem type, but
mastery is not expected until Grade 2.
Students may employ a range of diverse strategies to
solve the problem, as depicted in the images to the right.
During the Debrief, invite students to share their
strategies as well as the drawings and notation they used
to record their thinking. If students find solving the
problem difficult, they can practice acting out their
solution with a partner as a way to check their thinking.

 Coin Drop 1.OA.6, 1.NBT.6 (3 minutes)
 Race to the Top 1.OA.6 (5 minutes)

Date: 9/20/13 4.F.72

Note: Excitement should be building in this third consecutive day of core fluency practice. Students have
had two days, and on this third day will have the chance to look back at their progress. Students who
completed all questions correctly on their most recent Practice Set should be given the next level of
difficulty. All other students should try to improve their scores on their current levels.
Students complete as many problems as they can in 90 seconds. Assign a counting pattern and start
number for early finishers, or tell them to practice make ten addition or subtraction on the backs of their
papers. Collect and correct any Practice Sets completed within the allotted time.
Coin Drop (3 minutes)

Materials: (T) 4 dimes, 10 pennies
Note: In this activity, students practice adding and subtracting ones and tens.
See yesterday’s fluency for instructions.
Race to the Top (5 minutes)

Materials: (S) Personal white boards with Race to the Top insert
Note: This fluency primarily targets the core fluency for Grade 1.
Students take turns rolling the dice, saying an addition sentence and recording the sums on the graph. The
game ends when time runs out or one of the columns reaches the top of the graph.
Concept Development (32 minutes) NOTES ON

MULTIPLE MEANS
Materials: (T) Chart paper (S) Personal white board, 4 ten- FOR ACTION AND
sticks from math toolkit (optional), game cards for EXPRESSION:
Addition and Subtraction with Cards labeled F Encourage students to describe and
compare methods, strategies and
Have students gather in the meeting area with their materials. written notation with their partners.
The time allotted for Lesson 29’s Concept Development is also At this point, most of your students
set aside to consolidate and solidify the learning that has should be as comfortable solving the
problems as they are describing their
occurred in Lessons 24–28. Just as in Lesson 28, three sets of
thinking while solving.
problems have been provided for practice so that students
gain accuracy and efficiency when adding a pair of double-digit
numbers.
NOTES ON
Students should be encouraged to use their number bonds and MULTIPLE MEANS
the arrow way to solve problems while having full access to OF ENGAGEMENT:
drawing materials and manipulatives (MP.5). Note that Appropriate scaffolds help all students
Problems 11–15 involve sums greater than 40. This is intended feel successful. As students are
to serve as a challenge set for advanced learners. working, keep a close eye to see if any
would benefit from some one-on-one
problem solving with you.
Date: 9/20/13 4.F.73

Challenge students to describe and compare methods, strategies, and written notation with their partners
MP.5 and explain why they chose to solve the way they did using terms such as tens, ones, addend, take apart,
add on the tens, and make the next ten.

16 + 12 26 + 12 34 + 23
28 + 12 27 + 13 24 + 42
18 + 15 17 + 15 23 + 27
18 + 18 16 + 15 28 + 25
17 + 16 18 + 17 26 + 37
For the last five minutes, partners play Addition and NOTES ON
Subtraction with Cards (follow instructions from G1–M4–
MULTIPLE MEANS
Lesson 12) with the new cards labeled, F.
FOR ACTION AND
EXPRESSION:
Continue to challenge your advanced
Students should do their personal best to complete the students. After they have completed
Problem Set within the allotted 10 minutes. For some classes, Problems 11–15 above, encourage
it may be appropriate to modify the assignment by specifying them to write a word problem to
which problems they work on first. match one of the number sentences.
Have students who write a word
problem trade papers and solve each
other’s problem.
Lesson Objective: Add a pair of two-digit numbers with varied sums in the ones.
Invite students to review their solutions for the Problem Set. They should check work by comparing answers
with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can
be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the
lesson.
Date: 9/20/13 4.F.74

 Look at Problems 2(b) and 2(h). Did you make

a new ten in both problems? Explain why this
is so.
 Look at Problem 1(h). Explain which method
or strategy you used to solve. Why did you
choose this particular method or strategy?
 How can you solve 2(f) using doubles?
 For problems where you need to make a new
ten (i.e., Problems 2(d), 2(g), 2(h), etc.), do you
prefer to add on the tens first or make a new
ten? Explain your choice.
 Share your drawings and solution with your
partner. What was your strategy for solving
this? Check your work by acting out each part
of the story and matching them to the parts of
your drawing.

Date: 9/20/13 4.F.75

Names Date
Race to the Top!
2 3 4 5 6 7 8 9 10 11 12
Date: 9/20/13 4.F.76

Name Date
a. b.
13 + 12 = ____ 23 + 12 = ____
c. d.
13 + 16 = ____ 23 + 16 = ____
e. f.
13 + 27 = ____ 17 + 16 = ____
g. h.
14 + 18 = ____ 18 + 17 = ____
Date: 9/20/13 4.F.77

2. Solve using quick ten drawings, number bonds, or the arrow way. Be prepared to
discuss how you solved during the Debrief.
a. b.
17 + 11 = ____ 17 + 21 = ____
c. d.
27 + 13 = ____ 17 + 14 = ____
e. f.
13 + 26 = ____ 17 + 17 = ____
g. h.
18 + 15 = ____ 16 + 17 = ____
Date: 9/20/13 4.F.78

Name Date
Solve using quick ten drawings, number bonds, or the arrow way.
a. b.
18 + 14 = ____ 14 + 23 = ____
c. d.
28 + 12 = ____ 19 + 21 = ____
Date: 9/20/13 4.F.79

Name Date
a. b.
13 + 15 = ____ 26 + 12 = ____
c. d.
23 + 16 = ____ 17 + 16 = ____
e. f.
14 + 17 = ____ 27 + 12 = ____
g. h.
15 + 18 = ____ 18 + 16 = ____
Date: 9/20/13 4.F.80

2. Solve using quick ten drawings, number bonds or the arrow way. Be prepared to
discuss how you solved during the Debrief.
a. b.
17 + 12 = ____ 21 + 17 = ____
c. d.
17 + 15 = ____ 27 + 12 = ____
e. f.
23 + 14 = ____ 18 + 17 = ____
g. h.
18 + 11 = ____ 18 + 18 = ____
Date: 9/20/13 4.F.81

G1-M4-Topic F Flashcards (and Review Subtraction)
13 + 14 26 + 13 F F
17 + 22 29 + 11 F F
15 +15 16 + 24 F F
28 + 12 29 + 11 F F
Date: 9/20/13 4.F.82

19 + 14 18 + 17 F F
17 + 15 16 + 15 F F
19 + 17 18 + 13 F F
17 + 16 18 - 6 F F
17 - 3 F
19 - 4 F
Date: 9/20/13 4.F.83

NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Task Lesson
1•4
2•3
Name Date
1. Fill in the missing numbers in the sequence.
16, ____, 18, ____, ____ 39, 38, ____, 36, ____, ____
36, ____, ____, 39, ____ 23, 22, ____, ____, ____
2. Write the number as tens and ones in the place value chart, or use the place value
chart to write the number.
tens ones tens ones
a. 31 b. 19
tens ones tens ones
c. _____ 2 6 d. _____ 1 5

Date: 9/20/13 4.S.1
3. Some numbers have been placed below in order from 0 to 40.

a. Place the numbers from the rectangle in order between the tens.
3 22 19 29 35
0 10 20 30 40
b. Shade in the tens or the ones on the place value charts below to show which digit
you looked at to help you put the pair of numbers in order from smallest to
greatest.
tens ones tens ones tens ones tens ones
2 2 2 9 2 9 3 5
4. Complete each sentence.
a. 39 is ____ tens and ____ ones.
b. 40 = ____ tens ____ ones.
c. 2 tens and 3 ones is the same as ______ ones.

Date: 9/20/13 4.S.2
5. Match the equal amounts.
a. 21 40 ones
b. 4 tens 3 tens 6 ones
c. 36 ones 1 ten 2 ones
d. 12 ones 2 tens 1 one
6.
a. Circle the number in each pair that is greater.
32 40 33 28
b. Circle the number that is less.
36 20 21 12
7. Use <, =, or > to compare the pairs of numbers.
a. 3 tens 5 ones 2 tens 8 ones
b. 30 3
c. 23 32
d. 19 21

Date: 9/20/13 4.S.3
8. Erik thinks 32 is greater than 19. Is he correct? Draw and write about tens and
ones to explain your thinking.
9. Find the mystery numbers. Use the arrow way to explain how you know.
a. 10 more than 19 is _______ b. 10 less than 19 is _______
c. 1 more than 19 is ________ d. 1 less than 19 is ________
10. Beth said 30 – 20 is the same as 3 tens – 2 tens. Is she correct? Explain your
thinking.

Date: 9/20/13 4.S.4
11. Solve for each unknown number. Use the space provided to draw quick tens, a
number bond, or the arrow way to show your work.
a. 30 + 6 = _____ b. 3 tens - _______________ = 1 ten
c. 11 + 10 = _____ d. 40 – 30 = _____
e. 17 + 20 = _____ f. 20 + _____ = 40
g. 15 + _____ = 35 h. 2 tens + 1 ten 2 >

Date: 9/20/13 4.S.5
Mid-Module Assessment Task Topics A–C

Standards Addressed


1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits, recording
the results of comparisons with the symbols >, =, and <.
based on place value, properties of operations, and/or the relationship between addition
and subtraction; relate the strategy to a written method and explain the reasoning used.
Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and
(positive or zero differences), using concrete models or drawings and strategies based on
place value, properties of operations, and/or the relationship between addition and
1
2
Focus on numbers to 40
3

Date: 9/20/13 4.S.6
Evaluating Student Learning Outcomes

A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing
understandings that students develop on their way to proficiency. In this chart, this progress is presented
from left (Step 1) to right (Step 4). The learning goal for each student is to achieve Step 4 mastery. These
steps are meant to help teachers and students identify and celebrate what the student CAN do now, and
what they need to work on next.

Date: 9/20/13 4.S.7
1•4
2•3
A Progression Toward Mastery
Assessment STEP 1 STEP 2 STEP 3 STEP 4

Task Item Little evidence of Evidence of some Evidence of some Evidence of solid
and reasoning without reasoning without reasoning with a reasoning with a
Standards a correct answer. a correct answer. correct answer or correct answer.
Assessed evidence of solid
reasoning with an
incorrect answer.
(1 Point) (2 Points) (3 Points) (4 Points)
1 The student is unable The student completes The student completes The student identifies
to complete any one at least one sequence. at least one sequence all numbers in the
sequence of numbers. as well as at least two sequences:
1.NBT.1 numbers in each  16, 17, 18, 19, 20
additional sequence OR
 39, 38, 37, 36, 35,
the student completes
34
two or more sequences
correctly.  36, 37, 38, 39, 40
 23, 22, 21, 20, 19
2 The student does not The student The student The student completes
demonstrate demonstrates demonstrates some all correctly:
understanding of tens inconsistent understanding of most a. 3-1 (or 2-11; 0-
1.NBT.2 and ones, and is unable understanding of tens aspects of tens and 31)
to complete more than and ones, completing ones, completing at
b. 1-9 (or 0-19)
one answer correctly. only two answers least three answers
correctly. correctly. c. 26
d. 15
3 The student The student The student The student correctly

demonstrates little or demonstrates limited demonstrates some orders numerals:
no understanding of understanding of the understanding of the  0 3 10 19 20 22 29
1.NBT.3 number sequence, and sequence of numbers sequence of numbers 30 35 40
orders one number or as greater or less than as greater or less than
 Accurately shaded
none correctly. each multiple of 10, each multiple of 10,
correctly ordering at correctly ordering  2 and 9 (ones)
For Part (b), the
student was unable to least two numbers three or four numbers.  2 and 3 (tens)
shade the pairs correctly. For Part (b), the
correctly. Or, for Part (b), the student shaded at least
student shaded at least one of the two pairs
one of the two pairs correctly.
correctly.

Date: 9/20/13 4.S.8
4 The student does not The student The student The student identifies
demonstrate demonstrates demonstrates any correct
understanding of tens inconsistent understanding of most interpretation of each
1.NBT.2 and ones within a given understanding of tens aspects of tens and quantity. For example,
number, and is unable and ones within a given ones within a given Part (a) is accurate with
to complete any number, answering number, answering at answers such as 0 tens
section correctly. one section correctly. least two sections 39 ones, 2 tens 19
correctly. ones, etc. Typical
answers may be:
a. 3 tens 9 ones
b. 4 tens 0 ones
c. 23 ones
5 The student does not The student The student The students matches
demonstrate demonstrates limited demonstrates some all four equal amounts
understanding of the understanding of the understanding of the as follows:
1.NBT.2 equivalent equivalent equivalent a. 21 = 2 tens
representations of tens representations of tens representations of tens 1 one
and ones, and is unable and ones, matching and ones, matching
b. 4 tens = 40 ones
to match any equal one or two equal three equal amounts.
amounts. amounts. c. 36 tens
6 ones
d. 12 ten
2 ones
6 The student The student The student The students correctly

demonstrates limited demonstrates some demonstrates the identifies:
ability to compare ability to compare ability to compare a. The greater
1.NBT.3 numbers, correctly numbers, (e.g., most numbers, numbers as
comparing one or none identifying greater by correctly comparing 40 33
of the four sets of not less), correctly three of the four
b. The lesser
numbers. comparing two of the comparisons.
numbers as
four sets of numbers.
20 12
7 The student is unable The student has limited The student has some The student correctly
to use symbols to ability to use symbols ability to use symbols answers:
compare numbers, and to compare numbers, to compare numbers, a. >
1.NBT.2 is unable to correctly correctly answering correctly answering
b. >
1.NBT.3 answer any of the four one of the four two or three of the
comparisons. comparisons. four comparisons. c. <
d. <

Date: 9/20/13 4.S.9
8 The student The student uses The student The student correctly:
demonstrates little to drawings or words to demonstrates some  Uses drawings or
no understanding of accurately depict at understanding of using words that depict
1.NBT.2 comparing numbers least one of the two place value to compare place value to
1.NBT.3 based on tens and numbers, numbers. accurately explain
ones, answering demonstrating limited The student correctly that 32 is greater
incorrectly. There is no understanding of the identifies the greater than 19.
evidence of reasoning. use of place value to number but does not
compare numbers. fully explain reasoning
using place value.
OR
The student answers
incorrectly due to error
such as transcription
but demonstrates
strong understanding
of place value through
drawing or words.
9 The student The students The students The student identifies

demonstrates little or demonstrates limited demonstrates ability to 29, 9, 20, and 18, and
no understanding of understanding of mentally add or accurately completes
1.NBT.5 mentally adding or mentally adding or subtract 10, correctly the charts to depict the
subtracting 10. subtracting 10, identifying four arrow way.
Answers are incorrect identifying at least two mystery numbers, but
and there is no correct mystery reasoning is unclear
evidence of reasoning. numbers, but does not because no charts have
complete any charts been completed
accurately. accurately.
OR
The student accurately
completes charts but
makes an error in
mental calculation on
one or two of (a), (b),
(c), or (d.)

Date: 9/20/13 4.S.10
10 The student’s answer is The student’s answer The student’s answer is The student correctly:
incorrect and there is includes some correct but there is no  Draws or writes to
1.NBT.2 no evidence of indication of response. explain that Beth is
reasoning. understanding either OR correct.
the connection  Grounds explanation
The student’s
between 30 and 3 tens in understanding of
explanation is
or 20 and 2 tens, but place value in some
mathematically correct
the student does not way.
and rooted in an
follow through with
understanding of place
this thinking to
value, but there is an
correctly answer the
error in their
question.
transcription of the
numerals or other
calculation error that
leads to an incorrect
response.
11 The student The student The student The student correctly:

demonstrates little or demonstrates some demonstrates the  Solves
1.NBT.4 no ability to add or ability to add (or ability to add (and
a. 36
subtract two-digit subtract) two-digit subtract) two-digit
1.NBT.6 numbers to 40, numbers, answering numbers, answering at b. 2 tens
answering two or least four of eight least six of eight c. 21
fewer questions correctly, and correctly, or uses d. 10
correctly. demonstrates sound process
e. 37
misunderstandings in throughout with at
place value. most four calculation f. 20
errors. g. 20
h. 3 tens 2 ones
(or 32)
 Represents process
to accurately solve
through drawings,
number bonds, or
the arrow way. The
notation
demonstrates use of
a sound strategy for
adding or
subtracting.

Date: 9/20/13 4.S.11

Date: 9/20/13 4.S.12

Date: 9/20/13 4.S.13

Date: 9/20/13 4.S.14

Date: 9/20/13 4.S.15

Date: 9/20/13 4.S.16
NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment Task Lesson
1•4
2•3
Name Date
1. Use the RDW process to solve the following problems. Write the answer in the
place value chart.
a. Maria is having a party for 17 of her friends. She already invited some friends.
She has 12 more invitations to send. How many friends has she already invited?
tens ones
Maria already invited _____ friends.
b. Maria bought 11 red balloons and 8 white balloons. How many balloons did she
buy?
tens ones
Maria bought _____ balloons.
c. Maria had 17 friends at her party. Some of them went outside to see the piñata.
There were 4 friends remaining in the room. How many friends went outside?
tens ones
_____ friends went outside.

Date: 9/20/13 4.S.17
1•4
2•3
2. Fill in the missing numbers in each sequence:

a. 27, 28, _____, _____, _____, 32 b. _____, 17, _____, 19, _____
3.
a. Mark says that 34 is the same as 2 tens and 14 ones. Suki says that 34 is the
same as 34 ones. Are they correct? Explain your thinking.
b. Use <, =, or > to compare the pairs of numbers.
i. 3 tens 25 ones ii. 1 tens 14 ones 2 tens 4 ones
iii. 33 2 tens 12 ones iv. 26 1 ten 25 ones
c. Find the mystery numbers. Explain how you know the answers.
10 more than 29 is _______ 10 less than 29 is ________
1 more than 29 is _______ 1 less than 29 is ________

Date: 9/20/13 4.S.18
1•4
2•3
4. Solve for each unknown number. Use the space provided to draw quick tens, a
number bond, or the arrow way to show your work. You may use your kit of ten-
sticks if needed.
a. 18 + 3 = ____ b. 28 + 10 = ____ c. 40 - 30 = ____
d. 28 + 2 = ____ e. 28 + 6 = ____ f. 28 + 12 = ____
g. 15 + 15 = ____ h. 19 + 14 = ____ i. 16 + 18 = ____

Date: 9/20/13 4.S.19
1•4
2•3
End-of-Module Assessment Task Topics A–F

Standards Addressed
Represent and solve problems involving addition and subtraction.
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of
adding to, taking from, putting together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a symbol for the unknown
number to represent the problem. (See CCLS Glossary, Table 1.)
1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits, recording
the results of comparisons with the symbols >, =, and <.
based on place value, properties of operations, and/or the relationship between addition
and subtraction; relate the strategy to a written method and explain the reasoning used.
Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and
(positive or zero differences), using concrete models or drawings and strategies based on
place value, properties of operations, and/or relationship between addition and
1
2
Focus on numbers to 40
3

Date: 9/20/13 4.S.20
1•4
2•3
Evaluating Student Learning Outcomes

A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing
understandings that students develop on their way to proficiency. In this chart, this progress is presented
from left (Step 1) to right (Step 4). The learning goal for each student is to achieve Step 4 mastery. These
steps are meant to help teachers and students identify and celebrate what the student CAN do now, and
what they need to work on next.
Assessment STEP 1 STEP 2 STEP 3 STEP 4

Task Item Little evidence of Evidence of some Evidence of some Evidence of solid
and reasoning without reasoning without reasoning with a reasoning with a
Standards a correct answer. a correct answer. correct answer or correct answer.
Assessed evidence of solid
reasoning with an
incorrect answer.
(1 Point) (2 Points) (3 Points) (4 Points)
1 The student’s answers The student’s answers The student’s answers The student correctly:
are incorrect and there are incorrect but there are correct, but the  Solves each word
1. OA.1 is no evidence of is evidence of responses are problem
1. NBT. 2 reasoning. reasoning. For incomplete (e.g., may
a. She needs to
example, the student is be missing labels for
write 5 more
able to write a number the drawing, an
cards.
sentence. addition sentence, or
an explanation). The b. She has 19
student’s work is balloons.
essentially strong. c. 12 friends came
late.
 Circles the parts in
each drawing.
 Completes place
value charts
a. 0-5
b. 1-9
c. 1-2
2 The student is unable The student completes The student completes The student identifies
to complete any at least part of one at least one sequence all numbers in the
sequence of numbers. sequence. as well as at least one sequences:
1.NBT.1 number in the  27, 28, 29, 30, 31, 32
additional sequence.
 16, 17, 18, 19, 20

Date: 9/20/13 4.S.21
1•4
2•3
3 The student does not The student The student The student correctly:
demonstrate demonstrates demonstrates a. Uses drawings or
understanding of inconsistent understanding of tens words to explain
1.NBT.2 comparing numbers understanding of tens and ones and is able to that 1 ten and 24
1.NBT.3 based on tens and and ones, answering a generally compare the ones is the same as
ones. Fewer than one few of the parts quantities. The student 34 ones.
1.NBT.5 section is correctly correctly within a correctly answers all
b. Answers (i) > (ii) =
answered. section but showing parts of two out of the
(iii) > (iv) < .
errors in understanding three sections.
in at least two of the c. Identifies mystery
three sections. numbers as 39, 19,
30, 28 respectively
and accurately
completes the charts
to depict the arrow
way.
4 Answers two or fewer Answers at least three Answers at least six of The student correctly:
questions correctly. of nine correctly, and nine correctly, or uses  Solves
1.NBT.4 demonstrates sound process a. 21
misunderstandngs of throughout with
1.NBT.6 b. 38
place value. calculation errors.
c. 10
d. 30
e. 34
f. 40
g. 30
h. 33
i. 34
 Represents process
to accurately solve
through drawings,
number bonds, or
the arrow way. The
notation
demonstrates use
of a sound strategy
for adding or
subtracting .

Date: 9/20/13 4.S.22
1•4
2•3

Date: 9/20/13 4.S.23
1•4
2•3

Date: 9/20/13 4.S.24
1•4
2•3

Date: 9/20/13 4.S.25

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New York State Common Core

Module Overview ......................................................................................................... i

Topic A: Tens and Ones ......................................................................................... 4.A.1

Topic B: Comparison of Pairs of Two-Digit Numbers .............................................. 4.B.1

Topic C: Addition and Subtraction of Tens ............................................................. 4.C.1

Topic D: Addition of Tens or Ones to a Two-Digit Number .....................................4.D.1

Topic E: Varied Problem Types Within 20 .............................................................. 4.E.1

Topic F: Addition of Tens and Ones to a Two-Digit Number................................... 4.F.1

Module Assessments ............................................................................................. 4.S.1

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Focus Grade Level Standards1

Extend the counting sequence.3

Understand place value.4

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Focus Standards for Mathematical Practice

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Overview of Module Topics and Lesson Objectives

1.NBT.3 B Comparison of Pairs of Two-Digit Numbers 4

1.NBT.2 C Addition and Subtraction of Tens 2

Mid-Module Assessment: Topics A–C (assessment 1 day, return 1 day, 3

1.NBT.4 D Addition of Tens or Ones to a Two-Digit Number 6

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Standards Topics and Objectives Days

1.NBT.4 F Addition of Tens and Ones to a Two-Digit Number 7

End-of-Module Assessment: Topics D–F (assessment 1 day, return 1 day, 3

Familiar Terms and Symbols6

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Suggested Tools and Representations

Hundred Chart to 40 Number Bond

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Module 4: Place Value, Comparison, Addition and Subtraction to 40

Topic A: Tens and Ones

A Teaching Sequence Towards Mastery of Tens and Ones

Objective 6: Use dimes and pennies as representations of tens and ones.

Topic A: Tens and Ones

Suggested Lesson Structure

Fluency Practice (10 minutes)

 Break Apart Numbers 1.OA.6 (4 minutes)

Break Apart Numbers (4 minutes)

Change 10 Pennies for 1 Dime (4 minutes)

Lesson 1: Compare the efficiency of counting by ones and counting by tens.

This work is licensed under a

Happy Counting by Tens (2 minutes)

T/S: 0 10 20 (pause) 10 0 (pause) 10 20 30 (etc.)

Application Problem (5 minutes)

Concept Development (35 minutes)

Lesson 1: Compare the efficiency of counting by ones and counting by tens.

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S: (Look in bag and make prediction.)

Lesson 1: Compare the efficiency of counting by ones and counting by tens.

This work is licensed under a

Problem Set (10 minutes)

Student Debrief (8 minutes)

Lesson Objective: Compare the efficiency of counting by

Lesson 1: Compare the efficiency of counting by ones and counting by tens.

This work is licensed under a

You may choose to use any combination of the questions

There are _ grapes. There are _ carrots.

There are _ apples. There are _ peanuts.

There are _ grapes. There are _ carrots.

There are apples. There are peanuts.

There are _ marbles. There are _ balloons.

There are _ straws. There are _ cubes.

There are _ juice boxes. There are _ crayons.

There are _ cubes. There are _ cubes.

There are _ cubes. There are _ cubes.

1. 2 + 0 = _ 16. 1 + 6 = _ 31. 5 + 3 = ___

2. 2 + 1 = _ 17. 6 + 1 = _ 32. 3 + 5 = ___

3. 2 + 2 = _ 18. 6 + 2 = _ 33. 3 + 4 = ___

4. 4 + 0 = _ 19. 5 + 2 = _ 34. 3 + 3 = ___

5. 0 + 4 = _ 20. 4 + 3 = _ 35. 4 + 4 = ___

6. 0 + 3 = _ 21. 2 + 3 = _ 36. 5 + 4 = ___

7. 0 + 0 = _ 22. 2 + 4 = _ 37. 4 + 6 = ___

8. 3 + 1 = _ 23. 4 + 2 = _ 38. 2 + 7 = ___

9. 1 + 3 = _ 24. 3 + 2 = _ 39. 2 + 8 = ___

10. 1 + 4 = _ 25. 9 + 1 = _ 40. 2 + 5 = ___

11. 1 + 5 = _ 26. 8 + 2 = _ 41. 5 + 5 = ___

12. 5 + 1 = _ 27. 7 + 2 = _ 42. 4 + 5 = ___

13. 1 + 7 = _ 28. 7 + 3 = _ 43. 2 + 6 = ___

14. 7 + 1 = _ 29. 6 + 3 = _ 44. 3 + 6 = ___

15. 1 + 8 = _ 30. 6 + 4 = _ 45. 3 + 7 = ___

17 = ten ones 26 = tens ones

28 = tens ones tens >
5. 6.

There are _ balloons. There are _ flowers.

There are _ marbles. There are _ peanuts.

There are _ cubes. There are _ cubes.

There are _ cubes. There are _ cubes.

There are _ cubes. There are _ cubes.

There are _ cubes. There are _ cubes.