1 e 13 Modified
1 e 13 Modified
1 e 13 Modified
Lesson 13
Objective: Use place value understanding to decompose to smaller units
once using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
Note: This math fluency activity prepares students for understanding the importance of the addition
algorithm.
T: (Write 316 + 473 =____.) Solve by writing an addition sentence horizontally or vertically.
S: (Write 316 + 473 = 789.)
Repeat the process and sequence for 6,065 + 3,731; 13,806 + 4,393; 5,928 + 124; and 629 + 296 + 962.
Note: This mental math fluency activity prepares students for understanding the importance of the
subtraction algorithm.
T: (Project 707.) Say the number in unit form.
S: 7 hundreds 7 ones.
T: (Write 707 202 =____.) Say the subtraction sentence and answer in unit form.
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
190
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13
Jennifer texted 5,849 times in January. In February, she texted 1,263 more times than in January. What was
the total number of texts that Jennifer sent in the two months combined? Explain how to know if the answer
is reasonable.
Note: This Application Problem reviews content from the previous lesson of a multi-step addition problem.
Materials: (T) Millions place value chart (Lesson 11 Template) (S) Personal white board, millions place value
chart (Lesson 11 Template)
Problem 1: Use a place value chart and place value disks to model subtracting alongside the algorithm,
regrouping 1 hundred into 10 tens.
Display 4,259 2,171 vertically on the board.
T: Say this problem with me. (Read problem together.)
T: Watch as I draw a tape diagram to represent this problem. What is the whole?
S: 4,259.
T: We record that above the tape as the whole and record the known part of 2,171 under the tape.
It is your turn to draw a tape diagram. Mark the unknown part of the diagram with the variable A.
T: Model the whole, 4,259, using place value disks on your place value chart.
T: Do we model the part we are subtracting?
S: No, just the whole.
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
191
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13
T: First, lets determine if we are ready to subtract. We look across the top number, from right to left,
to see if there are enough units in each column. Lets look at the ones column. Are there enough
ones in the top number to subtract the ones in the bottom number? (Point to the 9 and the 1 in the
problem.)
S: Yes, 9 is greater than 1.
T: That means we are ready to subtract in the ones column. Lets look at the tens column. Are there
enough tens in the top number to subtract the tens in the bottom number?
S: No, 5 is less than 7.
T: (Show regrouping on the place value chart.) We ungroup or unbundle 1 unit from the hundreds to
make 10 tens. I now have 1 hundred and 15 tens. Lets rename and represent the change in writing
MP.6
using the algorithm. (Cross out the hundreds and tens to rename them in the problem.)
T: Show the change with your disks. (Cross off 1 hundred, and change it for 10 tens as shown below.)
T: Are there enough hundreds in the top number to subtract the hundreds in the bottom number?
S: Yes, 1 is equal to 1.
T: Are there enough thousands in the top number to subtract the thousands in the bottom number?
S: Yes, 4 is greater than 2.
T: Are we ready to subtract?
S: Yes, we are ready to subtract.
T: (Point to the problem.) 9 ones minus 1 one?
S: 8 ones.
T: (Cross off 1 disk; write an 8 in the problem.)
T: 15 tens minus 7 tens?
S: 8 tens.
T: (Cross off 7 disks; write an 8 in the problem.)
Continue subtracting through the hundreds and thousands.
T: Say the number sentence.
S: 4,259 2,171 = 2,088.
T: The value of the A in our tape diagram is 2,088. We write A = 2,088 below the tape diagram.
What can be added to 2,171 to result in the sum of 4,259?
S: 2,088.
Repeat the process for 6,314 3,133.
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
192
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
193
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13
Problem 3: Solve a subtraction word problem, regrouping 1 ten thousand into 10 thousands.
The paper mill produced 73,658 boxes of paper. 8,052 boxes have been sold. How many boxes remain?
T: Draw a tape diagram to represent the boxes of paper
produced and sold. I will use the letter P to represent
the boxes of paper remaining. Record the subtraction
NOTES ON
problem. Check to see that you lined up all units.
MULTIPLE MEANS
T: Am I ready to subtract? OF ENGAGEMENT:
S: No. Ask students to look at the numbers in
T: Work with your partner, asking if there are enough the subtraction problem and to think
units in each column to subtract. Regroup when about how the numbers are related.
needed. Then ask, Am I ready to subtract? before Ask them how they might use their
you begin subtracting. Use the standard algorithm. discovery to check to see if their
(Students work.) answer is correct. Use the tape
diagram to show if 8,052 was
S: 73,658 8,052 = 65,606. subtracted from 73,658 to find the
T: The value of P is 65,606. In a statement, tell your unknown part of the tape diagram, the
partner how many boxes remain. value of the unknown, 65,606, can be
S: 65,606 boxes remain. added to the known part of the tape
diagram, 8,052. If the sum is the value
T: To check and see if your answer is correct, add the two of the whole tape diagram, the answer
values of the tape, 8,052 and your answer of 65,606, to is correct.
see if the sum is the value of the tape, 73,658.
S: (Add to find that the sum matches the value of the
tape.)
Repeat with the following: The library has 50,819 books. 4,506 are checked out. How many books remain in
the library?
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
194
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This file derived from G4-M1-TE-1.3.0-06.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
195
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This file derived from G4-M1-TE-1.3.0-06.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13
After we get our top number ready to subtract, do we have to subtract in order from right to left?
When do we need to unbundle to subtract?
What are the benefits to modeling subtraction using place value disks?
Why must the units line up when subtracting? How might our answer change if the digits were not
aligned?
What happens when there is a zero in the top number of a subtraction problem?
What happens when there is a zero in the bottom number of a subtraction problem?
When you are completing word problems, how can you tell that you need to subtract?
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
196
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This file derived from G4-M1-TE-1.3.0-06.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Problem Set
Name Date
a. 7, 5 2 5 b. 1 7, 5 2 5 c. 6, 6 2 5
3, 5 0 2 1 3, 5 0 2 4, 4 1 7
d. 4, 6 2 5 e. 6, 5 0 0
4 3 5 4 7 0
Draw a tape diagram to represent each problem. Use numbers to solve, and write your answer as a
statement. Check your answers.
2. What number must be added to 13,875 to result in a sum of 25,884?
n= number
13.875 n =?
s= sum
s = 25,884
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
197
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Problem Set
3. During the month of March, 68,025 pounds of king crab were caught. If 15,614 pounds were caught in
the first week of March, how many pounds were caught in the rest of the month?
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
198
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Exit Ticket
Name Date
a. 8, 5 1 2 b. 1 8, 0 4 2
2, 5 0 1 4, 1 2 2
Draw a tape diagram to represent the following problem. Use numbers to solve. Write your answer as a
statement. Check your answer.
2. What number must be added to 1,575 to result in a sum of 8,625? n = number
s = sum
1,575 n=?
s = 8,625
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
199
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Homework
Name Date
a. 2,431 b. 422,431
341 14,321
f. 243,089
137,079
h . 892,431 520,800 =
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
200
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Homework
s = 38,773
A computer shop sold $356,291 worth of computers and accessories. It sold $43,720 worth of accessories.
How much did the computer shop sell in computers?
c = $ worth of computers
t = total worth of computers and accessories sold
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
201
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This file derived from G4-M1-TE-1.3.0-06.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Homework
Lesson 13: Use place value understanding to decompose to smaller units once
using the standard subtraction algorithm, and apply the algorithm to
solve word problems using tape diagrams.
202
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This file derived from G4-M1-TE-1.3.0-06.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.