Solving Two-Digit Multiplication Problems Using Area Models

Name of Teacher Candidate Angela Hoang

Lesson Overview
Grade Level 4th Grade
Estimated Time Needed 45 minutes
In this lesson, the students will learn how to solve two-digit
multiplication problems, including perfect squares through 15 by 15,
using area models. The students must be able to decompose (break
Lesson Description apart) the factors in the two-digit multiplication problem. They will be
able to draw the area models and fill out each portion to solve the
problem. Lastly, they will add up the product in each part of the area
model to find the answer to the problem.
(4) Number and operations. The student applies mathematical process
standards to develop and use strategies and methods for whole
number computations and decimal sums and differences in order to
Content Area Standards solve problems with efficiency and accuracy. The student is expected
to:
(C) represent the product of 2 two-digit numbers using arrays, area
models, or equations, including perfect squares through 15 by 15
Technology Standards N/A
Students will be able to represent the product of 2 two-digit numbers
Objectives
using area models including perfect squares through 15 by 15.

Resources/Materials/Tools
Terms/Vocabulary Array, area model, factors, product
Computer, projector, smart board
I will be doing most of the instruction on the smart board. I will create
Technology Resources PowerPoint slides to support my instruction and modeling. The
computer and projector are used to open the PowerPoint slides and
display them on the board, so the students can see.
 Students will need their problem-solving spiral notebooks,
pencils, and their math composition notebook.
Other Resources
 Students will also need to tear out page 317 in their math
textbook for the independent practice.

Lesson Procedures
A step-by-step description of the scope and
sequence of lesson activities, with estimated time on Describe how each stage
Cite specifically what
task noted in parentheses for each step. In other of the lesson will be
This template words, completely describe the flow of the lesson-the managed, including role of
resources for this activity
is built on the will be used and
content to be presented, and the strategies to be teacher and learners (who
describe in detail how
traditional used. Include actual words you will use and questions is doing what at each
they will be used.
“Madeline you will ask students. Consider items such as: parts point), location (e.g.,
Note who will be using the
Hunter” lesson of the lesson that might be difficult, and how you will classroom, computer lab,
tool and in what ways.
know whether you can go on; how to ensure that outside), and any special
structure. students completely understand directions before considerations, such as for
Note any safety
considerations needed.
releasing them to work independently; and what differentiated instruction.
students will do if they finish their work early.
The teacher will open the PowerPoint slide Role of teacher: Computer, projector,
Focus/
to display a contextual word problem on the introduce problem to smart board to do
Solving Two-Digit Multiplication Problems Using Area Models

Anticipatory board. the students and walk the warm-up

Set around to make sure
(motivational “Okay boys and girls, I would like for you all they stay on task; The teacher will
hook) to take out your problem-solving notebook observe the students’ introduce the
to complete the warm-up.” work to see how problem to the
they’re doing students and ask
The teacher will read the word problem to the students
the students and explain the question and Students: solving the questions.
expectations for solving it. warm-up problem at
their desks The students will
“For this problem, I want you all to draw a solve their problems
picture or an array to solve the problem.” on the smart board.

The teacher will give the students a few Students will need a
minutes to solve the problem. Then the pencil and their
teacher will go over the problem with the problem-solving
entire class. spirals to solve the
problem.
The teacher will ask:
 What did you get for your answer?
How many cookies did Joshua
have to buy?
 How did you get your answer?
 What kind of picture did you draw
to solve the problem?

The teacher will have a few students come

up to the smart board to draw their visual
models.

The teacher will introduce the lesson to the

The teacher will be at
class and call all students to the carpet with
the front of the
their math composition notebook and a
classroom modeling The teacher will use
pencil. If the students prefer to stay at their
the expectations for the smartboard to
desks, they can.
how to solve two-digit model the lesson or
Content-input
multiplication use markers to
(Could include “Okay boys and girls, for today’s mini-
problems using area model the lesson on
content lesson, we will be learning about solving
models. He or she will an anchor chart.
outline, two-digit multiplication problems using area
review the vocabulary
presentation, models.
terms before diving The students will be
questioning,
into the area model. writing down notes
modeling, A few days ago, we learned about how to
in their math
examples) solve multiplication problems using arrays,
The students will be composition
but now we’re going to be solving them
answering the notebook as the
using area models.
questions the teacher teacher models.
asks and will be
First, let’s review the vocabulary terms for
writing down notes in
multiplication. 6 x 7 = 42
Solving Two-Digit Multiplication Problems Using Area Models

their math composition

For 6 x 7 = 42, the 6 and the 7 are factors notebook.
of the problem. Factors are the numbers
that are being multiplied. The 72 is the
product of the multiplication problem, or the
answer.

Let’s try another one.

What is 8 x 9? (Students should answer

72).

In the number sentence 8 x 9 = 72, what

numbers are the factors? (8 and 9 are the
factors)

Which number is the product? (72 is the

product)

Great job everyone!

Does anyone know what an area model is?

An area model is a pictorial model used to

represent multiplication. The length and
width are the factors of the problem, and
the area is the product.

For example, let’s say we have 13 x 13.

The teacher will draw the outline of the
area model. Since it’s hard to multiply 13 x
13, let’s decompose or break apart the
factors.

I’m going to decompose 13 into 10 and 3.

Now we just solve the multiplication

problem by each part in the area model.

*The teacher will write the number

sentences in the appropriate boxes in the
area model.

10 x 10 = 100
3 x 10 = 30
10 x 3 = 30
3x3=9
Solving Two-Digit Multiplication Problems Using Area Models

When we add up each of the products

(100+30+30+9), we will get 169. The
product or answer for 13 x 13 equals to
169.
Now let’s try to solve a problem together.

15 x 23

The teacher will draw the outline of the

area model.

What are the factors in this problem? (15

and 23)

How can I break apart or decompose 15 to

make it friendlier? (10 and 5)

How can I break apart 23 to make it

The teacher will
friendlier? (20 and 3) The teacher will use
introduce the next
the smart board to
problem to the
Do you guys notice anything about how the draw out the area
students. This time,
factors are decomposed or broken apart? model. The students
the teacher will ask
(We are separating the tens and the ones) will be doing the
Guided the students questions
calculations and
Practice and guide them
Exactly! When you have trouble figuring out answering the
(identify through solving the
how to decompose or break down the teacher’s questions.
students who question. The students
factors, you can just break the factor into The students will
failed to will be answering the
the tens place and the ones place. also be writing down
master lesson questions and doing
notes in their math
objectives.) the bulk of the work by
What would the number sentence be for composition
decomposing the
the first box in the area model? (10 x 20) notebooks as the
factors and finding the
What is 10 x 20? (200) teacher is solving
products for each
the problem with the
box/part of the area
What about the second box? (5 x 20) class.
model.
5 x 20 equals to… 100

The third box? (10 x 3)

10 x 3?  30

What about the last box? (5 x 3)

5 x 3 = 15

The products are 200, 100, 30, and 15.

What do we get when we add up these
numbers together?
(200+100+30+15 = 345)

*The teacher will fill in the area model on

Solving Two-Digit Multiplication Problems Using Area Models

the board, but the students will be doing the

bulk of the work by decomposing the
numbers and figuring out the calculations.

This time, you guys are going to be solving

the problem! You don’t have to write down
the notes for this problem unless you want
to.

The problem is 36 x 52.

*The teacher will draw the outline of the

area model.
The teacher will be
guiding and facilitating
What are the factors of the problem? The teacher and the
the students as they
Students will answer 36 and 52. students will use the
solve the last problem
smart board to solve
on the board together.
How can we decompose or break down 36 the multiplication
The students will write
so it can be friendlier? problem. The
out the number
teacher will ask the
sentences for each
(30 and 6) students questions
portion of the area
and have the
model. They will add
How can we decompose or break down 52 students come up to
up the products to find
so that it can be friendlier? solve the problem
Independent the answer to the
themselves. They
Practice problem. Afterward,
(50 and 2) are not required to
(reteaching the teacher will
write down notes in
and introduce the
I’m going to call on 5 students to complete their math notebook
enrichment) assignment (Page 317
the area model and add up all the products for this problem.
of their math
to find the answer. 4 of you will be filling in Afterward, the
textbook.) The
each part of the area model. 1 person will students will tear out
students are only
be adding up the products to get the page 317 from their
required to finish
answer. math textbook and
numbers 1, 2, 5, 6, 7,
solve numbers 1-2
and 8 of the page. The
30 x 50 = 1,500 and 5-8. They will
teacher will monitor
6 x 50 = 300 need a pencil to
the classroom and
30 x 2 = 60 complete the
answer questions if
6 x 2 = 12 assignment.
the students need
help.
1,500 + 300 + 60 + 12 = 1,872

Awesome job everyone!

We won’t be having stations today. We are

just going to do a short assignment. I want
you guys to open your math textbook and
tear out page 317. Today, you’re going to
be working on numbers 1, 2, 5, 6, 7, and 8.
Solving Two-Digit Multiplication Problems Using Area Models

Go ahead and circle those numbers so that

you know which problems you’re going to
do.

I know that the boxes/parts of the area

models on the page are small. Instead of
trying to fit the number sentence in each of
the boxes, you can draw an arrow out and
write the number sentence like this
(Teacher will show on the board).

For this assignment, I’m going to allow you

to work with a partner. You can ask your
partner for help and they can guide you
through the questions. However, they
should not be doing the assignment for you
or solving the questions for you. They can
only answer questions and help guide you
through solving the problem. If I hear you
guys get off-talk and talk about things
unrelated to the assignment, you will not be
allowed to work with your partner anymore.
You can also use your notes in your math
notebook if you need to. I will also be
walking around to answer any questions if
needed. (Tentative)

After about 10 minutes of working on the

assignment, the students should have
completed the page. The teacher will tell
the students to clean up their area and
clear their desks.
The teacher will briefly
The teacher will ask: review today’s mini-
The students will
 What was today’s learning lesson and talk about
need a pencil to
objective? (The learning objective the expectations for
complete their post-
is to solve two-digit multiplication solving two-digit
assessment. The
problems using area models.) multiplication
Closure teacher will have a
problems with area
 What are factors? student volunteer
models. The students
 What is a product? pass out the post-
will complete the post-
 What is an area model? assessments to the
assessment and turn
 How can you use an area model to class.
them into the AM class
solve multiplication problems? drawer.
The teacher will have a student helper pass
out the post-assessment to the students.
The teacher will go over expectations for
the post-assessment and remind the
Solving Two-Digit Multiplication Problems Using Area Models

students that they must use the area model

to solve the multiplication problem because
that is an important portion of the learning
objective.

Once the students are done with the post-

assessment, the students will turn it in the
AM class drawer.

Students who have completed the post-

assessment early will get to work on any
uncompleted assignments in their WIP
folder or complete their workbook page if
they did not finish.

Plans for Differentiated Instruction/Accommodations

There are several SPED students in my class. I would give the SPED
students extra time to complete the assignments. I would also modify the
assignments and assessment by simplifying the sentence structure and
vocabulary, so it is easier for them to read. Word banks can also be given if
Special Education Students the students need it. Lastly, I would give them orally administer the
assessment if necessary and shorten/break down the directions. If the
SPED students need a break or feel overwhelmed, they can go to the safe
zone to rest for 5 minutes. However, after the 5 minutes, they must join the
rest of the classroom and get back to work.
I would explain any vocabulary terms they are unfamiliar with by having a
vocabulary bank or chart where there are direct translations of the terms. I
could also modify the word problems to use simpler words. I could give more
wait time so that the students can have enough time to read the problems,
let the information and instructions sink in, and solve the problems. I could
English Language Learners
help the ELLs by partnering them up with students who can speak the same
language as them but are fluent in English. In doing so, if the ELLs need
help with a certain word or definition, their partners can explain it to them in
their language. If needed, I could further explain the vocabulary and put it in
simpler terms, so the ELLs can understand.
Gifted and Talented N/A
Other N/A

Potential Challenges/Plan B
 Technological difficulties – The computer, projector, and the smart board may have issues. If I
encounter an issue while using the devices, I could teach my lesson using the whiteboard and expo
markers or anchor chart. I will print out my lesson and the PowerPoint slides beforehand to have a
paper copy of the problems.
 Students may have different paces of completing the assignment. Some students may recall their
multiplication facts faster, so they may be able to complete the assignment quickly. Others may require
more time to solve the problems and draw the area models. For fast-paced learners, the teacher can
ask them to double-check their work to make sure they answered the questions correctly. They could
also work on the rest of the workbook page. For the students who work at a slower pace, the teacher
Solving Two-Digit Multiplication Problems Using Area Models

can give them more time to work on the activities. The teacher can also reassure them that there is no
need to rush or feel antsy.
 Students may get off-task. The students may start talking and engage in off-task behavior instead of
doing their assignments. To prevent that from happening, I will tell the students my expectations before
starting the assignment. I will redirect the students who are engaging in disruptive behavior. I will
reward the students who stay focused by giving them dojo points. I could also reward the entire class
with class bank money if they are staying on task. On the other hand, I could take away dojo points or
class bank money if they are being disruptive.

Assessment
I will formatively assess the students as I teach the lesson. When I am teaching the students how to
solve two-digit multiplication problems using area models, I can observe the students and see who
understands how to draw the area models. The students who raise their hands to participate will most
likely have a grasp on the material. On the other hand, students who do not would not participate. During
the independent practice, the students will be working on a page from their textbook to practice using
area models to solve two-digit multiplication problems. I will be walking around the classroom to assist
students if they need help, and I could also observe the students to find out which students understand
how to do it and which students do not.

The pre-assessment let me know that the students do not know what an area model is. It also let me
know that the students are not at the point where they can solve two-digit multiplication problems. By
giving the post-assessment, I can find out which students can successfully use area models to solve two-
digit multiplication problems. I can also find out which students know their multiplication facts, and which
students do not.

Notes and Credits

N/A