Math module 4 lesson 13

Multiplication and Area
Topic D: Applications of Area
Using Side Lengths of Figures
Module 4: Lesson 13
Objective: Find areas by decomposing into rectangles
or completing composite figures to form rectangles.

Fluency Practice
(12 minutes)
Group Counting (4 minutes)
Now we’re going to count forward and backward!
* Threes to 30
* Sixes to 60
* Eights to 80
* Nines to 90

Fluency Practice
(12 minutes)
Find the Common Products (8 minutes)
Materials: Blank paper
• Fold your paper in half vertically.
• On the left half, count by fours to 40 down the side of
your paper.
• On the right half, count by eights to 80 down the side
of your paper.
• Draw lines to match the numbers that appear in both
columns.

Fluency Practice
(12 minutes)
• Now write _2_ x 4 = 8, and so on, next to each matched
number on the left half of the paper.
• Now write 8 = _1_ x 8, and so on, next to each matched
number on the right half of the paper.
2 x 4 = 1 x 8 Say the number sentence.
• Now write the remaining equal facts as number sentences.
Discuss the patterns in your number sentences with
a partner. What do you notice?
That’s right! Each multiple of 8 is also a multiple of 4!

Application Problem
(6 minutes)
Anil finds the area of a 5 inch by 17 inch rectangle
by breaking it into 2 smaller rectangles.
Show one way that he could have solved the problem.
*Be sure to use the RDW process: read the problem,
draw a model of the problem, write a number sentence
and a word sentence answering the problem.*
What is the area of the rectangle?

Application Problem
(6 minutes)

Concept Development (32 minutes)
Materials: grid template
Problem 1: Add using the break apart strategy to find
the area of a composite shape.
Draw and shade this shape on your
grid template.
How do you find the area of a
rectangle? That’s right –
by multiplying the side lengths!
Talk to your partner: Can we find the area of the shaded
figure by multiplying side lengths? How do you know?

In the Application Problem, we used the break apart and
distribute strategy to find the area of a larger rectangle by
breaking it into smaller rectangles.
Turn and talk to your partner: how might we use a
strategy like that to find the area of the shaded figure?
Draw a dotted line to show how to break the shaded
figure apart into a square and rectangle.

What equation tells you the area of
the square on top?
That’s right: 2 x 2 = 4!
What equation tells you the area of
the rectangle on the bottom?
That’s right: 2 x 4 = 8!
How do we use those measurements to find the area of
the shaded figure? That’s right – add them together!
What is the sum of 8 and 4? What is the area of the
shaded figure? That’s right – 12 square units!

We can also find the area of the
shaded figure by thinking about a
4 x 4 square with missing units.
Turn and talk to your partner:
how can we find the shaded area
using our square?
There are different strategies of finding the area of a figure.
It just depends on how you choose to look at it!
The area of the square is 16 square units. If we subtract
the 4 units that are unshaded, we get 12 square units!

Continue with the following suggested examples:

Problem 2: Subtract to find the area of a composite shape.
This figure shows a small rectangle
cut out of a larger, shaded rectangle.
How can we find the area of the
shaded figure?
I’m going to shade in the white shape
so we have a large, shaded square.
Write a number sentence to find the area of the large
square. What is the area of the square?
That’s right: 6 x 6 = 36 square centimeters.

The shading inside the white rectangle
is now erased.
Beneath the number sentence you just
wrote, write a number sentence to find
the area for the shape we “cut out.”
What is the area of the white shape?
That’s right: 2 x 4 = 8 square centimeters.
The area of the square is 36 square centimeters. We cut out,
or took away, 8 square centimeters of shading.
Turn and talk to your partner:
How can we find the area of the shaded region?

That’s right! You can subtract 8 square centimeters
from 36 square centimeters!
Write a number sentence to find the area of the shaded
region. What is the area of the shaded region?
That’s right: 36 – 8 = 28 square centimeters!
Continue with this next example:

Problem 3: Subtract to find the area of a composite shape with
missing side lengths.
This figure also shows a small
rectangle cut out of a larger,
shaded rectangle, but what
is missing?
Do we have enough information
to find the side lengths of the
smaller rectangle?
Opposite sides of a rectangle are equal. Since we know
the length of the rectangle is 11 feet, what is the opposite
side length? That’s right: 11 feet!

Problem 3: Subtract to find the area of a composite shape with
missing side lengths.
You can then find the missing
lengths by subtracting the
known length, 5 feet, from the
total length, 11 feet.
So the missing length is 6 feet,
because 11 – 5 = 6!
Use the same strategy to find the missing width. What is
the missing width? That’s right: 9 feet – 4 feet = 5 feet!
With your partner, now find the area of the shaded figure!

Problem Set (10 minutes)
Do your personal best to complete the Problem Set
in 10 minutes.
In Problem 2, a 4-cm by 3-cm rectangle
was cut out of a bigger rectangle.
What other measurements could have
been cut out to keep the same area for
the shaded region?
Debrief (10 minutes)
Let’s review your solutions for the Problem Set.
First, turn to your partner and compare answers.
How did you find the unknown measurements in Problem 3?

Exit Ticket
(3 minutes)
This is where you are going to show
that you understand what we learned today!
Are you ready for the next lesson?!

Homework
3-4 Lesson 13
Homework
Is Due Tomorrow!

Math module 4 lesson 13

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Math module 4 lesson 13