This document provides instructions and examples for a math lesson on multiplication and area measurement. It includes examples of using square tiles to form rectangles with given side lengths or areas, drawing arrays, and writing multiplication equations to represent the relationships between side lengths and area. Students practice skip-counting, identifying common products, solving word problems involving area, and showing commutativity through area problems.

1. Multiplication and Area
Topic B: Concepts of Area Measurement
Module 4: Lesson 5
Objective: Form rectangles by tiling
with unit squares to make arrays.

2. Fluency Practice
(14 minutes)
Group Counting (3 minutes)
Now we’re going to count forward and backward!
* Threes to 30
* Sixes to 60
* Sevens to 70
* Nines to 90

3. Fluency Practice
(14 minutes)
Products in an Array (3 minutes)
How many rows of stars do you see?
How many stars are in each row?
Write two multiplication sentences
that can be used to find the total number of stars.
Continue with the following possible sequence:
3 x 6, 7 x 5, 8 x 4, and 9 x 6.

4. Fluency Practice
(14 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.

5. Fluency Practice
(14 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 = 8 x 1 Say the equation.
Now write the remaining equal facts as equations.
Discuss the patterns in your equations with a partner.
That’s right! Each multiple of 8 is also a multiple of 4!

6. Fluency Practice
(14 minutes)

7. Application Problem
(6 minutes)
Candice uses square-centimeter
tiles to find the side lengths of a
rectangle as shown. She says the
side lengths are 5 centimeters and
7 centimeters. Her partner, Luis,
uses a ruler to check Candice’s
work and says that the side lengths
are 5 centimeters and 6
centimeters.
Who is right? How do you know?

8. Concept Development (30 minutes)
Materials: 15 square-inch tiles per student, straight edge, blank paper
Concrete: Understand the relationship between side lengths and
area.
it Use square-inch tiles to show this rectangle
as an array. What information do we know?
That’s right! There are 2 rows, because a
side length is 2 inches. Place tiles to make the known side.
If the area of this rectangle is 12 sq. in., how many total
tiles will we use to make our rectangle?
That’s right – 12 tiles! How many twos are in 12?
Use your tiles to make 6 twos, then skip-count
to check your work.

9. Concept Development (30 minutes)
Materials: 15 square-inch tiles per student, straight edge, blank paper
Concrete: Understand the relationship between side lengths and
area.
Push your twos together to make a rectangle.
What is the unknown side length?
Tell your partner about the relationship
between the side lengths and the area.
Write an equation to show your thinking.
Be sure to include the units.
That’s right: 2 in. x 6 in. = 12 sq. in.
Repeat the process using a rectangle with a known side length
of 5 inches and an area of 15 square inches. Write an unknown
factor problem, 5 x ___ = 15, then use the tiles to solve.

10. Concept Development (30 minutes)
Concrete/Pictorial: Form rectangles and determine area
or side lengths by drawing to make arrays.
Lay tiles on your paper to make a side 3 inches tall.
Trace the outline of all 3 tiles. Then, draw horizontal
lines to show where they connect.
Label the side length.
Use your tiles to make another side, 7 inches long.
Trace the outline of the tiles. Draw vertical lines to
show where they connect. Label the side length.
How many threes will be in this rectangle?

11. Talk to your partner. Which strategy
might you use to find the total area of
the rectangle?
Many of you suggested multiplying the side lengths to find
the area. Let’s check this strategy by drawing in the rest of
the squares. Use your straight edge to draw the rest of the
tiles in the rectangle, then skip-count to find the total area.
Does 7 inches x 3 inches = 21 square inches accurately give
the area of the rectangle?
Concept Development (30 minutes)
Concrete/Pictorial: Form rectangles and determine area
or side lengths by drawing to make arrays.

12. Concept Development (30 minutes)
Concrete/Pictorial: Form rectangles and determine area
or side lengths by drawing to make arrays.
Now use your tiles to make a side length of 6 inches.
Trace the outline of all 6 tiles. Then draw horizontal lines to
show where they connect. Label the side length.
Write 6 x ___ = 24. Talk to a partner. How can you use
this equation to help you find the other side length?
Choose a strategy to find the other side length and then fill
in the blank in the equation. What is the other side length?

13. Problem Set (10 minutes)
Do your personal best to complete the Problem Set
in 10 minutes.
Compare Problems 1(b) and 1(e).
How does the pair show
commutativity?
Debrief (10 minutes)
Let’s review your solutions for the Problem Set.
First, turn to your partner and compare answers

14. 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?!

15. Homework
3-4 Lesson 5
Homework
Is Due Tomorrow!