This document provides lesson plans and materials for teaching equivalent fractions using area models with linking cubes or other objects. The lesson introduces equivalent fractions through examples where the shape of the whole is different, but the fractions represented are the same, such as 1/4 and 1/4. Students then complete an activity cutting shapes from a rectangle to show other equivalent fractions. Assessment includes a problem set, debrief, and exit ticket to check understanding of equivalent fractions.

1. Fractions as Numbers On a
Number line
Topic E: Equivalent Fractions
Module 5: Lesson 20
Objective: Recognize and show that equivalent
fractions have the same size, though not
necessarily the same shape.

2. Fluency Practice (9 minutes)
Skip-count by sevens.
7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
7 x 5 = _____ Let’s skip count by 7’s to find the answer.
7 x 3 = _____ Let’s skip count up again.
Let’s see how we can skip-count down to find the answer
too. Start at 35.
7 x 9 = _____ Let’s skip count by sevens.
Let’s see how we can skip-count down to find the
answer too. Start at 70.
Let’s get some practice multiplying by 7!

3. Fluency Practice (12 minutes)
Sprint: Multiply by 7 (9 minutes)
Sprint A: Do as many problems as you can!
Sprint B: Try to get one more right than you
did on Sprint A!

4. Application Problem (8 Minutes)
Max ate 2 of his pizza for lunch.
3
He wanted to eat a small snack in the
afternoon, so he cut the leftover pizza in
half and ate 1 slice. How much of the
pizza was left? Draw a picture to help you
think about the pizza.

5. Application Problem (8 Minutes)

6. Concept Development (31 minutes)
Materials: (S) Personal white boards, linking cubes, coins, rods
The whole is all the blocks. Whisper the fraction of cubes that are
blue to your partner.

7. Concept Development (31 minutes)
Again, the whole is all the blocks. Whisper the
fraction of cubes that are blue to your partner.
Discuss with your partner whether or not the fraction of cubes that are blue is
equal, even though the models are not the same shape.
I hear you noticing that the units make a different shape in the second model.
It’s square rather than rectangular. Good observation. Take another minute to
notice what is similar about our models.
The size of the units and the size of the whole didn’t change. That means 1/4
and 1/4 are equal, or what we call equivalent fractions, even though the
shapes our wholes make are different.

8. Concept Development (28 minutes)
Why isn’t the fraction represented by the
blue cubes equal to the other ones we
made with cubes?
When we are finding equivalent fractions in
area models, the shapes of the wholes can
be different. However, equivalent fractions
describe an equal amount of shaded and
unshaded units.

9. Concept Development (28 minutes)
Equivalent Shapes Collage Activity
Materials: (S) copy of Model 4 (shown above), red crayon, scissors, glue
stick, and blank paper.
Directions:
1. Color the white stripe red.
2. Cut out the rectangle. Cut it into 2-4 smaller shapes.
3. Reassemble the pieces into a new shape with no overlaps.
4. Glue the new shape onto a blank paper.
Each of the 6 shapes pictured to the right is an example of possible
student work. Each of the new shapes is equivalent to Model 4. All
show 2/3 grey, although clearly in different shapes.

10. Concept Development (28 minutes)

11. Problem Set (10 minutes)
You have 10 minutes to complete the problem set pages.
Debrief (10 minutes)
Let’s review your solutions for the problem set.

12. Exit Ticket
(3 minutes)
This is where you are going to show
us that you understand what we learned today!
We will learn if you are ready for the next lesson!

13. Homework
3-5 Lesson 20
Homework
Worksheet
Is Due Tomorrow!