Focus on Math Concepts
Lesson 16
Part 1: Introduction
CCSS
3.NF.A.3a
Understand Equivalent Fractions
How can two different fractions be equal?
Two fractions can be equal if they show the same amount of the whole.
These are called equivalent fractions. The same area
in each of the circles is shaded. Each circle is divided
into a different number of parts. So, the fractions
used to name the parts are different.
​ 1 ​​  2 ​
2
··
You can also see equivalent fractions using a number
1
2
0
line. ​ 1 ​ and ​ 2 ​are located at the same point on the
2
··
4
··
4
··
number line. This shows they are equivalent.
0
1
4
2
4
1
3
4
1
Think To find equivalent fractions, the size of the wholes must be the same.
Shade the parts of the
first two rectangles
that show that ​ 1 ​ and ​ 2 ​
2
4
··
··
are equivalent.
The rectangles below are the same size. They show
that ​ 1 ​ and ​ 2 ​are equivalent.
2
··
4
··
The rectangles below are not the same size. They show that ​ 1 ​of a small rectangle is
not equivalent to ​ 2 ​of a large one.
4
··
144
2
··
L16: Understand Equivalent Fractions
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Part 1: Introduction
Lesson 16
Think It takes more than one smaller part to equal a bigger part.
Once you make sure the wholes are the same size, you can
look at the size of the parts in each whole.
1
2
1
2
1
4
Each part is ​ 1 ​ .
1
4
1
4
1
4
Each part is ​ 1 ​ .
2
··
4
··
To cover the same amount as ​ 1 ​ ,
2
··
you need two ​ 1 ​ s.
Remember, two ​ 1 ​  s are
4
··
2
the same as ​   ​  , three ​ 1 ​  s
4
6
··
··
3
are the same as ​   ​  , and
6
··
1
four ​   ​  s are the same
8
··
4
as ​   ​  .
8
··
1
2
4
··
1
4
1
4
You can also divide the rectangle in different ways to find other fractions that are
equivalent to ​ 1 ​ .
2
··
1
2
1
2
1
6
1
6
To cover the same amount as ​ 1 ​ ,
2
··
you could also use three ​ 1 ​ s
6
··
or four ​ 1 ​ s.
8
··
So, ​ 1 ​is equivalent to ​ 2 ​ , ​ 3 ​ , and ​  4 ​ .
2
··
4 ··
6
··
8
··
1
6
1
6
1
6
1
6
1 1 1 1 1 1 1 1
8 8 8 8 8 8 8 8
1
2
1
6
1
6
1
6
1 1 1 1
8 8 8 8
Reflect
1 Explain why it takes more ​ 1 ​ s than ​ 1 ​ s to make a fraction equivalent to ​ 1 ​ .
8
4
2
··
··
··
L16: Understand Equivalent Fractions
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145
Part 2: Guided Instruction
Lesson 16
Explore It
Models and numbers lines are two ways to show equivalent fractions.
2 Count the equal parts in each model.
Then write the correct unit fraction in
each section of both models.
1
3
1
6
How many ​ 1 ​ s does it take to cover the same amount as ​ 1 ​ ? 6
··
3
··
1
How many ​   ​ s does it take to cover the same amount as two ​ 1 ​ s? 6
3
··
··
3 Fill in the missing fractions on each number line.
1
3
0
0
1
1
6
3
6
1
Use the models and number lines above to answer question 4.
4 Write the equivalent fractions: ​ 1 ​ 5 ​ 2 ​ 5 3
3
··
··
Now try these problems.
5 Fill in the missing fractions on each number line.
2
4
0
0
3
8
1
1
What fraction is at the same place on the number line as ​ 1 ​ ? 4
··
What fraction is at the same place on the number line as ​ 6 ​ ? 8
··
6 Write the equivalent fractions: ​ 1 ​ 5 ​  6 ​ 5 4
8
··
··
146
L16: Understand Equivalent Fractions
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Part 2: Guided Instruction
Lesson 16
Talk About It
Solve the problems below as a group.
7 How is using number lines like using models to find equivalent fractions?
What is different about using number lines and using models to find equivalent
fractions?
8 Mila thinks ​ 1 ​is equivalent to ​ 2 ​ and ​ 3 ​ . Label the number lines below and use them
2
3
6
··
··
··
to explain whether or not Mila is correct.
0
1
0
1
0
1
Try It Another Way
Work with your group to use the fraction strips to show equivalent fractions.
9 Shade a fraction equivalent to ​ 2 ​ .
3
··
1
3
1
6
1
3
1
6
1
6
4
10 Shade a fraction equivalent to ​   ​ .
8
··
1
3
1
6
1
6
1
6
1
6
What fraction did you shade? L16: Understand Equivalent Fractions
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1
8
1
6
1
8
1
8
1
6
1
6
1
8
1
8
1
6
1
8
1
6
1
8
1
8
What fraction did you shade? 147
Part 3: Guided Practice
Lesson 16
Connect It
Talk through these problems as a class, then write your answers below.
1
2
11 Demonstrate: Use the fraction strips below to show ​   ​ 5 ​   ​ .
4 ··
8
··
1
4
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
8
2
2
12 Explain: Cooper used the models below to show ​   ​ 5 ​   ​ . What did Cooper
3 ··
6
··
do wrong?
1
13 Illustrate: The number line below shows ​   ​ . Add marks to show eighths. Above
2
··
the number line, label the fractions you added to the number line.
0
1
2
1
What fraction is equivalent to ​ 1 ​ ? 2
··
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L16: Understand Equivalent Fractions
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Part 4: Common Core Performance Task
Lesson 16
Put It Together
14 Use what you have learned to complete this task.
Four friends each ate a part
of their own granola bar.
All the granola bars were
the same size. The table
below shows how much of a
granola bar each friend ate.
Friend
Part of Granola Bar Eaten
4
Meg
​   ​
6
··
Joe
​  4 ​
Beth
​  6 ​
Amy
​  2 ​
8
··
8
··
3
··
AWhich two friends ate the same amount? Draw models to show that your
answer is correct. Circle the names of the two children who ate the same
amount.
BFred also had a granola bar. He divided it into fourths. He ate the same
amount as Beth. Draw two number lines to show what fraction of his
granola bar Fred ate.
What fraction of his granola bar did Fred eat? L16: Understand Equivalent Fractions
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149
Focus on Math Concepts
Lesson 16
Understand Equivalent Fractions
Lesson Objectives
The Learning Progression
•Understand that two fractions are equivalent if they
are the same size, cover the same area, or are on the
same point on a number line.
In this lesson students use fraction models and number
•Recognize and generate simple equivalent fractions
using fraction models and number lines.
•Explain why two fractions are equivalent by using a
fraction model or number line.
lines to extend their understanding of fractions. They
learn that more than one fraction can name a fractional
part or point on a number line. They reason about the
area two fractions cover and understand that both
fractions can name the same area or amount. They
realize that because ​ 1 ​is smaller than ​ 1 ​ , it takes more
4
··
2
··
Prerequisite SkilLs
fourths to cover the same area. Students explore
•Understand the meaning of fractions.
finding equivalent fractions.
•Identify fractions represented by models.
Students also use number lines to find and generate
•Understand that the size of a fractional part is
relative to the size of the whole.
equivalent fractions. By comparing two fractions, such
•Understand how to use number lines to count and
identify fractional parts.
because they name the same point on the number line
Vocabulary
equivalent fractions: fractions that name the same
number
as ​ 3 ​ and ​ 6 ​ , they understand that they are equivalent
4
··
8
··
and are the same distance away from zero.
The understanding of equivalent fractions is
foundational for comparing fractions and for solving
problems involving fraction operations.
Review the following key terms.
Teacher Toolbox
denominator: the number below the fraction bar in
a fraction that tells the number of equal parts in the
whole
Teacher-Toolbox.com
Prerequisite
Skills
fraction: part of a whole
Ready Lessons
numerator: the number above the fraction bar in a
fraction that tells the number of equal parts out of
the whole
Tools for Instruction
3.NF.A.3a
✓
✓✓
Interactive Tutorials
✓
CCSS Focus
3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a.
Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.
STANDARDS FOR MATHEMATICAL PRACTICE: SMP 2, 3, 4 (see page A9 for full text)
162
L16: Understand Equivalent Fractions
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Part 1: Introduction
Lesson 16
At a Glance
Focus on Math concepts
Students explore how two different fractions can be
equal when they name the same amount of a whole.
Lesson 16
ccss
3.nF.a.3a
Understand Equivalent Fractions
Step By Step
how can two different fractions be equal?
•Introduce the Question at the top of the page. Draw
one circle on the board and shade in ​ 1 ​ . Draw the
2
··
same size circle and divide it into fourths. Shade
in ​ 2 ​ . Explain that two different fractions can name
4
··
the same amount or area. Introduce the term
“equivalent” to describe the two fractions ​ 2 ​ and ​ 1 ​ .
4
··
Two fractions can be equal if they show the same amount of the whole.
These are called equivalent fractions. The same area
in each of the circles is shaded. Each circle is divided
into a different number of parts. So, the fractions
used to name the parts are different.
1
You can also see equivalent fractions using a number
··
4
··
1
2
0
line. 21 and 42 are located at the same point on the
2
··
•Read the Think statement together. Remind students
that ​ 1 ​of an apple is not the same size or amount of
2
··
fruit as ​ 1 ​of a watermelon. Ask students if the first
2
··
two rectangles that show ​ 1 ​ and ​ 2 ​are the same size.
2
4
··
··
Ask them to shade the parts of both rectangles to
show that ​ 1 ​ are ​ 2 ​name the same amount or area.
2
2
··
··
number line. This shows they are equivalent.
•Direct students’ attention back to the number line on
the board that shows fourths. Put a point on ​ 2 ​ and
4
··
explain that this point can have more than one
fraction name. Explain that when the number line is
divided into fourths, that point is named ​ 1 ​and also
2
··
​ 2 ​ . They are equivalent because both ​ 2 ​ and ​ 1 ​are the
4
4
2
··
··
··
same distance away from 0.
2
··
Part 1: introduction
0
1
4
2
4
1
3
4
1
think To find equivalent fractions, the size of the wholes must be the same.
shade the parts of the
first two rectangles
that show that 1 and 2
2
4
··
··
are equivalent.
The rectangles below are the same size. They show
that 1 and 2 are equivalent.
2
··
4
··
The rectangles below are not the same size. They show that 1 of a small rectangle is
not equivalent to 2 of a large one.
2
··
4
··
144
L16: Understand Equivalent Fractions
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4
··
•Show two different size rectangles and divide one
into halves and the other into fourths. Use this as an
example to show that when using models to show
equivalent fractions, the wholes of both fractions
must be the same size to show that ​ 1 ​ and ​ 2 ​ are
2
4
··
··
equivalent.
•Emphasize that models must be the same size when
showing equivalent fractions because being
equivalent means they are the same size or amount.
ELL Support
•To give students, especially ELL students, extra
support using the term “equivalent,” ask them to
write the word and underline “equi.” Explain that
this part of the word is similar to and means
“equal” or the same amount or the same area.
L16: Understand Equivalent Fractions
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Mathematical Discourse
•How are the two fractions shown by the shaded
circles the same?
They are the same size or show the same
amount.
•How are they different?
One circle has one part out of two shaded and
the other has two parts out of 4 shaded. They
have different fraction names.
•Why must the wholes of fraction models be the same
size to show that ​ 2 ​is equivalent to ​ 1 ​ ?
4
2
··
··
The areas or amount that the two fractions
represent are not equivalent or the same.
163
Part 1: Introduction
Lesson 16
At a Glance
Students explore dividing rectangles in different ways
to find other fractions equivalent to ​ 1 ​ .
Part 1: introduction
Lesson 16
think It takes more than one smaller part to equal a bigger part.
2
··
Once you make sure the wholes are the same size, you can
look at the size of the parts in each whole.
Step By Step
Remember, two 1 s are
4
··
the same as 2 , three 1 s
4
··
1
2
•Read the Think statement together. Point out that to
model or create fractions that are equivalent to ​ 1 ​ , it
2
··
will take more equal parts to be the same size as ​ 1 ​ .
2
··
Use a paper square cut into fourths to point out that
it takes two ​ 1 ​ s in order for the fraction to be
1
4
1
4
1
4
Each part is 1 .
2
··
4
··
To cover the same amount as 1 ,
2
··
you need two 1 s.
4
··
1
2
1
4
1
4
You can also divide the rectangle in different ways to find other fractions that are
equivalent to 1 .
2
··
1
2
equivalent to ​ 1 ​ .
2
··
•Direct students’ attention to the rectangles divided
in one half of each of the rectangles. Ask students for
]
the fractions that are equivalent to ​ 1 ​ . ​ 2 ​ , ​ 3 ​ and ​ 4 ​ 1
2
1
6
1
6
1
6
1
6
1
6
To cover the same amount as 1 ,
2
··
you could also use three 1 s
6
··
or four 1 s.
1
6
So, 1 is equivalent to 2 , 3 , and 4 .
2
··
4 ··
6
··
1
6
1 1 1 1 1 1 1 1
8 8 8 8 8 8 8 8
1
2
8
··
into sixths and eighths on the page. Have them shade
[
1
4
Each part is 1 .
4
··
2 ··
4 ··
6
8
··
··
Point out that you can see that ​ 1 ​ , ​ 2 ​ , ​ 3 ​ , and ​ 4 ​ all
2 ··
4 ··
6
8
··
··
1
2
6
··
are the same as 3 , and
6
··
four 1 s are the same
8
··
as 4 .
8
··
1
6
1
6
1 1 1 1
8 8 8 8
8
··
reflect
1 Explain why it takes more 1 s than 1 s to make a fraction equivalent to 1 .
8
4
2
··
··
··
Possible answer: an eighth is smaller than a fourth, so it takes more of
them added together to make 1 .
2
··
name the same amount when they are stacked on top
of each other.
•Ask students to discuss and write a response to the
145
L16: Understand Equivalent Fractions
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Reflect directive. Ask students to share. Expect them
to say something similar to “an eighth is smaller
than a fourth, so it takes more of them added
Hands-On Activity
together to make ​ 1 ​ .”
Find fractions that are equivalent to ​ 1 ​ .
SMP Tip: Students reason quantitatively about
Materials: paper cut into equal-sized strips (4 strips
per pair)
how it takes more (and smaller) parts to create
Have students work in pairs to build models of
fractions that are equivalent to ​ 1 ​ (SMP 2).
fractions that are equivalent to ​ 1 ​ . Ask them to fold
2
··
2
··
2
··
Mathematical Discourse
•What pattern do you notice in the fractions
​  1 ​ , ​ 2 ​ , ​ 3 ​ , ​ 4 ​ ?
2 ··
4 ··
6 ··
8
··
The numerator is ​ 1 ​of the denominator
2
··
​1  ​ 4 ​means 4 out of 8 parts or half of 8 2​.
8
··
•Based upon this pattern, what are some other
fractions that would be equivalent to ​ 1 ​ ?
​  5  ​  , ​  6  ​  , ​  7  ​  , etc.
10 ··
12 ··
14
··
164
2
··
each of the strips in half by making the opposite
2
··
edges meet. Instruct them to color in ​ 1 ​of the first
2
··
strip and label it ​ 1 ​ . Have pairs take another strip,
2
··
fold each half into two equal parts to make fourths.
Instruct them to color in ​ 2 ​and label each ​ 1 ​ . Model
4
··
4
··
for students how to fold each of the halves into
3 equal areas to create sixths. Have students fold the
strip into sixths, color in ​ 3 ​ , and label each ​ 1 ​ . Model
6
··
6
··
for students how to fold their next strip into eighths.
Have them color in ​ 1 ​and label each ​ 1 ​ .
2
··
8
··
L16: Understand Equivalent Fractions
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Part 2: Guided Instruction
Lesson 16
At a Glance
Part 2: guided instruction
Students use models and number lines to find fractions
that are equivalent to other fractions, such as thirds and
fourths.
Lesson 16
explore it
Models and numbers lines are two ways to show equivalent fractions.
2 Count the equal parts in each model.
Step By Step
•Tell students that they will have time to work
individually on the Explore It problems on this page
and then share their responses in groups. You may
choose to work through the first problem together as
a class.
1
3
1
3
1 1 1 1 1 1
6 6 6 6 6 6
How many 1 s does it take to cover the same amount as 1 ?
6
··
2
3
··
How many 1 s does it take to cover the same amount as two 1 s?
6
··
4
3
··
3 Fill in the missing fractions on each number line.
0
2
3
1
3
0
•As students work individually, circulate among them.
This is an opportunity to assess student
understanding and address student misconceptions.
Use the Mathematical Discourse questions to engage
student thinking.
1
6
2
6
3
6
1
4
6
5
6
1
use the models and number lines above to answer question 4.
2
4 Write the equivalent fractions: 1 5
3
··
4
25
6
··
6
··
3
··
now try these problems.
5 Fill in the missing fractions on each number line.
•Discuss the Explore It problems as a class. When
sharing about problems 3 and 5, ask students to
explain their reasoning behind the labeling of each
fraction on the number lines.
1
4
0
0
1
8
2
8
2
4
3
8
4
8
3
4
5
8
6
8
1
7
8
1
2
What fraction is at the same place on the number line as 1 ?
8
··
What fraction is at the same place on the number line as 6 ?
4
··
4
··
3
8
··
•You may wish to post a chart on the wall that shows
all the equivalent fractions students have found so
1
3
Then write the correct unit fraction in
each section of both models.
6 Write the equivalent fractions: 1 5
4
··
146
2
8
··
65
8
··
3
4
··
L16: Understand Equivalent Fractions
©Curriculum Associates, LLC
far for the simple fractions of ​ 1 ​ , ​ 1 ​ , ​ 3 ​ , ​ 2 ​ , ​ 3 ​ , and
2 ··
3 ··
4 ··
3 ··
4
··
Copying is not permitted.
1 whole. Students may use the chart for future
reference and support.
•Take note of students who are still having difficulty
and wait to see if their understanding progresses as
they work in their groups during the next part of the
lesson.
Concept Extension
•In addition to showing equivalent fractions using
models that are side-by-side, help students see that
they can create equivalent fractions by cutting a
fraction that is shown into smaller equal pieces.
For example, draw the rectangle showing thirds on
the board. Then ask students how to make the
model show sixths. [cut each third into 2 smaller
and equal pieces] This can help student visualize
that the same amount or area is both ​ 1 ​ and ​ 2 ​ or
3
6
··
··
that these two fractions name the same area.
L16: Understand Equivalent Fractions
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Mathematical Discourse
•Why does it take more sixths for the fraction ​ 4 ​to be
equivalent to ​ 2 ​ ?
3
··
Because a sixth is smaller than a third.
6
··
•Is there a fraction that is equivalent to ​ 1 ​ ? If so, how
do you know?
5
··
To make fractions equivalent to ​ 1 ​ , ​ 1 ​ , ​ 1 ​ ,
2 ··
3 ··
4
··
I needed to cut the fractional parts into smaller
pieces. That would be possible with the
fraction ​ 1 ​ , too.
5
··
165
Part 2: Guided Instruction
Lesson 16
At a Glance
Students revisit the problems on page 146. They think
about how number lines and models are alike and
different when using them to find equivalent fractions.
They use them to determine other equivalent fractions.
Part 2: guided instruction
Lesson 16
talk about it
solve the problems below as a group.
7 How is using number lines like using models to find equivalent fractions?
Possible answer: With both models and number lines, you are looking for
Step By Step
parts that are the same size.
•Organize students into pairs or groups and ask them
to answer the Talk About It questions as a group.
•Walk around to each group, listen to, and join in on
discussions at different points. Use the Mathematical
Discourse questions to help support or extend
students’ thinking.
What is different about using number lines and using models to find equivalent
fractions?
When you use models, the fractions cover the same area of the shape.
When you use number lines, the fractions mark the same distance on the
number line.
8 Mila thinks 1 is equivalent to 2 and 3 . Label the number lines below and use them
2
3
6
··
··
··
to explain whether or not Mila is correct.
Problem 8: ​ 1 ​is equivalent to ​ 3 ​because they are both
2
··
6
··
at the same place on the number line. However, ​ 2 ​ is
8
··
not equivalent to 2 , because they
1
3
··
are not at the same place on the
•Ask students to share their responses to problems 7
and 8. Expect students’ ideas to be similar to:
Problem 7: With both models and number lines, you
are looking for fractions that are the same size.
Fraction models show that the areas are the same.
Number lines show that both distances are the same
from zero.
Mila is both right and wrong. 1 is
2
··
1
2
0
1
3
0
2
3
number line. 1 is equivalent to 3
1
2
··
6
··
because they do line up at the
1
6
0
2
6
3
6
4
6
5
6
1
same place on the number line.
try it another Way
Work with your group to use the fraction strips to show equivalent fractions.
9 Shade a fraction equivalent to 2 .
3
··
1
3
1
6
1
3
1
6
1
6
10 Shade a fraction equivalent to
1
3
1
6
1
6
1
6
1
6
What fraction did you shade?
1
8
4
6
··
1
6
11
88
11
88
1
6
1
6
11
88
11
88
1
6
11
88
4.
8
··
1
6
11
88
11
88
What fraction did you shade?
3
6
··
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L16: Understand Equivalent Fractions
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not, so it is not equivalent to the other two fractions.
•Direct the groups’ attention to Try It Another Way.
Have a volunteer from each group come to the board
to draw and explain the group’s solutions to
problems 9 and 10.
SMP Tip: Students make use of fraction models
and number lines to map out and reason about how
the parts relate to the whole and relate to other
equivalent fractions (SMP 4).
Concept Extension
•Direct students’ attention to problem 8 and to the
0 to 1 number line that shows sixths. Ask them to
predict the name of the unit fraction if they cut
each sixth into 2 equal pieces (12ths). Have them
show the 12ths on the number line. Ask: How
many twelfths would be equivalent to ​ 1 ​ ? to ​ 1 ​ ? to ​ 1 ​ ?
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Mathematical Discourse
•How can you use the three number lines to prove
which fractions are equivalent?
One way is to draw a line from ​ 1 ​down through
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the other two number lines to prove that ​ 1 ​
and ​ 3 ​line up and that ​ 2 ​does not.
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•Why does it take fewer sixths to be equivalent to ​ 4 ​ ?
It takes more eighths because eighths are
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smaller than sixths. So, it takes fewer sixths 1​ ​  3 ​  2​
to be equivalent to ​ 4 ​ .
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L16: Understand Equivalent Fractions
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Part 3: Guided Practice
Lesson 16
At a Glance
Part 3: guided Practice
Students demonstrate their understanding of equivalent
fractions using fraction models and number lines.
Lesson 16
connect it
talk through these problems as a class, then write your answers below.
Step By Step
11 Demonstrate: Use the fraction strips below to show
1
4
•Discuss each Connect It problem as a class using the
discussion points outlined below.
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
8
12 explain: Cooper used the models below to show
•You may choose to have students work in pairs to
encourage sharing ideas.
Possible answer: cooper kept the size of the parts the same. instead, he
should have kept the size of the whole the same and divided it into smaller
•Lead a short discussion for number 11 by asking:
parts. then he would see that 2 5 4 .
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How did you prove that ​ 1 ​ and ​ 2 ​were equivalent?
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1 . Add marks to show eighths. Above
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the number line, label the fractions you added to the number line.
1
8
2
8
0
equivalent? [Draw a line from the edge of ​ 1 ​to the
3
8
4
8
5
8
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2
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6
8
7
8
8
8
1
What fraction is equivalent to 1 ?
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edge of ​ 2 ​or cut out the ​ 2 ​and place it on top of ​ 1 ​ on
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13 illustrate: The number line below shows
How else could you prove that the two fractions are
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2 5 2 . What did Cooper
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do wrong?
Demonstrate:
the model.]
1 5 2.
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4
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SMP Tip: Students practice justifying their
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answers as they prove that the fractions are
equivalent (SMP 3).
Copying is not permitted.
Illustrate:
Explain:
•Ask students to explain what Cooper did wrong.
Emphasize again that the models of the wholes must
be the same size in order for the fractions to cover
the same area or be the same size.
•For a quick and easy assessment, ask pairs to draw
on white boards or paper how they would show that
the two fractions are equivalent. Choose a few
students to share.
•Draw the 0 to 1 number line on the board (without
marks). Ask a student to model a strategy they used
to show eighths.
•Use the following to lead a discussion and extend
students’ thinking:
Did anyone do it differently? Explain.
Use the number line with eighths to show which
fraction is equivalent to ​ 6 ​ and which is equivalent
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to ​ 2 ​ . This gets students thinking about fractions
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made of larger pieces that are equivalent, rather than
only finding equivalent fractions with smaller-sized
pieces or areas.
L16: Understand Equivalent Fractions
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167
Part 4: Common Core Performance Task
Lesson 16
At a Glance
Part 4: common core Performance task
Students use models and number lines to solve
problems involving equivalent fractions.
Lesson 16
Put it together
14 Use what you have learned to complete this task.
Step By Step
Four friends each ate a part
of their own granola bar.
All the granola bars were
the same size. The table
below shows how much of a
granola bar each friend ate.
•Direct students to complete the Put It Together task
on their own.
•Go over the directions with students.
• As students work on their own, walk around to
assess their progress and understanding, to answer
their questions, and to give additional support, if
needed.
Friend
Part of granola bar eaten
4
Meg
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4
Joe
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6
Beth
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2
Amy
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a Which two friends ate the same amount? Draw models to show that your
answer is correct. Circle the names of the two children who ate the same
amount.
Meg
Joe
•If time permits, have students volunteers share how
they decided what to draw for each of the 3 pizzas.
Beth
Amy
Scoring Rubrics
A
b Fred also had a granola bar. He divided it into fourths. He ate the same
amount as Beth. Draw two number lines to show what fraction of his
granola bar Fred ate.
Beth
Points Expectations
2
1
0
0
The student identified the two students
who ate the same amount. The model was
accurately drawn to show that the answer
was correct.
The student identified the fractional
amounts that were equivalent, but the
models were not accurately drawn.
The student was unable to identify the
equivalent fractional amounts or draw
models to show the answer is correct.
1
8
2
8
3
8
4
8
5
8
6
8
7
8
1
Fred
1
4
0
2
4
3
4
1
What fraction of his granola bar did Fred eat?
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B
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Points Expectations
2
The student drew a number line to show
the amount that Beth ate 1​ ​  6 ​  2​ . The student
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drew a number line that accurately
showed ​ 3 ​and identified the amount that
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Fred ate as ​ 3 ​ .
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1
The student correctly identified the amount ​
1 ​ ··34 ​  2​that was equivalent to what Beth ate ​1 ​ ··68 ​  2​ ,
but the number lines did not clearly show
that the two fractions were equivalent
OR The number lines accurately showed
that ​ 3 ​ and ​ 6 ​were equivalent, but the
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student did not specify the fraction of the
bar that Fred ate.
0
168
The student did not provide accurate
number line models and did not correctly
specify the fraction of bar that Fred ate.
L16: Understand Equivalent Fractions
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Differentiated Instruction
Lesson 16
Intervention Activity
On-Level Activity
Practice building equivalent fractions using
fraction tiles or circles.
Create an equivalent fraction notebook.
Materials: fraction tiles or fraction strips (wholes,
halves, thirds, fourths, sixths, eighths)
Students may work individually or in pairs to create
Have students work in pairs. Have them take a whole
fraction tile, place it on the top of their paper and
carefully trace around it, then remove the tile.
make a few simple fractions, like ​ 1 ​ , ​ 1 ​ , ​ 1 ​ , ​ 2 ​ , and ​ 3 ​ .
Ask students to find a way to cover the whole with
groups of same-colored tiles. Have students share the
unit fraction they used to cover the whole and the
equivalent fraction they built (​ 2 ​ , ​ 3 ​ , ​ 4 ​ , ​ 5 ​ , etc.). Have
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Materials: pattern blocks or 0–1 number line strips
a notebook that contains a “study” of many ways to
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If students use number lines, they divide each
number line into smaller parts, label each part and
show the fraction with a point on the number line.
All the fractions equivalent to ​ 1 ​are on one page,
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fractions equivalent to ​ 1 ​are on another page, etc.
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students remove the fraction tiles and take out one
If students use pattern blocks, they trace the whole
half and place it on the whole on their paper. Have
and outline the fraction. Next, they lay smaller
them find groups of same-colored tiles that are the
blocks on the traced outline to make a fraction that
same size as ​ 1 ​ . Ask them for the equivalent fractions
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is equivalent. Students trace the blocks and label the
and write them on the board or chart paper. Have
fractions. For example, they lay two red trapezoids
students trace and label the tiles to keep a record of
on ​ 1 ​to show that ​ 2 ​is equivalent to ​ 1 ​ .
all the ways they can make a certain fraction.
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Challenge Activity
Build a fraction using the fewest fraction pieces.
Materials: fraction tiles or circles
Write the fraction ​ 4  ​ on the board. Explain to students that they will find a fraction that is equivalent to ​ 4  ​  , but
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try to find one that uses fewer fractional pieces. Draw a fractional model of ​ 4  ​ on the board that looks like the
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fraction models students are using. Have students work in pairs and ask them to take a one-whole fraction tile
or circle and trace it at the top of their paper. Instruct them to use tenths to build the fraction ​ 4  ​ inside the
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traced one whole.
Explain that during the lesson, they usually found equivalent fractions that were made of more (and smaller)
fractional pieces. For example, ​ 1 ​is equal to 4 eighths. Ask them to think about finding a fraction equivalent
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to ​  4  ​ that has fewer and larger pieces. Encourage them to explore by trying out different size tiles to cover ​ 4  ​  
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on their paper. Have students explore finding an equivalent fraction for ​ 8  ​  , ​  9  ​  , ​ 3 ​ , and ​ 6 ​ .
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