ExplorActio

Investigate Equivalent Fractions Students use Cuisenaire" Rods to show equivalent fractions. In this activity,

students will

explore fractions on a number line

recognize equivalent fractions, and

generate equivalent fractions

Common Core State Standard

g 3.NF.A.3b Recognize and

generate simple equivalent

fractions, e.g., 1/2 : = 2/4, 4/6

2/3. Explain why the fractions are Have students explore the following problem

equivalent, e.9., by using a visual Using Cuisenaire Rods, find all equivalent fractions that can be generated for fraction model

1 3 1 2 5

and 6

Help students get started, if necessary. Have them use the dark green rod as a

whole, and ask them to find rods to divide this whole into thirds. Have students Materials

explain their thinking. Elicit that 3 red rods can be used to divide the whole into

Cuisenaire Rods thirds. Then have students use rods to divide the whole into sixths. Confirm that the

Fraction Number Lines students use 6 white rods

(Number 3, the blank line) Have students use the rods to model these relationships on Fraction Number Lines

dry erase markers (Number 3, the blank line) and/or BLM 3 (Number Lines). Ask them to mark and label

BLM 3 (Number Lines) the number line using a dry erase marker (or pencil on BLM 3). Make sure students

2

can identify , and . Make sure they can identify 1 2 3 4

5 and 3

3

6' 6' 6' 6 6

T

0

3

2

4 5

6

6 6

6 6

Confirm that students are on the right track. Have them inspect the relationships tha

can be found between the rods on the number line. For example, you might ask

What can you say about the locations of 2

and? [They are the same.] 3

6

What can you say about the locations of and ? [They are the same.] 2

4

3

6

2 How are and 2

related? How are and related? (In both cases they are equal 4

3

6

6

they are equivalent.]

Have students continue their exploration by generating equivalent fractions for 1 1

3 1 2 5 214 and

Initiate students as follows 4'5'5 6

Work with a partner. Use rods to generate equivalent fractions

Suggest to students that the whole does not always have to be made from a single

rod. For example, to investigate twelfths, the whole can be made using an orange rod with a red rod

Record your findings by drawing the sets of rods you used and the number line models you built,

Be ready to explain why the equivalent fractions that you have found are the same number.

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ha

Have students share with the class which rods they used to generate the

equivalent fractions, Organization of their data might look like this Teacher Talk

Rods Fraction Many students have trouble identifying Equivalent Fractions

equivalent fractions. Consider the xurple/red/white browT pUrH

following dark greer

Equivalent fractions don't "look"

prangeyellow/white the same to students. This is

different from their experience browTred/white

with whole numbers

brown/r Visual fraction models make

equivalent fractions look the inge/red/White

same. By exploring the number

orangefred/whte relationships that make two different

pictures of equivalent fractions look orange

the same, students develop their

number sense relative to fractions

Number line models further reinforce

Note that} and can be expressed as twelfths, as well, In fact, the the idea that two different fractions

number of equivalent fractions that can be built is limited only by the can, in fact, be equal (because

number of rods in the set they are the same point on the

number line) Have students draw some of their number line models on the board, Use

Working with Cuisenaire Rods can prompts such as these to promote class discussion

help greatly. In finding equivalent = Why did some students use different rods than others used to 1

fractions for , for example, students

represent equivalent fractions? will likely star identifying a rod they

can easily divide into whole-number What are two ways that you can verify that two fractions

halves. If they happen to pick a red are equivalent?

rod, they will find that only white rods

What other relationships could you find between two of the equivalent can be used to make halves. Then

fractions you generated? they might reason that the purple rod

being twice the length of the red rod

will generate more fractions. They

discover that two white rods are half

2

of a purple rod and conclude that 4

is equivalent to .They may continue

this reasoning by investigating even

longer rods. Or, if they had started

with longer rods, they might reverse

the reasoning and investigate Look at the ingredients in this recipe

shorter rods

for pickles cup sliced cucumbers

Give students the following scenario: All you cup Vinegar

cup is a -cup

cup sugar measure. How could you use what you know

about equivalent fractions to make this recipe?

Ask students to find, write, and explain their answers. Have students

rewrite the ingredients for this recipe in eighths

Ask the following questions

In eighths, what is the

6

8

equivalent racton

In eighths, what is the equivalent fraction for?

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