LESSON 6.1 Investigate • Equivalent Fractions

3

Response to Intervention

2

1

LESSON

6.1

Investigate ? Equivalent

Fractions

Reteach

Tier 1

Kinesthetic / Visual

Whole Class / Small Group

Materials color pencils, paper

? Give each student a sheet of paper. Ask them to fold one

sheet in half, make a crease, and then unfold the paper and

shade half of the page. Elicit from students that a ??1_2 ?-size

part of the paper is shaded.

? Have the students fold their sheets of paper in ??1_4 ?-size

parts, or quarters, using the crease they already made and

another fold. Have them unfold the paper and discuss

how ??2_4 ?represents the shaded part of the paper.

? Repeat the process one more time to fold the paper into

??1_8 ?-size parts and generate the fraction ??4_8 ?.

? Conclude the activity with a discussion of how equivalent

fractions name the same-size part, but the size and number

of the parts differ.

Tier 2

Kinesthetic / Visual

Small Group

Materials crayons, Fraction Circles (see eTeacher Resources)

? Provide students with a set of fraction circles. Have students

model ??3_4 ?by shading three ??1_4 ?-size pieces.

? Then, ask students to use ??1_8 ?-size pieces to cover their model

of ??3_4 ?. Guide students to line up the ??1_8 ?-size pieces carefully to

avoid any gaps or overlaps.

? How many ??1_8 ?-size pieces did you use? 6 What fraction can

you write for the ??1_8 ?-size pieces? ??6_8 ?

? Discuss with students how their models show ??6_8 ?is equivalent

to ??3_4 ?.

? Continue the activity with different same-size pieces to find

other fractions equivalent to ??3_4 ?.

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Grade 4

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Response to Intervention

2

1

LESSON

6.2

Generate Equivalent

Fractions

Reteach

Tier 1

 inesthetic / Visual

K

Whole Class / Small Group

Materials Fraction Strips (see eTeacher Resources)

? Have students model ??1_2 ?using a ??1_2 ?fraction strip. Work

with students to write the fraction ??1_2 ?, reviewing what the

numerator and denominator represent in the fraction.

? Next, have students find how many fourth-size pieces

are needed to model ??1_2 ?. Work with students to write the

fraction ??2_4 ?.

? Compare the pieces for ??1_2 ?and ??2_4 ?. How does the number of

pieces used relate to the sizes of the pieces? Possible answer:

the model for ??2_4 ?has twice as many equal parts as the model for ??1_2 ?, and the

parts are half the size.

? Discuss with students how that relationship is shown when

multiplication is used to generate the equivalent fraction:

1¡Á2

2

_

??1_2 ?= ??____

2 ¡Á 2 ?= ??4 ?.

Tier 2

Kinesthetic / Visual

Small Group

Materials color pencils

? Fold a sheet of paper in half. Shade one half of the paper.

? What fraction of the paper is shaded? ??1_2 ?

? Fold the paper in half again.

? What fraction of the paper is shaded? ??2_4 ?

? Discuss with students how the same amount of the paper is

shaded, so the fractions represent the same amount.

? Why can we use two different fractions to represent the

same amount? Possible answer: ??1_2 ?is used when the paper is in two

equal parts; ??2_4 ?is used when the paper is in four equal parts.

? Repeat the process, using thirds and sixths, to reinforce the

meaning of equivalent fractions for students.

? Houghton Mifflin Harcourt Publishing Company

47

Grade 4

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Response to Intervention

2

1

LESSON

6.3

Simplest Form

Reteach

Tier 1

Kinesthetic / Visual

Whole Class / Small Group

Materials Fraction Strips (see eTeacher Resources)

5

1

__

? Have students model ??__

10 ?using ??10 ?-size pieces. Then, have

students use different-size pieces to try to find the simplest

5

1

_

form of ??__

10 ?. Ask students to start with ??3 ?-size pieces.

? Did the ??1_3 ?-size pieces work? Why or why not? No; possible

1

answer: I could not match the length of the five ??__

10 ?-size pieces using

5

??1_3 ?-size pieces. So, I could not model the simplest form of ??__

10 ?using

1

_

??3 ?-size pieces.

? Repeat with ??1_2 ?-, ??1_4 ?-, ??1_5 ?-, and ??1_8 ?-size pieces.

? Suppose you used ??1_7 ?-size or ??1_9 ?-size pieces. Would they

work? No; possible answer: the pieces would not match the length of the

1

five ??__

10 ?-size pieces.

5 1_

? What is the simplest form of ??__

10 ?? ??2 ?

Tier 2

Kinesthetic / Visual

Small Group

Materials Fraction Strips (see eTeacher Resources)

? Have students model ??4_6 ?using ??1_6 ?-size pieces. Explain to

students that when they use models to show simplest form,

they want to use the fewest number of pieces possible.

? To show the fraction in simplest form, should we use ??1_3 ?-size

1

1

_

pieces or ??__

12 ?-size pieces? ??3 ?-size pieces

? Have students use ??13_ ?-size pieces to model ??4_6 ?in simplest form.

Work together to write ??4_6 ?= ??2_3 ?.

? How do you know ??2_3 ?is in simplest form? Possible answer: it uses

the fewest number of pieces possible.

? Repeat the process for other fractions, letting students

select their own pieces to model the simplest form of the

given fraction.

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Grade 4

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Response to Intervention

2

1

LESSON

6.4

Common Denominators

Tier 1

Reteach

Visual / Kinesthetic

Whole Class / Small Group

Materials pattern blocks or Pattern Block Patterns (see eTeacher Resources)

? Roy had two yellow hexagon shapes that were the same

size and shape. He cut one of the hexagons into ??1_2 ?-size

pieces. He cut the other hexagon into ??1_3 ?-size pieces. He now

wants to cut the hexagons so that all of the pieces are the

same size. How many pieces could each hexagon have?

? Have students use pattern blocks to model one hexagon

in ??1_2 ?-size pieces and the other hexagon in ??1_3 ?-size pieces.

Then have students model a way to ¡°cut¡± those pieces so

they are all the same size. Tell students that 6 is a common

denominator for ??1_2 ?and ??1_3 ?.

Verbal / Linguistic

Small Group

Tier 2

__

__?

? Write the following fractions on the board: 1

? ???1

2

3

? Circle each denominator. Tell students that the goal is to

rewrite the two fractions with the same denominator.

? First, list multiples of each denominator. Start with the

denominator, 2. List the multiples, and have students say

them aloud: 2, 4, 6.

? Guide students to list the multiples of 2 aloud as you write

them: 2, 4, 6, 8, 10, 12. Then repeat for the multiples of 3:

3, 6, 9, 12, 15, 18.

? Help students identify the common multiple. Have a

__?as 3

__

? ?and ?

volunteer circle it. Then guide students to rewrite ?1

2

6

1

__?and 2

__

? ?.

3

6

? Houghton Mifflin Harcourt Publishing Company

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Grade 4

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Response to Intervention

2

1

LESSON

6.5

Problem Solving ? Find

Equivalent Fractions

Reteach

Tier 1

Visual / Spatial

Whole Class / Small Group

? Present students with the following situation:

A class is planning a mural made up of equal sheets of paper.

There will be no more than 8 sheets of paper. One-half of

the mural will be painted red. What other fractions can name

the part of mural that will be painted red?

? Draw a ¡°mural¡± on the board, and adapt it as you work.

Work with students to make a table, draw models, and

write equivalent fractions.

1

2

Tier 2

2

4

3

6

4

8

Visual / Kinesthetic

Small Group

Materials sheets of paper

? Let students know that they will be finding equivalent

fractions using a sheet of paper.

? Have each student fold a sheet of paper in half. Have them

shade in the top half. Together, draw the model in a table,

and write the fraction ??1_2 ?.

? Have students then fold the same paper into fourths with

two parts in each of two rows. The top two parts will be

shaded.

? What is the new denominator this fold has made? 4 What

is the fraction that names the shaded part of the whole

now? ??_42 ?

? Discuss the idea that the shaded part of the fourths is

equivalent to the ??1_2 ?from before. Record.

? Continue similarly to show ??4_8 ?.

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50

Grade 4

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