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 ?.
? Houghton Mifflin Harcourt Publishing Company
46
Grade 4
3
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
3
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.
? Houghton Mifflin Harcourt Publishing Company
48
Grade 4
3
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
49
Grade 4
3
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 ?.
? Houghton Mifflin Harcourt Publishing Company
50
Grade 4
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