Equivalent Fractions
Objective To provide experiences with the idea that many
different fractions can name the same fractional part of a whole.
d
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
Teaching the Lesson
Key Concepts and Skills
• Count equal parts of a circle. [Number and Numeration Goal 1]
• Label fractional parts of a circle. [Number and Numeration Goal 3]
• Identify and write equivalent fractions. [Number and Numeration Goal 6]
Key Activities
Children find equivalent fractions by
matching fractional parts of circles.
Key Vocabulary
equivalent equivalent fractions
Materials
Math Journal 2, pp. 196 and 197
Home Link 83
Math Masters, p. 239
transparency of 1 set of fraction circles
cut from Math Masters, p. 239 (optional) 18 pennies or other counters (optional) scissors glue Class Data Pad
EM Facts
Workshop
Game™
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Name That Number
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Math Masters, p. 462 (optional)
My Reference Book, pp. 138 and 139
per group: 4 each of number cards 0–10 and 1 each of number cards
11–20 (from the Everything Math
Deck, if available)
Children practice naming equivalent
names for numbers.
Sorting Circles
Math Boxes 8 4
Math Masters, p. 242
pattern blocks (trapezoids, rhombuses, and
triangles) 2 different-colored crayons
Children apply their understanding of
equivalent fractions by covering hexagons
with pattern blocks.
Math Journal 2, p. 195
Children practice and maintain skills
through Math Box problems.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 3. [Number and Numeration Goal 2]
Home Link 8 4
Math Masters, p. 240
Children practice and maintain skills
through Home Link activities.
Math Masters, p. 241
scissors
Children compare circles with equal and
unequal parts.
ENRICHMENT
Covering Hexagons Activity
EXTRA PRACTICE
Making Fraction Name-Collection Boxes
per group: 1 large piece of posterboard,
markers, straightedge
Children create name-collection boxes
for fractions.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 142
Children add the term equivalent fraction
to their Math Word Banks.
Advance Preparation
Before beginning the Math Message, make one copy of Math Masters, page 239 for each child, as well as
a few extras. Place them near the Math Message. During the Making a Display of Equivalent Fractions
activity in Part 1, you may want to use the overhead projector to display a set of fraction circles cut from
Math Masters, page 239 or a set of fraction circles commercially made for the overhead.
Teacher’s Reference Manual, Grades 1–3 p. 61
Lesson 8 4
621
Mathematical Practices
SMP1, SMP2, SMP5, SMP6, SMP7
Content Standards
Getting Started
2.G.3
Mental Math and Reflexes
Math Message
Invite children to use pennies or other counters to solve
the following problems:
Take a copy of Math Masters, page 239. Carefully
cut out each circle.
1
Make a pile of 12 pennies. Show me _2 of this pile. How
many pennies are in _12 of the pile? 6 pennies _13 of the pile?
4 pennies
1
_
4
of the pile? 3 pennies
1
I am thinking of a pile of pennies. There are 9 pennies in _2
of the pile. Show me the whole pile. 18 pennies
Home Link 8 3 Follow-Up
Share solution strategies for Problem 1. Review
strategies for 1 and 2 of the practice problems.
Discuss the objects that children brought from home for the
Fractions Museum.
1
I am thinking of a pile of pennies. What if 3 pennies are _3 of
the pile? How many pennies are in the whole pile? 9 pennies
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Math Masters, p. 239)
Check that children have cut out all 4 circles. Give children who
have made a mistake an extra copy of Math Masters, page 239 so
they can complete their collection of circles.
Making a Display of
Equivalent Fractions
WHOLE-CLASS
ACTIVITY
SOLVING
(Math Journal 2, pp. 196 and 197)
Teaching Master
Name
LESSON
84
Date
Have children label the parts of each circle they cut out with the
appropriate fraction— _14 , _16 , or _18 . Remind children that each circle
represents ONE. Review the words: fourths, sixths, and eighths.
Time
Fraction Circles
Work with the class to complete Problem 1 on journal page 196,
using a set of fraction circles for the overhead. Model the following
steps while children carry them out at their desks:
1. Cut the circle that has 4 equal parts into fourths along the
dashed lines. Have children count the fourths.
2. Glue two of the fourths onto the circle on journal page 196
so half of the circle is covered. Count the fourths. One fourth,
two fourths This shows that _24 of the circle is equivalent
to _12 of the circle.
3. Say that _24 and _12 are called equivalent fractions. Both
fractions name the same fractional part of the circle.
Math Masters, p. 239
227-251_EMCS_B_MM_G2_U08_576949.indd 239
622
2/9/11 12:35 PM
Unit 8 Fractions
4. Fill in the missing numerator of the fraction that is
equivalent to _12 . 2; _12 = _24
Student Page
Have children repeat this procedure on their own for the other
circles on the two journal pages. For each problem, children follow
these steps:
1. Find the appropriate fractions of a circle, cutting them apart
along the dashed lines if necessary;
2. Glue the correct number of pieces on part of the circle on the
journal page and count the equal parts; and
Date
Time
LESSON
Equivalent Fractions
8 4
Do the following:
Use the circles that you cut out of Math Masters, page 239.
Cut these circles apart along the dashed lines.
Glue the cutout pieces onto the circles on this page and the next,
as directed.
Write the missing numerators to complete the equivalent fractions.
_1
1. Cover 2 of the circle with
3. Write the equivalent fraction below the circle.
Summary: Remind children that numbers have many names.
Similarly, a fractional part of a whole can be named in many
different ways with equivalent fractions.
eighths.
1
2
For example, in Problem 2, children cut the circle that was divided
into 8 equal parts into eighths and glue two of the eighths onto
the circle so _14 of the circle is covered. Children count the eighths.
This circle shows that _28 is equivalent to _14 . Children fill in the
missing numerator of the fraction so it is equivalent to _14 . Circulate
and offer help as needed.
After children have completed their equivalent-fractions displays,
bring the class together to list the equivalent fractions on the
Class Data Pad for reference.
1
2
_1 =
2
2
Equivalent Fractions
8 4
_2
1
4
1
4
1
4
2
8
Math Journal 2, p. 196
184_208_EMCS_S_SMJ_G2_U08_57640X.indd 196
2/10/11 9:31 AM
Name that Number
_1
1
4
1
4
Games
continued
3. Cover 4 of the circle with eighths. 4. Cover 2 of the circle with sixths.
1
4
1
4
Student Page
Time
LESSON
1
4
_1 =
4
4
Student Page
Date
_1
2. Cover 4 of the circle with
fourths.
1
2
1
2
Materials ❑ number cards 0–20 (4 of each card
0–10, and 1 of each card 11–20)
Players
2 to 4 (the game is more fun when
played by 3 or 4 players)
Skill
Using addition and subtraction to
name equivalent numbers
Object of the game To collect the most cards.
Directions
4
_2 =
4
_1 =
2
8
1
_
5. Cover 3 of the circle with sixths.
6
2
_
6. Cover 3 of the circle with sixths.
1
3
1
3
1
3
1
3
1 =
_
3
3
2
6
1
3
2. Players take turns. When it is your turn:
• Try to name the target number by adding or
subtracting the numbers on 2 or more of the
5 cards that are number-side up. A card may
be used only once for each turn.
1
3
2 =
_
3
1. Shuffle the deck and place 5 cards number-side
up on the table. Leave the rest of the deck
number-side down. Then turn over the top card
of the deck and lay it down next to the deck.
The number on this card is the number to be
named. Call this number the target number.
My Reference Book, p. 138
4
6
Math Journal 2, p. 197
184_208_EMCS_S_SMJ_G2_U08_57640X.indd 197
2/10/11 9:31 AM
Lesson 8 4
623
Student Page
Date
Time
LESSON
2 Ongoing Learning & Practice
Math Boxes
8 4
12
6
3
24
2.
1. Fill in the missing numbers.
1,196 1,197
1,207 1,208
1,216 1,217 1,218
months = 1 year
1
months = _
2 year
Playing Name That Number
1
months = _
4 year
months = 2 years
SMALL-GROUP
ACTIVITY
(Math Masters, p. 462; My Reference Book, pp. 138 and 139)
3. Circle the digits in the
4. There are 9 dinosaurs.
hundreds place.
1 2 8
9 7 2
2, 4 6 5
3 are plant eaters. Which
fraction shows how many are
plant eaters? Fill in the circle
next to the best answer.
1
_
9
A _
C
4 6 3
3, 0 9 1
2
3
6 6, 2 5 0
Because this lesson focuses on equivalent fractions, it may be
helpful to remind children that all numbers have many names.
Name That Number reinforces this idea. Directions for this game
are found on pages 138 and 139 of the My Reference Book. Math
Masters, page 462 is an optional record sheet.
3
B _
9
2
_
D
3
12
5. Draw a triangle. Measure each
6. Count the shaded squares to
side to the nearest inch.
Math Boxes 8 4
find the area.
Sample answers:
about 2 in.
about 2 in.
about 1 in.
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 195)
Area =
6
sq cm
Mixed Practice Math Boxes in this lesson are linked with
Math Boxes in Lessons 8-2 and 8-6. The skills in
Problems 5 and 6 preview Unit 9 content.
69
Math Journal 2, p. 195
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8/24/11 4:03 PM
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 3
Use Math Boxes, Problem 3 to assess children’s understanding of the value of
digits in numbers. Children are making adequate progress if they can circle the
digit in the hundreds place. Some children may be able to identify digits in the
thousand place and the 6 in the ten-thousands place.
[Number and Numeration Goal 2]
Home Link 8 4
Home Link Master
Name
Date
HOME LINK
(Math Masters, p. 240)
Time
Shading Fractional Parts
84
Family
Note
Home Connection Children shade rectangles and squares
to create equivalent fractions.
In this lesson, your child learned that a fractional part of a whole can be named in many
3
2 _
1
2
, 4 , and _
are names for _
, while _
and
different ways with equivalent fractions. For example, _
4 8
6
2
8
4
1
_
are names for _
. Help your child shade each of the shapes below to show the appropriate
4
16
fraction. Make sure your child understands that the fractions are equivalent because
they name the same part of the shape.
15
Please return this Home Link to school tomorrow.
1
_
1. Shade 2 of the rectangle.
1
2
1
_
2. Shade 2 of the rectangle.
2
1
2
4
1
_
3. Shade 4 of the square.
3 Differentiation Options
4
8
1
_
4. Shade 4 of the square.
4
1
16
4
Try This
1
4
2
8
READINESS
Sorting Circles
4
1
5
20
7. 37 + 45 =
100
82
Math Masters, p. 240
227-251_EMCS_B_MM_G2_U08_576949.indd 240
624
Unit 8 Fractions
5–15 Min
To explore fractional parts of a circle, have children cut out each
circle card. Children sort the circle cards into groups. Give children
several minutes to come up with a sorting strategy on their own.
Solve.
6. 130 - 30 =
SMALL-GROUP
ACTIVITY
(Math Masters, p. 241)
Practice
1
_
5. Shade 5 of the rectangle.
INDEPENDENT
ACTIVITY
2/23/11 7:32 AM
Teaching Master
Name
When most are finished, have children describe how they sorted the
cards. If not mentioned, explain that they can be sorted into circles
that are divided equally into fractional parts and circles that are not
divided equally into fractional parts.
Date
LESSON
84
䉬
Time
Circle Parts
Children may shade and label the shaded fraction for circles that
are divided into equal parts.
ENRICHMENT
Covering Hexagons Activity
PARTNER
ACTIVITY
5–15 Min
EXTRA PRACTICE
Making Fraction
g
py g
To apply children’s understanding of equivalent fractions, have
them cover hexagons with pattern blocks. Have children discuss
their strategies. Children may figure out that you can split the
blocks on your turn and put them in different hexagons to block
and “win” hexagons. When they finish, consider having children
figure out the total fraction of the board they have “won.” Note:
Each hexagon is _17 of the board.
p
(Math Masters, p. 242)
Math Masters, p. 241
SMALL-GROUP
ACTIVITY
15–30 Min
Name-Collection Boxes
To apply children’s knowledge of fractions, assign a familiar
fraction to each group—for example, _14 . Children make a
poster-sized name-collection box for their assigned fraction. The
name-collection boxes may include representations such as
the following:
fractions of a set: for example, 12 small circles with _14 of them
colored
fractions of a region: for example, a rectangle divided into
fourths with _14 colored
4
equivalent fractions: for example, _
16
Teaching Master
Name
LESSON
84
䉬
Date
Time
Covering Hexagons
Materials: 䊐 pattern blocks
䊐 Math Masters, p. 242
䊐 1 crayon per child (different colors)
Directions Take turns doing the following:
1. Choose pattern blocks that are worth exactly one trapezoid.
expressions with operations: for example, _18 + _18
expressions with words: for example, “one-half of one-half ”
Decide where to place your block(s) on the board below. (If you
are using more than 1 block, you can place them in different
hexagons.) Your blocks must fit in the outlines. You can place
your blocks in any hexagon that is not completely covered.
2. When you finish covering a hexagon, you “win” the hexagon.
ELL SUPPORT
Building a Math Word Bank
SMALL-GROUP
ACTIVITY
Remove the blocks and use your crayon to put your initials on the
hexagon. This hexagon cannot be covered again. When all
hexagons have been “won,” count to find out who has won
the most.
5–15 Min
(Differentiation Handbook, p. 142)
To provide language support for fractions, have children use the
Word Bank template found on Differentiation Handbook, page 142.
Ask children to write the term equivalent fractions, draw a picture
representing the term, and write other related words. See the
Differentiation Handbook for more information.
Math Masters, p. 242
Lesson 8 4
625