Equivalent Fractions - Everyday Math - Login€¦ · LESSON8 Equivalent Fractions 4 Date Time Do...

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AssessmentManagement

Common Core State Standards

Lesson 8�4 621

Advance PreparationBefore 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

Key Concepts and Skills• Count equal parts of a circle.

[Number and Numeration Goal 1]

• Label fractional parts of a circle.


• Identify and write equivalent fractions.


Key ActivitiesChildren find equivalent fractions by

matching fractional parts of circles.

Key Vocabularyequivalent � equivalent fractions

MaterialsMath Journal 2, pp. 196 and 197

Home Link 8�3

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

Playing Name That NumberMath 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.

Math Boxes 8�4Math 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�4Math Masters, p. 240

Children practice and maintain skills

through Home Link activities.

READINESS

Sorting CirclesMath Masters, p. 241

scissors

Children compare circles with equal and

unequal parts.

ENRICHMENTCovering Hexagons ActivityMath 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.

EXTRA PRACTICE

Making Fraction Name-Collection Boxesper group: 1 large piece of posterboard,

markers, straightedge

Children create name-collection boxes

for fractions.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 142

Children add the term equivalent fraction

to their Math Word Banks.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Equivalent FractionsObjective To provide experiences with the idea that many

different fractions can name the same fractional part of a whole.d

��

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622 Unit 8 Fractions

LESSON

8�4

Name Date Time

Fraction Circles

227-251_EMCS_B_MM_G2_U08_576949.indd 239 2/9/11 12:35 PM


Teaching Master

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 WHOLE-CLASS ACTIVITY

Equivalent Fractions(Math Journal 2, pp. 196 and 197)

Have children label the parts of each circle they cut out with the appropriate fraction— 1 _ 4 , 1 _ 6 , or 1 _ 8 . Remind children that each circle represents ONE. Review the words: fourths, sixths, and eighths.

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 2 _ 4 of the circle is equivalent to 1 _ 2 of the circle.

3. Say that 2 _ 4 and 1 _ 2 are called equivalent fractions. Both fractions name the same fractional part of the circle.

4. Fill in the missing numerator of the fraction that is equivalent to 1 _ 2 . 2; 1 _ 2 = 2 _ 4

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Getting Started

Math MessageTake a copy of Math Masters, page 239. Carefully cut out each circle.

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.

Mental Math and ReflexesInvite children to use pennies or other counters to solve the following problems:

Make a pile of 12 pennies. Show me 1

_ 2 of this pile. How

many pennies are in 1

_ 2 of the pile? 6 pennies

1

_ 3 of the pile?

4 pennies 1

_ 4 of the pile? 3 pennies

I am thinking of a pile of pennies. There are 9 pennies in 1

_ 2

of the pile. Show me the whole pile. 18 pennies

I am thinking of a pile of pennies. What if 3 pennies are 1

_ 3 of

the pile? How many pennies are in the whole pile? 9 pennies

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Equivalent FractionsLESSON

8 � 4

Date Time

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. Cover 1 _ 2 of the circle with 2. Cover 1 _ 4 of the circle with fourths. eighths.

12

12

14

14

14

14

1 _ 2 = 4 1 _ 4 = 82 2

184_208_EMCS_S_SMJ_G2_U08_57640X.indd 196 2/10/11 9:31 AM

Math Journal 2, p. 196

Student Page

Lesson 8�4 623

Equivalent Fractions continuedLESSON

8 � 4

Date Time

3. Cover 2 _ 4 of the circle with eighths. 4. Cover 1

_ 2 of the circle with sixths.

5. Cover 1 _ 3 of the circle with sixths. 6. Cover 2 _ 3 of the circle with sixths.

14

14

14

14

12

12

13

13

13

13

13

13

2 _ 4 = 8 1 _ 2 = 6

1 _ 3 = 6 2 _ 3 = 6

4

42

3

184_208_EMCS_S_SMJ_G2_U08_57640X.indd 197 2/10/11 9:31 AM


Student Page

Name that NumberMaterials ❑ 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 whenplayed by 3 or 4 players)

Skill Using addition and subtraction toname equivalent numbers

Object of the game To collect the most cards.

Directions

1. Shuffle the deck and place 5 cards number-sideup on the table. Leave the rest of the decknumber-side down. Then turn over the top cardof the deck and lay it down next to the deck.The number on this card is the number to benamed. Call this number the target number.

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 maybe used only once for each turn.

Games

My Reference Book, p. 138

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

3. Write the equivalent fraction below the circle.

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 1 _ 4 of the circle is covered. Children count the eighths.This circle shows that 2 _ 8 is equivalent to 1 _ 4 . Children fill in the missing numerator of the fraction so it is equivalent to 1 _ 4 . 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.

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.

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624 Unit 8 Fractions

� 12 8

4

Name Date Time

In this lesson, your child learned that a fractional part of a whole can be named in manydifferent ways with equivalent fractions. For example, �

24

�, �48

�, and �36

� are names for �12

�, while �28

� and�146� are names for �

14

�. Help your child shade each of the shapes below to show the appropriatefraction. Make sure your child understands that the fractions are equivalent because they name the same part of the shape.

Please return this Home Link to school tomorrow.

FamilyNote

1. Shade �12� of the rectangle. 2. Shade �

12� of the rectangle.

3. Shade �14� of the square. 4. Shade �

14� of the square.

5. Shade �15� of the rectangle.

� 15 20

4

� 14 8

2�

14 16

4

� 12 8

4�

12 4

2

HOME LINK

8�4 Shading Fractional Parts

Try This Practice

Solve.

6. 130 � 30 �

7. 37 � 45 � 82100

15


Home Link Master

Sample answers:

Math BoxesLESSON

8 � 4

Date Time

1. Fill in the missing numbers.

1,2071,216

1,196 1,1971,2081,2181,217

3. Circle the digits in thehundreds place.

1 2 8 9 7 2 4 6 3

2, 4 6 5 3, 0 9 1

6 6, 2 5 0

6. Count the squares to find thearea.

Area � sq cm6

2. months � 1 year

months � �12� year

months � �14� year

months � 2 years 243612

4. There are 9 dinosaurs.3 are plant eaters. Whichfraction shows how many areplant eaters? Fill in the circlenext to the best answer.

A �93� C �

12�

B �39� D �

23�

5. Draw a triangle. Measure eachside to the nearest inch.

about in.

about in.

about in.122

�

12

69


Student Page

2 Ongoing Learning & Practice

� Playing Name That Number SMALL-GROUP ACTIVITY

(Math Masters, p. 462; My Reference Book, pp. 138 and 139)

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.

� Math Boxes 8�4 INDEPENDENTACTIVITY

(Math Journal 2, p. 195)

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.

Ongoing Assessment: Math Boxes

Problem 3 �Recognizing Student Achievement

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.


� Home Link 8�4 INDEPENDENTACTIVITY


Home Connection Children shade rectangles and squares to create equivalent fractions.

3 Differentiation OptionsREADINESS

SMALL-GROUP ACTIVITY

� Sorting Circles 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.


pyg

gp

LESSON

8�4

Name Date Time

Circle Parts


Teaching Master

LESSON

8�4

Name Date Time

Covering Hexagons

Materials: � pattern blocks � Math Masters, p. 242

� 1 crayon per child (different colors)

Directions Take turns doing the following:

1. Choose pattern blocks that are worth exactly one trapezoid.Decide where to place your block(s) on the board below. (If youare using more than 1 block, you can place them in differenthexagons.) Your blocks must fit in the outlines. You can placeyour blocks in any hexagon that is not completely covered.

2. When you finish covering a hexagon, you “win” the hexagon.Remove the blocks and use your crayon to put your initials on thehexagon. This hexagon cannot be covered again. When allhexagons have been “won,” count to find out who has won the most.


Teaching Master

Lesson 8�4 625

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.

Children may shade and label the shaded fraction for circles that are divided into equal parts.

ENRICHMENT PARTNER ACTIVITY

� Covering Hexagons Activity 5–15 Min


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 1 _ 7 of the board.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

� Making Fraction 15–30 Min

Name-Collection BoxesTo apply children’s knowledge of fractions, assign a familiar fraction to each group—for example, 1 _ 4 . 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 1 _ 4 of them colored

� fractions of a region: for example, a rectangle divided into fourths with 1 _ 4 colored

� equivalent fractions: for example, 4 _ 16

� expressions with operations: for example, 1 _ 8 + 1 _ 8

� expressions with words: for example, “one-half of one-half ”

ELL SUPPORT SMALL-GROUP ACTIVITY

� Building a Math Word Bank 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.


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