Math fractions and graphs l3

'DWH UDFWLRQVDQG*UDSKVÔ/ reducing f ractions to lowest terms To reduce a fraction to lowest terms, divide both the numerator and the denominator evenly by the same number.. 'DWH redu

This book belongs to

Copyright © 2005, 2010 by Scholastic Inc.

Copyright © 2013 by Scholastic Education International (Singapore) Private Limited

All rights reserved.

Previously published as Reading & Math Jumbo Workbook Grade 3 and 4,

Summer Express 2-3, Summer Express 3-4, Success with Math Grade 2 and Success With Addition & Subtraction Grade 2

by Scholastic Inc.

This edition published by Scholastic Education International (Singapore) Private Limited

A division of Scholastic Inc.

No part of this publication may be reproduced in whole or in part, or stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the written permission of the publisher For information

regarding permission, write to:

Scholastic Education International (Singapore) Private Limited

81 Ubi Avenue 4 #02-28 UB.ONE Singapore 408830

education@scholastic.com.sg

Helping your child build essential skills is easy!

These teacher-approved activities have been specially developed to make learning

ERWKDFFHVVLEOHDQGHQMR\DEOH2QHDFKSDJH\RX¶OO¿QG

7KLVERRNDOVRFRQWDLQV

Instant assessment to ensure

your child really masters the skills.

&RPSOHWLRQFHUWL¿FDWH to celebrate your

child’s leap in learning.

Date:

6 )UDFWLRQDQG*UDSKVÔ/

f ractions review

Write the fraction that equals the part that is shaded.

Write the fraction for each word name.

VKDGHGSDUWV SDUWVLQDOO VKDGHGSDUWV

SDUWVLQDOO

VKDGHGSDUWV SDUWVLQDOO

L3 Fractions and Graphs.indd 6

Focus Skill

The focus of each activity

page is clearly indicated.

Instructions

The read-aloud instructions are easy for your child to understand.

Meaningful learning

Each activity has been

carefully designed to

make your child’s learning

meaningful and fun.

Instant assessment to ensure

Reading Skills

Practice Test

Fractions and Graphs

Practice Test

Fill in the bubble next to the correct answer.

1. Which fraction describes the shaded

part of the circle?

A 3

B 2

C 1

D 1

2. Which fraction describes the shaded

part of the circle?

L3 Fractions and Graphs.indd 62

Motivational cut-and-paste stickers to mark the

milestones of your child’s learning path.

reading and creating bar graphs 47–49 ordered pairs and coordinates 50–61 Fractions and Graphs Practice Test 62–73

Cut-and-Paste Stickers 79

understand fractions Most recipes have ingredients that are

measured in fractions.

Graphs are important to understand because they can show a

great deal of information in a way that is fun and easy to read.

What to do

The activities in this section introduce your child to concepts

related to fractions and graphing Read the directions together

Have your child complete the activity Then together, review

his or her work Reward your child with a sticker for work that

is well done!

Keep On Going!

Use food to reinforce fractions For example, have your child

count the number of slices of pizza in the pan Ask questions

such as “Dad ate 3 pieces of pizza What fraction describes

the amount of pizza he ate?” (3

8) Continue asking questions using other family members Challenge your child to use

the information to make a bar graph Label the vertical axis

1–8 Label the horizontal axis with the names of the family

members Bet you didn’t know you could eat math!

Fractions and

Graphs

)UDFWLRQVDQG*UDSKVÔ/  5

'DWH

f ractions review

Write the fraction that equals the part that is shaded.

Write the fraction for each word name.

The numerator WHOOVKRZPDQ\SDUWVDUHEHLQJLGHQWL¿HG

The denominator tells the total number of equal parts in the whole.

shaded parts

parts in all

shaded partsparts in all

shaded parts

parts in all

shaded parts

parts in all

Fill in the blanks

Chester Chipmunk was cutting cakes and pies Bobby Bear said, “Some aren’t cut in half When you cut something in half, there are _ pieces and both the pieces are of the same _.”

Here is how Chester cut the cakes and pies Circle the desserts that are cut in half correctly.

'DWH

identifying parts of a whole

Now try these fraction pictures Can you write the fraction each SLFWXUHVKRZV"7KH¿UVWRQHKDVEHHQGRQHIRU\RX

Here is a recipe for preparing peanut butter-oatmeal drops Gather the ingredients and follow the instructions given.

No-Bake Peanut Butter-Oatmeal Drops

(makes about 30 1-inch drops) cup peanut butter (smooth or crunchy)cup corn syrup

cup confectioner’s sugarcup powdered milkcup uncooked oatmealMix all the ingredients together Roll into balls Chill for about one hour Then eat!

3

6

4 8

= 3 =

6

1 2

Write each missing numerator to show equivalent fractions.

Write the number sentence that shows each set of equivalent fractions.

=

1

5

10

=

=

1 3

6

=

1 2

8

=

=

1 4

8

=

1 2

16

=

=

1 3

9

=

1 4

20

=

=

'DWH

making equivalent f ractions

0XOWLSO\ERWKWKHQXPHUDWRUDQGWKHGHQRPLQDWRUE\WKHVDPHQXPEHUWR¿QG equivalent fractions.

2 × 4

4 × 4 =

8 16

Find the missing term to make each pair of fractions equivalent.

5 = 25

'DWH

)UDFWLRQVDQG*UDSKVÔ/  11

making equivalent f ractions

Find the missing terms in each row of fractions.

'DWH

making equivalent f ractions

In each fraction wheel, make the fractions equivalent to the fraction in the center.

1 5

3 8

1.

1 3

12

7

5 6

4 15

2 5

9 20

3 4 1

2

'DWH

)UDFWLRQVDQG*UDSKVÔ/  

reducing f ractions to lowest terms

To reduce a fraction to lowest terms, divide both the numerator and the denominator evenly

by the same number.

Divide by 2 Can you

divide again? Yes!

Divide by 2 Can you divide again? No!

Divide by 4 Can you divide again? No!

1

2 and 4

8 are equivalent fractions, but 1

2 is in the lowest terms.

4 ÷ 4

8 ÷ 4 =

1 2

'DWH

reducing f ractions to lowest terms

Write the fraction for each shaded box Reduce to lowest terms Then draw the reduced fraction in the empty box.

'DWH

)UDFWLRQVDQG*UDSKVÔ/  15

reducing f ractions to lowest terms

Reduce each fraction to lowest terms

Then use the code to answer the

Why was the math teacher crying?

16 = 4

2 8

1

=

2 18

1

=

T 22

24 = 12

'DWH

reducing f ractions to lowest terms

Reduce each fraction to lowest terms.

10

20

6 36

3 15

9

30

25 30

5 20

2

8

6 18

16 24

20

24

14 35

12 30

'DWH

)UDFWLRQVDQG*UDSKVÔ/  17

reducing f ractions to lowest terms

Reduce each fraction to lowest terms.

12

14

30 40

8 32

12

40

10 40

15 30

4

16

4 12

15 21

14

21

12 36

21 24

1 6

1 6

1 6

1 6

1

5

1 5

1 5

1 5

1 5

1 10

1 8

1 7

1 9

1 10

1 8

1 7

1 9

1 10

1 8

1 7

1 9

1 10

1 8

1 7

1 9

1 10

1 8

1 7

1 9

1 10

1 10

1 8

1 7

1 9

1 9

1 10

1 8 1 9

1

11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 12

1 12

1 12

1 12

1 12

1 12

1 12

1 12

1 12

1 2

1 2 1

3

1 3

1 3 1

4

1 4

1 4

1 4

'DWH

)UDFWLRQVDQG*UDSKVÔ/  19

comparing f ractions

Write >, < or = in the box.

> (more than) < (less than) = (equal)

7

10

11 12

5

6

4 7

3

5

7 9

4 9

3 8

5 8

10 10

5 5

4 5

3 8

1 6

5 6

2 3

7 3

1 2

2 3

5 6 7

8

9

3

3 8

7 8

2 7

3 7

1 10

5 10

1 4

3 4

'DWH

)UDFWLRQVDQG*UDSKVÔ/  

adding f ractions with like denominators

Add the fractions and reduce to lowest terms.

Example

1

5

4 5

5 5

1

2

1 2

2 3

1 3

3 10

3 10

3

10

7 10

2 9

1 9

2 9

5 9

1

8

5 8

2 11

5 11

2 7

3 7

'DWH

adding f ractions with like denominators

Add the fractions and reduce to lowest terms.

3

10

3 10

3 5

2 5

3 7

4 7

1

5

3 5

3 8

1 8

5 12

1 12

4

9

2 9

3 11

6 11

1 10

3 10

'DWH

)UDFWLRQVDQG*UDSKVÔ/  25

adding f ractions with like denominators

Solve the problems Then rename the answers in lowest terms Finish the design by coloring the other shapes with colors of your choice.

1

4 15

2

2 12

1

3 10

2

2 6

1

1 14

1

2 4

1

2 10

4

5 12

6

5 10

4

7 12

4

8 10

1

2 5

1

6 14

4

2 10

6

2 9

4

2 8

4

3 8

4

2 9

1

1 8 1

'DWH

adding f ractions with related denominators

Add.

1 2

+

3 8

7 8

=

Step 2: Add the fractions.

3 8

4

8

7 8

+ =

2

5

3 10

1 4

1 2

1

6

5 12

3 8

1 2

'DWH

)UDFWLRQVDQG*UDSKVÔ/  27

adding f ractions with related denominators

Add the fractions and reduce to lowest terms.

2

3

2 9

2 3

1 6

4

14

4 7

1 3

5 9

1

10

3 5

1 12

5 6

1

5

7 10

3 6

3 12

adding f ractions with related denominators Date:

In each box there are two fractions that add up to equal another

fraction in the box Draw a box around the two fractions that equal the third fraction Draw a circle around the fraction that equals the sum of WKHRWKHUWZRIUDFWLRQV7KH¿UVWRQHKDVEHHQGRQHIRU\RX

7 8

1 8

5 9

2 3

3 4

1 2

1 6

3 10

1 5

1 4

1 2

2 3

2 15

8 15

2 5

3 8

5 8

4 7

1 4

1 5

3 10

1 2

7 10

3 14

1 2

2 7

11 14

5 10

4 4

2 5

3 5

3

4

3 8

1

4

5 8

5

8

2 3

1

9

7 9

7

15

3 10

7

10

2 5

1

6

2 3

5

6

7 8

'DWH

)UDFWLRQVDQG*UDSKVÔ/  29

adding f ractions with related denominators

Use these candy bars to see just how sweet fractions can be!

You will need scissors This is what you need to do:

1 12

1 12

1 4

1 12

1 12 1

6 1

4

1 3

1 6 1

2

1 Cut out the candy bars along the

dashed lines

2 Work with a partner Use both candy

bars to do the activity

3 Arrange some of the

pieces this way to

PDNHDZKROHEDU

Here’s how you can

show the combination of fractions in an

HTXDWLRQ

1

2

14

16

112

4  &DQ\RX¿QGDQRWKHUZD\WRPDNH one whole candy bar without using the 1

2 piece? What would it look like?

5 How would you write it in a fraction equation? _

6 How many ways can you use the pieces to make whole candy bars? (Each whole bar will have 12 pieces.) Draw a picture of each solution on a separate sheet of paper

1 2

1

4 1 6

1 12

wholecandy bar

How much is not colored?

 Solve this fraction equation Cross out the dogs to help you

Color to show the fractions Then subtract.

10

3 10

10

8 10

10

4 10

3 5

4 6

3 4

2 4

2 6

1 5

4 6

1 6

'DWH

subtracting f ractions with like denominators

Subtract the fractions Then draw lines to match the fractions with the correct answer.

O O

O O

O O

O

8

1 5

1 2

1 7

5 8

2

8 –

4 6

1

6 –

11 15

8

15 –

4 7

3

7 –

'DWH

  )UDFWLRQVDQG*UDSKVÔ/ 

subtracting f ractions with like denominators

Subtract the fractions and reduce to lowest terms.

8

11

4 11

5

8

2 8

2 6

10

2 10

5 9

4

6 4

8 4

7

1 7

 7

7

3 7

6 3

6

2 6

9 9

12

3 12

'DWH

subtracting f ractions with related denominators

Subtract.

1 2

– 3

8

1 8

=

Step 2: Add the fractions.

3 8

4

8

1 8

– =

1 3

5

3 10

 10

14

2 7

2 3

4

5 12

4 1

2

1 6

'DWH

  )UDFWLRQVDQG*UDSKVÔ/ 

subtracting f ractions with related denominators

Subtract the fractions and reduce to lowest terms.

1 3

4

8 12

 8

9

1 3

5 3

4

5 12

7 7

12

1 6

2 7

9

2 3

4 1

5

2 15

6 11

15

2 3

8 9

10

3 5

'DWH

subtracting f ractions with related denominators

Subtract Do not reduce to lowest terms.

1 3 –

1 12 –

1 3 –

1 4 –

1 6 –

13

14

3 7 –

1 7 –

2 14 –

1

14

14 –

1 2 –

1 2 –

'DWH

  )UDFWLRQVDQG*UDSKVÔ/ 

subtracting f ractions with related denominators

Write the following fractions in the box such that the vertical and horizontal differences between the fractions are the same

1 4

3 4

4 8

6 12

6

12 4 1

'DWH

word problems

Read the questions Write the number sentence for each question and solve the problem.

1. May and her sister painted their doll house together

May painted for 15 hour.

Her sister painted for 25 hour

What was the total number of hours they painted?

4 km more on Sunday than on Saturday

How many kilometers did he run on Sunday?

4 of a cup with milk.

She drank some milk from the cup

There was 1

4 cup of milk left.

What fraction of the cup of milk did Belinda drink?

3 9

5 hour to walk to school.

On Tuesday, Jamie takes 3

10 hour less to walk to school

How long does Jamie take to walk to school on Tuesday?

2. Joe ate 1

6 of a pizza

Jeremy ate 1

3 of the pizza

a What fraction of the pizza did Joe and Jeremy eat?

b What fraction of the pizza was left?

2. a Who used more sugar?

b How much more?

 a Who used less butter?

b How much less?

Betty and Tracey made some cupcakes Below are the amounts of ingredients they used

Tracey’s recipe 1

2 NJ VHOIUDLVLQJÀRXU

4 liters of water in the second glass.

How much water did Father drink altogether?

2. Jason ran 4

5 km.

Timothy ran 11

15 km.

a How far did Jason and Timothy run altogether?

b Who ran further? How much further?

'DWH

43 )UDFWLRQVDQG*UDSKVÔ/ 

reading bar graphs

The graph below shows the favorite colors of a group of children Study the graph and answer the questions that follow.

1. Which color is liked the most? _

2. Which color is liked the least? _

 a Are any colors tied? _

b Which ones? _ and _

'DWH

reading bar graphs

Add or subtract Use the graph to help solve each problem on

pages 45 and 46.

1. Mrs Randolph’s class used 523 pencils

How many are left?

2. Mr Kirk’s class used 156 scissors

How many are left?

markersfoldersscissorsglue stickspencils

100 200 300 400 500 600 700 800 900

'DWH

45 )UDFWLRQVDQG*UDSKVÔ/ 

reading bar graphs

 Mr Dean’s class took 248 folders Mr Jordan’s class took 176 folders

a How many did they take altogether?

b How many folders are left?

4. Mrs Fenton’s class used 96 glue sticks Mrs McBride’s class used 189 glue sticks

a How many did they use altogether?

b How many glue sticks are left?

5. Mrs Barry’s class needs 275 markers Mr Lopez’s class needs 398 markers

a How many do they need altogether?

b How many markers are left?

'DWH

reading and creating bar graphs

Which shape was used the most?

The picture was made with 7 different shapes How many of each shape were used? Color in the shapes using the code Then color in the boxes on the chart, 1 box for each shape used.

1 2

8 9 10

5 6 7

3 4

'DWH

47 )UDFWLRQVDQG*UDSKVÔ/ 

reading and creating bar graphs

A group of friends listed their favorite fruits as follows.

Fill in the table below with the data collected.

ApplePearMangoOrange

'DWH

reading and creating bar graphs

8VHWKHGDWDFROOHFWHGRQSDJHDQG¿OOLQWKHJUDSK&RORURQHER[

on the graph for each vote.

1. a Which fruit was the most popular?

b How many votes did it get?

2. a Which fruit was the least popular?

b How many votes did it get?

'DWH

)UDFWLRQVDQG*UDSKVÔ/ 

ordered pairs and coordinates

Follow the coordinates to the correct box, then draw in the underlined treasures on this treasure map

C3 A jeweled crown sparkles

B1 A ruby necklace can be found.

C5 A golden cup awaits you

D4 An X marks the spot!

A4 A wooden treasure chest\RX¶OO¿QG

E1 A silvery sword lies here.

'DWH

ordered pairs and coordinates

1 Find each number pair on the

graph Make a dot for each

2 Join the dots in the order

that you make them

3 What picture did you make?

'DWH

51 )UDFWLRQVDQG*UDSKVÔ/ 

ordered pairs and coordinates

Measure your height and the height of four friends in your class Record the names and heights in the table below.

Now plot a bar graph with the heights on the vertical axis and the names on the horizontal axis.