e a rni ng L3 Mathematics Ex pre ss Fractions and Graphs This book belongs to Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 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 and 4, Summer Express 2-3, Summer Express 3-4, Success with Math Grade and Success With Addition & Subtraction Grade 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 #02-28 UB.ONE Singapore 408830 education@scholastic.com.sg First edition 2013 ISBN 978-981-07-1372-0 Scholastic Learning Express: Fractions and Graphs, Level © Scholastic Welcome to eEa rpnreisns g ! x Helping your child build essential skills is easy! These teacher-approved activities have been specially developed to make learning ERWKDFFHVVLEOHDQGHQMR\DEOH2QHDFKSDJH\RX¶OO¿QG f ractions review Focus Skill The focus of each activity page is clearly indicated Date: A fraction consists of two parts 3 T henumeratorWHOOVKRZPDQ\SD UWVDUHEHLQJLGHQWL¿HG The denominatortells the total number of equal parts in the whole Write the fraction that equals the part that is shaded VKDGHGSDUWV VKDGHGSDUWV SDUWVLQDOO VKDGHGSDUWV Meaningful learning Each activity has been carefully designed to make your child’s learning meaningful and fun Instructions The read-aloud instructions are easy for your child to understand SDUWVLQDOO VKDGHGSDUWV SDUWVLQDOO Write the fraction for each word one-third six-eighths IRXU¿IWKV ¿YHWHQWKV SDUWVLQDOO name 10 two-sixths eight-tenths )UDFWLRQDQG*UDSKVÔ/ L3 Fractions and Graphs.indd 7KLVERRNDOVRFRQWDLQV ea rn i ng Fr aRcertariaoacdcntitsincicageenSd kGi lrl sa p h s TTe s t PP Fill in the bubble next to the correct Which fraction describes the shaded part of the circle? Expre ss answer Which fraction describes the shaded part of the square? Cong ratulatio ns! I, 62 A A B B C C D D Which fraction describes the shaded part of the circle? Which fraction describes the shaded part of the square? A A B B C C D D or draw a Paste a photo lf picture of yourse I ve co tic Su pe rs ta r! am a Sc ho las hs L3 tio ns an d Gr ap mp let ed Fr ac Pre sen ted on &RPSOHWLRQFHUWL¿FDWH to celebrate your child’s leap in learning )UDFWLRQDQG*UDSKVÔ/ L3 Fractions and Graphs.indd 62 Instant assessment to ensure your child really masters the skills Motivational cut-and-paste stickers to mark the milestones of your child’s learning path Scholastic Learning Express: Fractions and Graphs, Level © Scholastic Contents Fractions and Graphs fractions review identifying parts of a whole 7–8 equivalent fractions making equivalent fractions 10–12 reducing fractions to lowest terms 13–17 comparing fractions 18–21 adding fractions with like denominators 22–25 adding fractions with related denominators 26–29 subtracting fractions with like denominators 31–34 subtracting fractions with related denominators 35–38 word problems 39–43 reading bar graphs 44–46 reading and creating bar graphs 47–49 ordered pairs and coordinates 50–61 Fractions and Graphs Practice Test 62–73 Answer Key Certificate Cut-and-Paste Stickers 74–77 78 79 Scholastic Learning Express: Fractions and Graphs, Level © Scholastic Fractions and Graphs ,I\RXUFKLOGOLNHVWRFRRNKHRUVKHZLOO¿QGLWYHU\KHOSIXOWR 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 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 pieces of pizza What fraction describes the amount of pizza he ate?” 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! () )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic f ractions review 'DWH A fraction consists of two parts The numerator WHOOVKRZPDQ\SDUWVDUHEHLQJLGHQWL¿HG The denominator tells the total number of equal parts in the whole Write the fraction that equals the part that is shaded shaded parts shaded parts parts in all parts in all shaded parts shaded parts parts in all parts in all Write the fraction for each word name one-third six-eighths IRXU¿IWKV ¿YHWHQWKV 10 two-sixths eight-tenths )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic identifying parts of a whole 'DWH 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 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic identifying parts of a whole 'DWH 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 sugar cup powdered milk cup uncooked oatmeal Mix all the ingredients together Roll into balls Chill for about one hour Then eat! Now try these fraction pictures Can you write the fraction each SLFWXUHVKRZV"7KH¿UVWRQHKDVEHHQGRQHIRU\RX 8 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic equivalent f ractions 'DWH Equivalent fractions have the same amount = = Write each missing numerator to show equivalent fractions = = 6 = 10 = = = = 16 = 20 Write the number sentence that shows each set of equivalent fractions 10 = 11 = 12 = = )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic dnisn agnSd kGi lrl sa p h s Fr aRcPertariaoacctticicee T Te s t P Fill in the bubble next to the correct answer 17 18 65 is the same as 19 is the same as A A 10 15 B B 12 18 C C 15 18 D 12 D 15 20 is the same as 20 is the same as A A B B C 15 C 10 D D 15 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic dnisnagn Sd kGi lrlas Fr aRcPertariaoaccttiiccee Tes t p h s P Fill in the bubble next to the correct answer 21 22 reduced to lowest terms is 20 reduced to lowest terms is 24 A 2 A B 10 B C C 12 D D 12 reduced to lowest terms is 15 24 12 reduced to lowest terms is 20 A A 10 B B C C D D )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 66 dnisn agnSd kGi lrl sa p h s Fr aRcPertariaoacctticicee T Te s t P Fill in the bubble next to the correct answer 25 26 67 > 27 < A A 18 B 14 B 18 C C D 14 D < < 28 < < A A B B C C 12 D D )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 11 12 dnisnagn Sd kGi lrlas Fr aRcPertariaoaccttiiccee Tes t p h s P Read the questions Write the number sentence for each question and solve the problem 29 Mother bought a cake of it Sandra ate of it a Who ate more? How much more? She ate b What fraction of the cake did Sandra and Mother eat altogether? c What fraction of the cake was left? )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 68 dnisn agnSd kGi lrl sa p h s Fr aRcPertariaoacctticicee T Te s t P Read the questions Write the number sentence for each question and solve the problem A pole is painted in four different colors of the pole is painted green of the pole is painted blue of the pole is painted yellow The remainder of the pole is painted pink a What fraction of the pole is painted green and blue? b What fraction of the pole is NOT painted pink? c What fraction of the pole is painted pink? 69 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic dnisnagn Sd kGi lrlas Fr aRcPertariaoaccttiiccee Tes t p h s P UV-HDQ¶VFODVVWRRNDVXUYH\WR¿QGRXWZKLFKIRRGVWKHFODVVOLNHG best Use the information on the bar graph to answer the questions Fill in the bubble next to the correct answer pizza sandwiches salads noodles pies Which was the class’ favorite food? A pies B pizza C salad D noodles Which food was the class’ second favorite? A pies B noodles C pizza D salads Which food was the class’ least favorite? A pizza B pies C sandwiches D noodles )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 70 dnisn agnSd kGi lrl sa p h s Fr aRcPertariaoacctticicee T Te s t P The graph below is incomplete It shows the pets kept by the students in a class Read the sentences below Then draw bars to complete the graph more students kept pet rabbits than pet birds IHZHUVWXGHQWVNHSWSHWFDWVWKDQSHW¿VK Number of students 10 Pets Fish 71 Birds Rabbits Terrapins )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic Cats dnisnagn Sd kGi lrlas Fr aRcPertariaoaccttiiccee Tes t p h s P Complete the graph on page 71 Fill in the bubble next to the correct answer +RZPDQ\VWXGHQWVNHSW¿VKDVSHWV" A B C D 10 How many more students have pet rabbits than pet terrapins? A B C D How many more students kept pet birds than pet cats? A B C D How many students are there in the class? A 18 B 20 C 26 D 28 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic dnisn agnSd kGi lrl sa p h s Fr aRcPertariaoacctticicee T Te s t P Find each number pair on the graph Make a dot for each Join the dots in the order that you make them What picture did you make? _ Up 10 Across Up 2 4 6 6 8 10 11 73 10 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic Across Answer Key Page 6 4 5 10 10 10 Page 2, size; Circle: 1, 3, Page 6 4 3 8 2 6 = 12 11 = 18 8 = = Page 14 ÷ = 2 ÷ 3 = 12 4 ÷ = 10 7 ÷ = 14 Page 10 12 2 18 20 36 15 33 24 9 20 10 11 20 12 30 5, 3, 11 5, 5, 3, 12 4, > > < > = < = < > 10 > 11 = 12 > Page 22 2 ÷ = 6 ÷ = 15 5 ÷ = 10 ÷ = 3 O S A B 16 E ! T 11 H D 10 N 12 M 13 Y 14 P R L 9; HE HAD TOO MANY PROBLEMS! 2, 3, 4, 6, 9, 16, 20 4, 9, 8, 15 10, 12, 16, 25 Page 16 1 2 5 6 10 2, 18, 4, 30 14, 21, 12, 15 Page 17 Page 11 Page 12 , , , , , 15 21 12 18 14 , 12 , , , 10 , 20 30 10 35 25 15 , , , , , 14 12 10 , 18 , , 21 , 12 , 15 24 12 28 16 20 Page 21 10 4 or Page 15 Page 10 20 Page 13 2, 3, 2 5 4, 2, 7, 10 2, 5 10 10 3 11 10 12 Page 23 1 Page 24 2 3 10 12 8 11 > < > > > > < = > 10 > 11 < 12 > , , , , , 35 20 30 10 15 25 Page 20 < < > < > > > < 4 11 12 Pages 18–19 21 , , 18 , 15 , 12 , 56 16 48 40 32 24 5 Page 25 11 3 11 4 Page 26 10 10 11 12 12 10 5 4 > 10 > 11 > 12 > )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 74 Page 33 Page 27 11 10 12 7 10 Page 38 8 - 12 - Page 28 1 11 6 3 6 10 5 9 10 10 14 2 11 14 10 12 8 8 15 15 8 7 15 10 10 5 10 4 5 7 6 11 15 15 Page 34 1 8 4 11 Page 35 10 or 12 or 14 or Page 36 1 12 9 15 15 12 10 10 10 12 - 12 - 12 6 12 - 12 - 12 12 13 14 - 17 11 14 - 14 4 1 + = hours 5 + = = cup 6 3 + = km 4 Page 40 – = 7 1 – = 3 3 – = = 4 Page 42 Page 41 = – = hour – 10 10 10 10 1 a + = + = = 6 6 2 1 b 1– = – = Page 37 Page 32 - Page 39 Answers will vary 10 - Page 29 Page 31 10 Yes a Tracey b – = – = 10 10 10 10 a Betty 1 b = – = – 4 4 Page 43 or - 14 12 14 75 - - 14 - - 14 14 14 3 + = + = liters 8 8 a )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 11 12 11 23 + = + = km 15 15 15 15 b Jason ran further 11 12 11 – = – = km 15 15 15 15 Page 44 Page 49 48 Y 44 40 Apple 36 32 Pear Red Yellow Mango a Yes Orange 28 24 20 16 12 10 b Orange and green Page 45-46 a Apple b 700 – 523 = 177 a Orange b 300 – 156 = 144 b 600 – 424 = 176 a 189 + 96 = 285 Page 56-57 4, 9, 9, 2, Review that the treasures are 8, 8, 8, 6, drawn in the correct boxes on the 6, 11 10 7, 10 11 6, 12 4, treasure map 13 4, Page 51 b 400 – 285 = 115 X 12 16 20 24 28 32 36 40 44 48 An envelope Page 50 a 248 + 176 = 424 12 11 11 a 398 + 275 = 673 10 10 b 900 – 673 = 227 Y 9 7 6 Page 47 5 4 10 3 2 1 X 6 10 11 10 11 12 A candle A Star Page 58-59 Page 52-53 77, 49 70, 63 63, 77 Answers will vary 49, 70 35, 63 42, 14 Page 54-55 14, 21, 21, 21 12 21, 14 1 44, 44, 36 4, 36 10 28, 21 11 28, 14 4, 8, 12 12, 16 13 14, 14 14 14, The rectangle 16, 20 20, 24 4, 36 Page 48 10 24, 20 11 44, 36 12 28, 24 13 32, 20 14 36, 16 15 40, 12 84 Y 77 Apple 16 44, Pear Mango Orange 70 63 56 49 42 35 28 21 14 X 14 21 28 35 42 49 56 63 70 77 84 A Kite )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 76 Page 60-61 B 10 B 11 A 12 C 34 Number of students 11, 10, 2, 1, 13 C 14 C 15 B 16 A 6, 9, 8, 6, 17 A 18 B 19 C 20 C 3, 10 4, 11 6, 12 5, 21 D 22 A 23 B 24 D 13 6, 14 7, 15 6, 25 B 26 A 27 D 28 A 10 12 29 a Mother ate more 1 1 – = – = 8 8 Y 11 10 b 1 + = + = 8 8 c 1– = – = 8 8 Fish 35 D Birds 36 D Rabbits Terrapins Cats 37 B 38 D 39 10 1 + = + = 30 a 4 4 1 10 11 12 X A diamond ring Page 62-74 B C C A A D C C 77 6 b + = + = 8 8 c 8– = 8 31 B 32 D 33 D 1 A Christmas tree )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level © Scholastic 10 e a rni ng Scholastic Learning Express: Fractions and Graphs, Level © Scholastic Con Ex pre ss ! s n gratulatio I, am a Scholastic Superstar! Paste a photo or draw a picture of yourself I have completed Fractions and Graphs L3 Presented on G ood J o b Scholastic Learning Express: Fractions and Graphs, Level © Scholastic [...]... Express: Fractions and Graphs, Level 3 © Scholastic 25 adding f ractions with related denominators 1 'DWH 3 + 2 7 = 8 8 Step 1: Write equivalent fractions such that both fractions have the same denominator 1 4 = 2 8 Step 2: Add the fractions 4 3 + 8 7 = 8 8 Add 1 2 3 + = 5 10 2 1 1 + = 4 2 1 5 + = 6 12 4 3 1 + = 8 2 26 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, ... Express: Fractions and Graphs, Level 3 © Scholastic subtracting f ractions with related denominators 1 3 – 2 'DWH = 8 1 8 Step 1: Write equivalent fractions such that both fractions have the same denominator 1 = 2 4 8 Step 2: Add the fractions 4 3 – 8 = 8 1 8 Subtract 1 3 3 – = 5 10 2 3 5 – = 4 12 10 2 – = 14 7 4 1 1 – = 2 6 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, ... Learning Express: Fractions and Graphs, Level 3 © Scholastic adding f ractions with like denominators 'DWH Add the fractions and reduce to lowest terms Example 1 4 5 + = =1 5 5 5 1 1 1 + = 2 2 2 2 1 + = 3 3 4 3 7 + = 10 10 5 2 1 + = 9 9 6 2 9 + 5 = 9 7 1 5 + = 8 8 8 2 5 + = 11 11 9 2 7 + 3 = 7 3 3 + = 10 10 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 ©... Learning Express: Fractions and Graphs, Level 3 © Scholastic subtracting f ractions with like denominators 'DWH 6XEWUDFW7KH¿UVWRQHKDVEHHQGRQHIRU\RX 1 5 6 – 4 6 = 3 5 – 1 5 = 4 6 – 2 6 = 3 4 – 2 4 = 2 4 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic 1 6 subtracting f ractions with like denominators 'DWH Subtract the fractions Then... 12 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic adding f ractions with related denominators 'DWH Use these candy bars to see just how sweet fractions can be! You will need scissors This is what you need to do: 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... Learning Express: Fractions and Graphs, Level 3 © Scholastic reducing f ractions to lowest terms 'DWH To reduce a fraction to lowest terms, divide both the numerator and the denominator evenly by the same number 4÷2 2 = 4 8÷2 4÷4 1 = 2 8÷4 2÷2 1 = 2 4÷2 Divide by 2 Can you divide again? Yes! Divide by 2 Can you divide again? No! or Divide by 4 Can you divide again? No! 1 4 1 and are equivalent fractions, ... Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic = reducing f ractions to lowest terms 'DWH Write the fraction for each shaded box Reduce to lowest terms Then draw the reduced fraction in the empty box 1 2 ÷ ÷ = = ÷ ÷ 4 ÷ ÷ = = ÷ ÷ 5 6 ÷ ÷ = = ÷ ÷ 7 8 ÷ ÷ = ÷ 14 = ÷ )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic reducing... related denominators 'DWH Add the fractions and reduce to lowest terms 1 2 2 + = 3 9 2 2 1 + = 3 6 4 4 + = 14 7 4 1 5 + = 3 9 5 1 3 + = 10 5 6 1 5 + = 12 6 7 1 7 + = 5 10 8 3 3 + = 6 12 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic 27 adding f ractions with related denominators Date: In each box there are two fractions that add up to equal another... )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic reducing f ractions to lowest terms 'DWH Reduce each fraction to lowest terms 1 12 = 14 2 30 = 40 8 = 32 4 12 = 40 5 10 = 40 6 15 = 30 7 4 = 16 8 4 = 12 9 15 = 21 10 14 = 21 11 12 = 36 12 21 = 24 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic 17 comparing f... )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic comparing f ractions 'DWH Write >, < or = in the box > (more than) < (less than) = (equal) 2 4 9 7 9 3 10 5 5 8 3 8 5 11 12 8 5 5 10 10 9 3 3 4 7 11 8 3 4 5 12 8 1 3 4 2 4 4 7 10 7 6 10 5 5 6 1 6 6 7 3 2 3 2 1 2 7 5 6 )UDFWLRQVDQG*UDSKVÔ/ Scholastic Learning Express: Fractions and Graphs, Level 3 © Scholastic 19 comparing