Book
Book Developed by Education Development Center, Inc. through National Science Foundation Grant No. ESI-0099093 Published and distributed by: www.math.schoolspecialty.com
Copyright by Education Development Center, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission is hereby granted to individuals using the corresponding student s textbook or kit as the major vehicle for regular classroom instruction to photocopy entire pages from this publication in classroom quantities for instructional use and not for resale. Requests for information on other matters regarding duplication of this work should be addressed to School Permissions and Copyrights, School Specialty Math, Inc., 80 Northwest Boulevard, Nashua, NH 03063. Think Math! Book 1358072 Printed in the United States of America ISBN 13: 978-0-15-342501-1 Printing 2 ISBN 10: 0-15-342501-6 If you have received these materials as examination copies free of charge, School Specialty Math retains title to the materials and they may not be resold. Resale of examination copies is strictly prohibited and is illegal. Possession of this publication in print format does not entitle users to convert this publication, or any portion of it, into electronic format. This program was funded in part through the National Science Foundation under Grant No. ESI-0099093. Any opinions, findings, and conclusions or recommendations expressed in this program are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Contents Chapter 1 Building Operations 1.1 Counting and Larger Numbers... E1 1.2 Making 10, Adding 10... E2 1.3 Addition Puzzles... E3 1.4 Counting on the Number Line... E4 1.5 Adding on the Number Line.... E5 1.6 Subtracting on the Number Line... E6 1.7 Skip-Counting... E7 1.8 Finding Missing Parts... E8 Chapter 2 Multiplication Situations 2.1 Recognizing Rectangular Arrays... E9 2.2 Arrays of Square Tiles... E10 2.3 Intersecting Lines... E11 2.4 Visualizing Intersections... E12 2.5 Finding the Number of Intersections... E13 2.6 Pairing Objects... E14 2.7 Listing Combinations... E15 2.8 Using Multiplication... E16 2.9 Writing Number Sentences for Intersecting Lines... E17 2.10 Breaking Products into Factors... E18 2.11 Separating Arrays... E19 Chapter 3 Using Addition and Subtraction 3.1 Introducing Magic Squares.... E20 3.2 Completing Magic Squares... E21 3.3 How Many Marbles?... E22 3.4 Reasoning About Money... E23 3.5 Drawing Conclusions... E24 3.6 Using the Fewest Coins... E25 3.7 Adding and Subtracting with Coins... E26 3.8 Estimating Sums and Differences... E27 Chapter 4 Grouping, Regrouping, and Place Value 4.1 Grouping Units... E28 4.2 Adding and Subtracting Measurements... E29 4.3 Regrouping with Base-Ten Blocks... E30 4.4 Mystery Number Puzzles... E31 4.5 Focusing on Digits... E32 4.6 Working Strategically... E33 4.7 Place Value with Larger Numbers...E34 iii
Contents Chapter 5 Understanding Addition and Subtraction Algorithms 5.1 Grouping by Tens... E35 5.2 Rounding to the Nearest Ten or Hundred... E36 5.3 Finding Differences on the Number Line... E37 5.4 Using Tens and Hundreds to Estimate Sums... E38 5.5 Estimate and Adjust to Find Sums... E39 5.6 Using Cross Number Puzzles to Add...E40 5.7 Using a Common Addition Algorithm... E41 5.8 Estimate and Adjust to Find Differences...E42 5.9 Using Cross Number Puzzles to Subtract...E43 5.10 Using a Common Subtraction Algorithm...E44 Chapter 6 Rules and Patterns 6.1 Exploring Rules... E45 6.2 Finding Two Rules...E46 6.3 Rules That Use More Than One Input... E47 6.4 Cards with Three Rules...E48 6.5 Recording Rules with Fractions... E49 6.6 Patterns in Geometry... E50 6.7 Patterns on the Number Line Hotel... E51 6.8 Finding Rules for Sharing Machines... E52 6.9 More Rules with Sharing Machines... E53 6.10 Finding a Rule for an Unusual Machine... E54 Chapter 7 Fractions 7.1 Working with Fractions... E55 7.2 Making Equivalent Fractions... E56 7.3 Exploring Equivalent Fractions... E57 7.4 Fractional Relationships in Context...E58 7.5 Comparing Fractions in Context... E59 7.6 Comparing Fractions... E60 Chapter 8 Charts and Graphs 8.1 Introducing Pictographs... E61 8.2 Making Pictographs... E62 8.3 Introducing Bar Graphs... E63 8.4 Exploring Probability...E64 8.5 Experimenting with Probability... E65 8.6 Making and Using a Price Chart... E66 8.7 Finding Locations on a Map... E67 8.8 Naming Intersections on a Map... E68 8.9 Graphing Solutions to Open Number Sentences... E69 Chapter 9 Exploring Multiplication 9.1 Multiplication Facts Practice... E70 9.2 Connecting Multiplication and Division... E71 9.3 Using Multiplication Facts... E72 9.4 Combining Arrays... E73 9.5 Separating Arrays into Regions... E74 9.6 Separating Arrays into Four Regions... E75 iv
Chapter 10 Length, Area, and Volume 10.1 Measuring to the Nearest 1 Inch....E76 8 10.2 Measuring Circles... E77 10.3 Measuring Paths... E78 10.4 Measuring in Centimeters... E79 10.5 Area and Perimeter...E80 10.6 More Area and Perimeter... E81 10.7 Measuring Volume... E82 Chapter 11 Geometry 11.1 Classifying Polygons by the Number of Right Angles... E83 11.2 Classifying Polygons Using Pairs of Parallel Sides...E84 11.3 Identifying Congruent Figures... E85 11.4 Working with Lines of Symmetry... E86 11.5 Identifying Attributes of Two-Dimensional Figures... E87 11.6 Identifying and Defining Polygons...E88 11.7 Making a Figure Zoo... E89 11.8 Figure Safari...E90 11.9 Describing Three-Dimensional Figures... E91 Chapter 12 Multiplication Strategies 12.1 Multiplication and Addition... E92 12.2 Using Sums to Multiply... E93 12.3 Multiplying with Base-Ten Blocks...E94 12.4 Multiplying with Arrays... E95 12.5 Separating Arrays to Multiply...E96 12.6 Multiplying with Larger Numbers... E97 12.7 Finding Missing Factors... E98 12.8 Division... E99 Chapter 13 Time, Temperature, Weight, and Capacity 13.1 Measuring Temperature... E100 13.2 Measuring Time... E101 13.3 Comparing Times... E102 13.4 Weight in Ounces, Pounds, and Tons... E103 13.5 Weighing to Solve Problems... E104 13.6 Measuring Capacity... E105 13.7 Weight and Capacity... E106 13.8 Analyzing Temperature Data... E107 Chapter 14 Addition and Subtraction in Depth 14.1 Place Value and Expanded Form... E108 14.2 Breaking Up Numbers to Add... E109 14.3 Breaking Up Numbers to Subtract... E110 14.4 Comparing Addition and Subtraction....E111 14.5 Addition Shortcuts and Rounding... E112 14.6 Addition and Subtraction Situations.. E113 v
Contents Chapter 15 Multiplication and Division 15.1 Multiplying by Tens... E114 15.2 Separating Large Arrays... E115 15.3 Making a Vertical Record... E116 15.4 Multiplying Three-Digit Numbers...E117 15.5 Multiplication and Division Situations... E118 15.6 Using Arrays for Division... E119 15.7 Solving Division Puzzles... E120 15.8 Division with Remainders... E121 vi
Counting and Larger Numbers Each train is made from cubes. Suppose you want to count the cubes as fast as you can. What strategy could you use to quickly count all the cubes? Lesson 1 How could you use place value to find which group has the larger number of cubes? A B Chapter 1 Book E1
Making 10, Adding 10 Find 10 more ways to place 10 counters in 3 boxes. Write a number sentence to describe each way. Lesson 2 Box A Box B Box C Number Sentence 3 0 7 3 0 7 10 E2 Book Chapter 1
Addition Puzzles Complete this addition puzzle by filling in the boxes. Use the frames below to show all possible solutions. Lesson 3 There are solutions to this puzzle, but the number will always be in the empty circle. Chapter 1 Book E3
Counting on a Number Line Use the number lines from Problems 1 to 4 on LAB page 7 to answer the questions. Lesson 4 The number zero had a tag on every number line in Problems 1 to 3. Which other numbers had tags on all three number lines? What is the next number that would be tagged on every number line in Problems 1 to 3, if the number lines continued? What is the first number that would be tagged on every number line in Problems 1 to 4, if the number lines continued? E4 Book Chapter 1
Adding on the Number Line Lesson 5 If you jump from one labeled point to another labeled point on this number line, will the number of spaces you jump over be: always odd, always even, or sometimes odd and sometimes even? Try a few jumps and look for a pattern. Use the table to record your jumps. Circle the phrase above that matches the pattern. Start 3 15 Land 11 9 Spaces Jumped If you add an odd number to an odd number, will the answer be: (circle one) odd, even, or can t tell? Chapter 1 Book E5
Subtracting on the Number Line Label the number line and draw jumps to help complete the number sentences. Lesson 6 36 43 45 39 4 172 4 171 723 8 7 728 952 9 965 961 E6 Book Chapter 1
Skip-Counting Lesson 7 Put an X through the multiples of 3 and circle the multiples of 4. What marking do multiples of 6 always have? If multiples of 2 were marked with a triangle, what would be the first number with an X and a triangle? If multiples of 2 were marked with a triangle, what would be the first number with an X, a circle, and a triangle? Chapter 1 Book E7
Finding Missing Parts Find numbers that make this sentence true. Lesson 8 2 12 Record the numbers in the table below. 9 6 2 3 1 5 1 4 6 10 This number sentence has too many possible solutions to list them all. 2 Record some of the possible solutions in the table. E8 Book Chapter 1
Recognizing Rectangular Arrays Fill in the total number of dots for each box or group of boxes. Lesson 1 Fill in the total number of dots for each box and find the total. Chapter 2 Book E9
Arrays of Square Tiles These rectangular arrays of square tiles are partly covered by a striped card. How many tiles can you see? How many tiles are covered? Lesson 2 Can see Covered Total Can see Covered Total Can see Covered Total Can see Covered Total Can see Covered Total Can see Covered Total E10 Book Chapter 2
Intersecting Lines Look back at LAB pages 25 and 26. Lesson 3 There were There were There were There were There were different maps with 1 street. different maps with 2 streets. different maps with 3 streets. different maps with 4 streets. different maps with 5 streets. Predict how many different maps can be made with 8 streets. Using as many spaces as you need below, draw all the 8-street maps, and label each map with its number of intersections. Number of Number of Number of Intersections Intersections Intersections Number of Number of Number of Intersections Intersections Intersections Number of Number of Number of Intersections Intersections Intersections Chapter 2 Book E11
Visualizing Intersections Each circle touches two sets of lines. In each blank circle, write the number of intersections you would see if the two sets of lines were both part of the same map. Also draw any missing sets of lines. Lesson 4 E12 Book Chapter 2
Lesson 5 Finding the Number of Intersections Draw a map of a town that has Draw a map of a town that has 7 streets and 12 intersections. 13 streets and 12 intersections. Draw a map of a town that has Draw a map of a town that 8 streets and 12 intersections. has 8 streets and more than 15 intersections. Draw a map of a town that Draw a map of a town that has 9 streets and more than has 10 streets and fewer than 14 intersections. 16 intersections. Chapter 2 Book E13
Pairing Objects How many handshakes would there be? A group of three hikers met a group of three bicyclists. Lesson 6 How many people were there? If each hiker shook hands with each bicyclist, how many handshakes would there be? Now imagine that 2 hikers met 4 bicyclists. How many people were there? Draw a diagram to show all of the handshakes if each hiker shook hands with each bicyclist. How many handshakes were there? What other number of handshakes could occur for 6 total hikers and bicyclists? E14 Book Chapter 2
Listing Combinations List all of the three-digit numbers that have: a hundreds digit from this list: 1, 2, 3 a tens digit from this list: 4, 5 a ones digit from this list: 6, 7, 8, 9 Lesson 7 Chapter 2 Book E15
Using Multiplication Lesson 8 The map of a tiny town shows Mia arranged her baseball cards 8 streets and 12 intersections. into 5 equal rows. She had 30 Draw the map. cards. How many columns did she make? Tony had 8 nickels. How much money did he have? The T-Shirt Store has 4 colors of shirts. Each can be ordered in small, medium, or large. How many one color one size combinations are there? Ryan takes 6 steps forward and 1 step back. If he moves this way two more times, what is the total number of steps he will take? Map A has 7 horizontal streets and 8 vertical streets. Map B has 6 horizontal streets and 9 vertical streets. Which map has more intersections? Explain. E16 Book Chapter 2
Writing Number Sentences for Intersecting Lines Draw a map to match the number sentences. Fill in the missing numbers. Lesson 9 9 lines 9 lines 18 intersections 20 intersections 9 lines 10 lines 14 intersections 24 intersections 10 lines 10 lines 16 intersections 21 intersections Chapter 2 Book E17
Breaking Products into Factors Draw a map to match the number sentences. Fill in the missing numbers. Lesson 10 11 lines 11 lines 10 intersections 18 intersections 11 lines 11 lines 24 intersections 0 intersections 11 lines 11 lines 28 intersections 30 intersections E18 Book Chapter 2
Separating Arrays Each array was cut into four parts. The number of tiles in each part were added together to find the total number in the array. Draw lines to show how the array was cut, and fill in the blanks. Lesson 11 20 12 10 16 20 15 (4 5) (4 4) 32 16 16 9 18 30 (4 8) (3 3) 12 12 9 28 12 18 (4 3) (7 4) Chapter 2 Book E19
Introducing Magic Squares Fill in the blanks to make these squares into magic squares. Lesson 1 Jane says that, in a magic square, the sum of the top-left and bottom-right numbers are equal to the sum of the top-right and bottom-left numbers. Do you agree? Explain. E20 Book Chapter 3
Completing Magic Squares In a magic star, each line of 4 numbers has the same sum. Complete the magic stars. Lesson 2 Chapter 3 Book E21
How Many Marbles? Yara has 3 marbles. She puts them into 3 boxes marked A, B, and C in many different ways. Fill in the blanks in her table and find any ways she missed. Lesson 3 A B C Total 0 0 3 3 0 0 1 1 0 2 1 2 E22 Book Chapter 3
Reasoning About Money Dora collects aluminum cans for recycling. She gets 5 for each can she turns in. Lesson 4 If Dora gets $1.00, how many cans did she turn in? If Dora turns in 30 cans, how much money will she get? Complete the table. Graph the points from the table. Dora turned in cans... and she got. 5 10 25 75 $1.00 $1.50 Chapter 3 Book E23
Drawing Conclusions Jackie had some marbles and put all of them into three boxes marked A, B, and C. Decide if the statement is true (T) or false (F). Statement Lesson 5 If Jackie put the same number of marbles in each box, then the total T F number of marbles must be even. Statement If Jackie put an even number of marbles in each box, then the total T F number of marbles must be even. Statement If Jackie put an odd number of marbles in each box, then the total T F number of marbles must be odd. Statement If Jackie started with an even number of marbles, then she could not have put the same number of marbles in each box. Statement If Jackie put a different number of marbles in each box, the total T F number of marbles must be odd. T F E24 Book Chapter 3
Using the Fewest Coins 10 can be made in different ways. Are there any amounts of money that can be made in only one way? Explain. Lesson 6 For any amount, what coins would you use to get a combination using the largest number of coins? Explain. Linda had 7 coins worth 53 in her pocket. She used 3 coins to buy a pencil. She now has 22. What were the 3 coins she used? Explain. How many different amounts can you have with only 2 coins? Name the coins and amounts. David has 1 quarter, 1 dime, 2 nickels, and 1 penny. How many combinations of 3 coins can he make? List the combinations. Chapter 3 Book E25
Adding and Subtracting with Coins Add and subtract coins by completing the diagram. Show each amount with the fewest coins. Lesson 7 E26 Book Chapter 3
Estimating Sums and Differences Write a number in the box that makes the sum a little more than 60. Lesson 8 19 38 46 9 Write the exact sum for Problems 1 to 4 on the line. Write a number in the box that makes the difference a little less than 30. 12 115 92 43 Write the exact difference for Problems 6 to 9 on the line. How could knowing 350 540 help you solve 357 546? Chapter 3 Book E27
Grouping Units The games at the arcade only accept quarters. Sophia had some dollars and quarters. She traded all her dollars for quarters. Complete the table to show how many quarters she might have now. Lesson 1 It costs 75 to play one of the arcade games. Complete the table for different numbers of games. Games 1 2 3 5 Quarters 12 Cost 75 $1.50 $7.50 $15.00 E28 Book Chapter 4
Lesson 2 Adding and Subtracting Measurements Complete the table using the fewest units. Chapter 4 Book E29
Regrouping with Base-Ten Blocks Write the number that matches the group of base-ten blocks. Lesson 3 If you combine the three groups above, how many blocks are used? flat, rods, units Write the same amount using the fewest blocks. flats, rods, unit E30 Book Chapter 4
Mystery Number Puzzles This puzzle is not complete. Lesson 4 A I am greater than 6 4. B I am a multiple of 7. C I am not greater than 6 8. D? What numbers match the first 3 clues? You can use this space to keep track of your reasoning. Choose one of the numbers from Problem 1. Write a fourth clue so your number is the mystery number. D Mystery number: Chapter 4 Book E31
Focusing on Digits This puzzle is on LAB page 76. Lesson 5 A I am between 10 10 and 20 20. B h u 3 C I am a square number. D t h 2 Can you find the mystery number without using all the clues? Which clue didn t you use? E32 Book Chapter 4
Working Strategically Here are four clues for a mystery number puzzle. I am a two-digit number. I am an odd number. t u 6 t u Find the mystery number, and record the clues in the order you use them. A Who Am I? Lesson 6 B C D mystery number: Why did you choose to start with the clue you did? How did you choose your second clue? Chapter 4 Book E33
Place Value with Larger Numbers Round 530 to the nearest hundred. Lesson 7 Round 2,600 to the nearest thousand. Round 490 to the nearest hundred. Round 8,100 to the nearest thousand. Label the tags on the number line. Round 23,000 to the nearest ten thousand. Round 87,000 to the nearest ten thousand. Round 66,000 to the nearest ten thousand. E34 Book Chapter 4
Grouping by Tens Write a number or draw a picture to match. When drawing a picture, use the fewest blocks. Lesson 1 1,032 3,012 3,210 3,102 2,031 1,302 2,310 Write the numbers from Problems 1 12 in order from least to greatest. Chapter 5 Book E35
Rounding to the Nearest Ten or Hundred List as many numbers as you can for each situation. If you round me to the nearest ten, you get 380. I am greater than 380. Lesson 2 If you round me to the nearest ten, you get 270. I am less than 270. If you round me to the nearest ten, you get 320. If you round me to the nearest ten, you get 450. If you round me to the nearest hundred, you get 500. E36 Book Chapter 5
Finding Differences on the Number Line Complete the table. Use the blank space for number line pictures if you wish. Lesson 3 x 1,000 x 460 540 520 954 749 777 646 121 385 869 913 Chapter 5 Book E37
Using Tens and Hundreds to Estimate Sums Write a set of instructions that would help a friend decide if a pair of two-digit numbers have a sum of 100. Your instructions should work for pairs like 30 70 and 48 52. Lesson 4 E38 Book Chapter 5
Estimate and Adjust to Find Sums For each addition problem, predict the ones digit. A B C Lesson 5 For each addition problem, predict the tens digit. A B C For each addition problem, predict the hundreds digit. A B C For each addition problem, predict the thousands digit. A B C Chapter 5 Book E39
Using Cross Number Puzzles to Add Complete each Cross Number Puzzle. Lesson 6 E40 Book Chapter 5
Lesson 7 Using a Common Addition Algorithm Some of the digits are missing from these addition problems. Write the missing digits. Name Chapter 5 Book E41
Lesson 8 Estimate and Adjust to Find Differences For each subtraction problem, predict the ones digit. A B C For each subtraction problem, predict the tens digit. A B C For each subtraction problem, predict the hundreds digit. A B C For each subtraction problem, predict the thousands digit. A B C E42 Book Chapter 5
Lesson 9 Using Cross Number Puzzles to Subtract Complete each Cross Number Puzzle. Chapter 5 Book E43
Lesson 10 Using a Common Subtraction Algorithm Some of the digits are missing from these subtraction problems. Write the missing digits. Name E44 Book Chapter 5
Exploring Rules Complete the set of Find a Rule cards. Lesson 1 Make a table to show the data from the cards. If you know the number on the back of a card from the set in Problem 1, how can you find the number on the front of the card? Chapter 6 Book E45
Finding Two Rules The school store sells boxes that contain both pens and pencils. The boxes are all the same. Complete the FAR cards to show the numbers of pens and pencils in different numbers of boxes. Lesson 2 A B C D E F G H I If you know the number of boxes, how can you find the number of pens? If you know the number of boxes, how can you find the number of pencils? E46 Book Chapter 6
Rules That Use More Than One Input Complete the table. INPUTS RULE A RULE B RULE C 3, 5 8 10 1, 4 5 10 4, 6 10 12 20 10, 1 13 22 9, 6 8, 6 3, 9 5, 15 9, 9 Lesson 3 What do you do with the inputs to get Rule A? What do you do with the inputs to get Rule B? What do you do with the inputs to get Rule C? Chapter 6 Book E47
Cards with Three Rules Only the fronts of these Find a Rule cards are shown. These cards use three rules. Complete the table below. Then complete the cards. Lesson 4 A B C D E F Card Rule I Rule II Rule III A 9 6 3 B 12 3 9 C 7 8 D E 8 5 3 F 10 4 E48 Book Chapter 6
Recording Rules with Fractions Complete the Find a Rule cards. Shade the pictures to match the numbers. Lesson 5 A B C D E F If you know that the amount for Rule A is 2_ 5, how can you figure out the amount for Rule B? Chapter 6 Book E49
Patterns in Geometry Lesson 6 Describe the next figure following the pattern using words or pictures. How many small triangles ( or ) are in the next figure following the pattern? How do you know? E50 Book Chapter 6
Patterns on the Number Line Hotel The numbers are arranged to match the Number Line Hotel. Complete the shading pattern on the grid and then describe the pattern with at least 3 different rules. Lesson 7 Describe the pattern. Chapter 6 Book E51
Finding Rules for Sharing Machines Sharing Machine A shares groups of objects equally between two people. Sharing Machine B shares groups of objects equally among three people. The machines do not accept amounts that need to be cut in order to be shared. Circle the amounts below that Sharing Machine A will share. Draw a box around the amounts below that Sharing Machine B will share. Lesson 8 Write an amount that could be shared by Sharing Machine A and Sharing Machine B. How do you know both machines will accept your amount? E52 Book Chapter 6
More Rules with Sharing Machines These machines cannot be adjusted. Each makes the same number of packages every time it is used. Unlike other machines, they can split objects. Lesson 9 SHARING MACHINE X Contents of Each Input Package Number of Packages That Come Out Contents of Each Output Package 12 coins 3 dozen eggs 6 2 packs of books, 18 in each pack 6 2 whistles 11 blocks SHARING MACHINE Y Contents of Each Input Package 9 pears Number of Packages That Come Out Contents of Each Output Package 7 books 3 1 2 rulers 3 dozen apples 18 apples 42 erasers 21 erasers Chapter 6 Book E53
Finding a Rule for an Unusual Machine Find a rule and complete the table. Use the following coins: Lesson 10 INPUT OUTPUT 2 peaches and 2 peaches and 1 peach 1 peach and 2 peaches and 3 peaches E54 Book Chapter 6
Working with Fractions In two of these pictures, the shaded part shows 1_ 3. Circle the picture that does NOT have 1_ 3 shaded. Lesson 1 Explain how you knew the picture did not show 1_ 3. Chapter 7 Book E55
Making Equivalent Fractions Circle the pictures that have 2_ 3 shaded. Lesson 2 Circle the pictures that have 2_ 4 shaded. E56 Book Chapter 7
Exploring Equivalent Fractions Oh no! The labels got smudged, and most of the numbers were erased! What could this table be about? Fill in the numbers, and make up a story that could fit. Lesson 3 Chapter 7 Book E57
Fractional Relationships in Context Shade 1_ 2 of each picture. Lesson 4 E58 Book Chapter 7
Comparing Fractions in Context Lesson 5 One egg is 1_ 12 of a dozen eggs. Crystal had half a dozen eggs. She borrowed one more egg from her neighbor. How many eggs did she have then? eggs Complete the number sentence. 1_ 2 1 _ 12 1 twelfth of a dozen and 5 twelfths of a dozen is the same as twelfths of a dozen, or half dozen. 1_ 12 _ 5 12 _ 6 12 2 6_ 12 1 _ 12 2 Chapter 7 Book E59
Comparing Fractions Label the blank bars if you want. Lesson 6 Make true sentences using,, or. Examples: 3 5 3_ 4 3 _ 4 84 83 2_ 5 1_ 2 1 _ 2 3_ 4 3 _ 4 3 _ 6 1_ 3 1 _ 3 2_ 5 3 _ 5 5_ 12 1_ 2 1 _ 2 1_ 3 1 _ 2 1_ 2 1_ 3 1 _ 3 1_ 2 1 _ 3 2_ 3 1_ 3 1 _ 3 7_ 12 _ 5 12 5_ 6 1_ 2 1 _ 3 3_ 8 5 _ 8 2_ 5 3 _ 5 1_ 2 2 _ 3 1_ 9 1 _ 9 2_ 12 _ 1 12 2_ 3 1 _ 3 1_ 3 1 _ 3 E60 Book Chapter 7
Introducing Pictographs There are 24 students in Mr. Falco s class. They all cleaned out their desk and counted the number of pencils they found. No one found more than 6 pencils. 1 12 1_ 3 1_ 2 1_ 6 1_ 8 1_ 3 of the class found 0 pencils. of the class found 1 pencil or fewer. of the class found 2 pencils or fewer. of the class found exactly 5 pencils. of the class found 6 pencils. of the class found 4 or more pencils. Lesson 1 Complete the pictograph to show the number of pencils students found in their desks. Chapter 8 Book E61
Making Pictographs There are 24 students in Mr. Reeve s class. The students answered a survey about the number of hours they spent reading the day before. The pictograph shows the results of the survey. Lesson 2 What fraction of the class read only 1 hour? What fraction of the class read 2 hours or more? Jamal said, 1_ of the class read more than I did. 4 How many hours did Jamal read? E62 Book Chapter 8
Lesson 3 Introducing Bar Graphs A magazine published this bar graph about what third graders want to be when they grow up. They did not say how many students answered the survey or label the height of the bars. Is it possible to determine which career was chosen most often? If so, what is it? Is it possible to determine the number of 8-year-olds in the survey? If so, how many are there? If 6 students chose Other, how many students chose Veterinarian? If 12 more students chose Doctor than chose Firefighter, how many students chose Doctor? What fraction of the students in the survey answered Other? Could 90 people have answered the survey? Explain. Chapter 8 Book E63
Exploring Probability Imagine that you toss two number cubes numbered 1 through 6. One cube is black, and one cube is white. Classify the following events as possible (P) or impossible (I). Lesson 4 black white 8 black white 3 black white 6 black white 4 black white 5 black white 11 Find the smallest possible value for each. black white black white black white Find the largest possible value for each. black white black white black white List all the possible values for the product black white. E64 Book Chapter 8
Experimenting with Probability Imagine that you toss a coin five times and record whether each toss is heads or tails. Lesson 5 Is it possible to record all heads? If you have just tossed 3 heads in a row, which is more likely: the next toss lands heads or the next toss lands tails? Explain. Which is more likely: 1 head in five tosses or 3 heads in five tosses? Explain. Chapter 8 Book E65
Making and Using a Price Chart Lesson 6 Erasers cost 6. Pencils cost 9. No purchases over 25! Complete the table to show all the possible purchases. Erasers Pencils Price 0 1 9 Devi and Ann both spent the same amount, but they bought different things. What might they have spent? What might they have bought? E66 Book Chapter 8
Finding Locations on a Map Lesson 7 Use to mark every square in the grid where the product of the row and column number is even. Use to mark every square in the grid where the sum of the row and column number is even. What can you say about the row and column numbers if their intersection is marked (both and )? Chapter 8 Book E67
Naming Intersections on a Map Lesson 8 Ms. Tery hid a locked suitcase at an intersection where the sum of the street number and the avenue number is 8. Mark any intersections where the suitcase could be with a. Ms. Tery hid the key to the suitcase at an intersection where the street number is 2 more than the avenue number. Mark any intersections where the key could be with a. When you found the suitcase, the key was in the lock. Where was the suitcase? E68 Book Chapter 8
Graphing Solutions to Open Number Sentences Lesson 9 Complete the table for each open sentence and graph the points. Use an for Problem 1 and a for Problem 2. 9 9 7 5 3 1 12 0 1 2 3 4 5 6 Is there a pair of numbers that works for both sentences? How do you know? Chapter 8 Book E69
Multiplication Facts Practice There are many ways to write 120 as the product of two whole numbers. Here s one: 1 120 120. (120 1 120 counts as the same way.) Find as many ways as you can. Lesson 1 120 120 120 120 120 120 120 1 120 120 How do you know you found all the ways? E70 Book Chapter 9
Lesson 2 Connecting Multiplication and Division Write a story to match the sentence. Then complete the fact family. 132 12 Draw a picture to model the division sentence and your story. You can use the grid if you want. Chapter 9 Book E71
Using Multiplication Facts There are many ways to draw a rectangular array with 24 squares. Draw as many arrays as you can. Lesson 3 Find as many ways as you can to write 48 as the product of two whole numbers. 48 48 48 48 48 48 E72 Book Chapter 9
Combining Arrays Lesson 4 QW 4 4 JY 2 VW NW NZ QZ Chapter 9 Book E73
Separating Arrays into Regions Use the number of squares in each part to find the number of squares in the entire array. Lesson 5 Total number of squares: Here is another way to separate the array. Write number sentences for the two parts of this array. Write a number sentence for the entire array. E74 Book Chapter 9
Lesson 6 Separating Arrays into Four Regions Imagine an array with 8 rows of small squares. The array has been divided into four sections using two lines. You can see the number of squares in the two sections on the left, but not the two sections on the right. The two sections on the right of the array might have any number of columns! Think of at least three different arrays, and complete a Cross Number Puzzle to go with each of your arrays. You may use the grid at the bottom of the page if you wish. Chapter 9 Book E75
Measuring to the Nearest 1_ 8 Inch Lesson 1 On the ruler above, how many spaces is each inch divided into? Write the measurement of each segment to the nearest 1_ 8 inch. A: in. C: in. E: in. B: in. D: in. F: in. Write the lengths of the segments in order from shortest to longest. E76 Book Chapter 10
Measuring Circles The distance across a circle, through its center, is called the diameter of the circle. The distance around the circle is called the circumference of the circle. (You could measure it by bending a piece of string along the circle and then measuring the straightened-out string with a ruler.) Measure the diameter and circumference of each circle to the nearest 1 4 inch. Lesson 2 A B C D E Diameter Circumference Chapter 10 Book E77
Measuring Paths Lesson 3 Measure path MNOPQ to the nearest 1_ 4 inch. Measure path MPNOQ to the nearest 1_ 4 inch. Measure path MONPQ to the nearest 1_ 4 inch. Find and measure another path from M to Q that touches N, O, and P. E78 Book Chapter 10
Measuring in Centimeters Lesson 4 Measure each segment to the nearest centimeter. AB : AC : AD : AE : cm cm cm cm BC : BD : BE : cm cm cm CD : CE : DE : cm cm cm Measure the path AEDAB to the nearest centimeter. Find a path along the segments in the picture that starts at A and ends at B and is... A... about 28 cm long. B... about 36 cm long. cm Chapter 10 Book E79
Area and Perimeter For each problem, draw along the lines to make a figure that has the area (A) and perimeter (P) shown. Lesson 5 A: 4 sq cm A: 5 sq cm A: 6 sq cm A: 5 sq cm P: 10 cm P: 10 cm P: 10 cm P: 12 cm A: 9 sq cm A: 8 sq cm A: 6 sq cm P: 12 cm P: 12 cm P: 12 cm E80 Book Chapter 10
More Area and Perimeter Draw a figure along the lines with the smallest possible perimeter for each area. Lesson 6 A: 4 sq cm A: 5 sq cm A: 6 sq cm P: cm P: cm P: cm A: 7 sq cm A: 8 sq cm A: 9 sq cm P: cm P: cm P: cm Chapter 10 Book E81
Measuring Volume Each problem shows a picture of a model made from centimeter cubes. Build the model and find its volume. Lesson 7 volume: cubic cm volume: cubic cm volume: cubic cm volume: cubic cm volume: cubic cm volume: cubic cm E82 Book Chapter 10
Classifying Polygons by the Number of Right Angles Write the letter of each figure in the oval that describes it. Lesson 1 A B C D E F G H J K I Chapter 11 Book E83
Classifying Polygons Using Pairs of Parallel Sides Write the letter of each figure in the oval that describes it. Lesson 2 A B C D E F G H J K I E84 Book Chapter 11
Identifying Congruent Figures Draw as many figures as possible on the grid below. However: all figures you draw must have the same area as figure A, one figure must be congruent to figure A, there should be no congruent figures, and draw only on the grid lines. Lesson 3 A Use the grid to draw at least 4 figures that are congruent to figure B. Chapter 11 Book E85
Working with Lines of Symmetry Draw 3-sided polygons for each. Lesson 4 exactly 3 equal sides exactly 2 equal sides no equal sides Draw 4-sided polygons for each. 4 equal sides exactly 2 equal sides 2 pairs of equal sides Circle all the figures you drew that have at least 1 line of symmetry. E86 Book Chapter 11
Identifying Attributes of Two-Dimensional Figures Cut out the two congruent triangles at the bottom of the page. Create various figures by matching congruent sides. Trace your figures onto this page, and then draw all lines of symmetry on each figure. Lesson 5 Chapter 11 Book E87
Identifying and Defining Polygons Follow the directions. Place point A at (1,4). Place point B at (3,6). Place point C at (5,6). Place point D at (5,4). Place point E at (3,2). Place point F at (1,2). Draw AB. Draw BC. Draw CD. Draw AD. Lesson 6 A B C D A is the instruction for drawing a trapezoid with corners at 4 of the points you plotted. Use the points you plotted to give the instructions for drawing: a different trapezoid a square a pentagon a hexagon What other polygon can you make using the points on the grid? E88 Book Chapter 11
Making a Figure Zoo Make a three-dimensional figure by cutting the large net below along the heavy lines and folding along the dashed lines. Then answer the questions about the figure. Lesson 7 How many faces does figure DD have? faces Is figure DD a pyramid? Circle one: Yes No How many faces have at least 2 lines of symmetry? faces Is figure DD a prism? Circle one: Yes No On the small copy of the net, shade two faces that are congruent and opposite each other on the figure. DD DD Chapter 11 Book E89
Figure Safari Find all the figures in the class Figure Zoo that match this set of clues: CLUES: At least 1 of my faces is a triangle. All of my faces have at least 1 line of symmetry. Lesson 8 Figures: Choose one of the figures that matches the clues above. Figure: Write one or two more clues so your chosen figure is the only figure that matches all the clues. CLUES: At least 1 of my faces is a triangle. All of my faces have at least 1 line of symmetry. E90 Book Chapter 11
Describing Three-Dimensional Figures Use the diagrams of the three-dimensional figures to write the numbers in the blanks. Lesson 9 Face A has sides. Prism 1 has edges. the number of sides of the number of edges one of the parallel faces of the prism Face D has sides. Prism 2 has edges. the number of sides of the number of edges one of the parallel faces of the prism Face E of Pyramid 1 has Pyramid 1 has edges. the number of sides of the bottom face sides. the number of edges of the pyramid Chapter 11 Book E91
Multiplication and Addition Find the costs. Lesson 1 Cost of 5 cars 30 Cost of 7 hats $7.00 Cost of 5 trains Cost of 7 bows Cost of 5 of each item 90 Cost of 7 of each item $8.05 What is the cost of What is the cost of 1 car and 1 train? 1 hat and 1 bow? Cost of 3 pencils 12 Cost of 4 pencils 28 Cost of 6 pens 60 Cost of 8 pens $1.20 Cost of 6 of each item Cost of 4 of each item Show (8 3) 5 (8 5) (3 5) using the machines below. E92 Book Chapter 12
Using Sums to Multiply Make the third product equal to the sum of the first two products. 20 4 _ 80 7 4 _ 27 4 _ 8 _ 8 _ Lesson 2 31 8 _ 17 3 _ 3 _ 3 _ 6 _ 6 _ 6 _ 21 51 180 204 30 6 36 20 7 27 _ 120 144 _ 4 _ 4 _ 4 _ 162 _ 7 _ 7 _ 7 24 184 245 Chapter 12 Book E93
Multiplying with Base-Ten Blocks Complete the tables. Lesson 3 a 4 10 14 6 a a 4 10 14 10 a a 4 10 14 16 a b 8 10 18 7 b b 8 10 18 10 b b 8 10 18 17 b c 5 10 15 c 5 10 15 8 c 10 c c 5 10 15 18 c E94 Book Chapter 12
Multiplying with Arrays Lesson 4 19 10 (10 10) (9 10) 13 10 ( 10) ( 10) 15 10 ( 10) ( 10) 17 10 10 4 10 9 12 10 25 10 36 10 47 10 10 28 Chapter 12 Book E95
Separating Arrays to Multiply Fill in the missing numbers. Imagine or draw lines and intersections if needed. 18 6 37 4 Lesson 5 71 8 24 9 32 7 37 8 E96 Book Chapter 12
Multiplying with Larger Numbers Fill in the missing numbers. Imagine or draw the diagrams if needed. 27 13 19 25 Lesson 6 31 19 12 34 Chapter 12 Book E97
Finding Missing Factors Complete the multiplication sentences. You may imagine or draw the diagrams if you wish. Lesson 7 29 87 7 112 _ 7 _ 7 _ 7 112 4 76 24 192 _ 6 132 15 105 E98 Book Chapter 12
Division Missing Factor Describe how you might complete the following multiplication problem so that another student could understand your steps. Lesson 8 4 _ 132 Chapter 12 Book E99
Measuring Temperature Lesson 1 Fill in the missing temperature. Shade the thermometer to match. E100 Book Chapter 13
Measuring Time Fill in the missing numbers, times, and clock hands. Lesson 2 Chapter 13 Book E101
Comparing Times Fill in the missing times, clock hands, words, and numbers. Lesson 3 E102 Book Chapter 13
Weight in Ounces, Pounds, and Tons A tennis ball weighs 2 oz. How much does a baseball weigh? Lesson 4 How much does a football weigh? How much does a basketball weigh? How many tennis balls would it take to balance a basketball? The maximum weight for a bowling ball is 4 tennis balls less than 12 basketballs. What is the maximum weight for a bowling ball? Chapter 13 Book E103
Weighing to Solve Problems All bags with the same label have the same weight. weighs 2 lb, 13 oz. Lesson 5 weighs lb, oz. weighs lb, oz. weighs lb, oz. weighs lb, oz. weighs lb, oz. weighs lb, oz. E104 Book Chapter 13
Measuring Capacity If you only have a 5-gallon jug and a 3-gallon jug, how could you use them to measure exactly 4 gallons? Lesson 6 First, fill the jug to fill the -gallon jug. Then pour from that -gallon jug to the top. There are gallons left in the -gallon jug, and the -gallon jug is full. Empty the full jug. Then pour the gallons from the -gallon jug into the -gallon jug. Fill the -gallon jug to the top. Pour enough from the -gallon jug to fill the -gallon jug the rest of the way. To do that you will pour gallon out and have gallons left. There are 4 gallons in the -gallon jug. Chapter 13 Book E105
Weight and Capacity Suppose you have exactly 1 cup of each of these items. Lesson 7 You want to put the cups in order from lightest to heaviest. You have only a pan balance. You can compare two cups at a time. Suppose you start with the cooking oil and the water. It would look something like this. The water is heavier. So, you put that cup aside as you continue to find the lightest cup. Next, you compare the cooking oil with another cup. You put the heavier cup aside. You keep doing that until you find the lightest. Which cup do you think will be the lightest? Putting aside the lightest, you now have four cups left to order. You compare all of them using the balance. How many comparisons will you need to make? Which cup do you think will be the lightest this time? Now you have three cups left. How many comparisons will you make with three cups? Which cup do you think will be the lightest this time? Finally, you can find the heaviest cup of all by doing one more comparison. Which cup do you think it will be? E106 Book Chapter 13
Analyzing Temperature Data Lesson 8 Fill in the missing numbers and shading. Chapter 13 Book E107
Place Value and Expanded Form Find the mystery number. Lesson 1 I. I am a three-digit number. II. My ones digit is 4 times my hundreds digit. III. I am a square number. I. I am a three-digit number. h t u II. My hundreds digit minus my tens digit is 3. (h t 3) III. My tens digit minus my ones digit is 3. (t u 3) IV. The product of my digits is 80. (h t u 80) I. I am a three-digit number. II. I am a factor of 888. III. The product of my digits is 64. I. I am an even three-digit number less than 500. II. I am a multiple of 71. III. My tens digit is the product of my hundreds digit and my ones digit. E108 Book Chapter 14
Breaking Up Numbers to Add Find the sum. Write a story to go with the number sentence. Lesson 2 365 61 Chapter 14 Book E109
Breaking Up Numbers to Subtract Complete the number sentence. 849 213 37 642 Lesson 3 216 304 311 48 734 400 59 177 609 818 29 111 747 66 612 115 725 907 521 1,016 E110 Book Chapter 14
Lesson 4 Comparing Addition and Subtraction Each letter stands for a digit from 0 through 9. Each letter only has one value, but two different letters might have the same value. Figure out what digit each letter stands for. AC,ACA BC,BCB ACA,CAC W,XYZ W,XVZ YZ,VWZ If the letter O stands for 8 and the letter U stands for 7, what do the rest of the letters stand for? TWO TWO FOUR Chapter 14 Book E111
Addition Short cuts and Rounding Each letter stands for a digit from 0 through 9. Different letters must have different values. Figure out what digit each letter stands for. Lesson 5 ABC ABC ABC B,2AD E112 Book Chapter 14
Lesson 6 Addition and Subtraction Situations Complete the number sentence and write a story to go with it. 614 128 243 A On a separate sheet of paper, secretly write and complete a number sentence with at least 1 addition and 1 subtraction in it. B On this page, write a story to go with the number sentence. C Have a partner write a number sentence to match your story. D Compare your partner s number sentence to yours. Chapter 14 Book E113
Multiplying by Tens Write and complete multiplication sentences for each array of quarters. Write as many as you can. Lesson 1 100 6 600 150 4 4 6 24 25 E114 Book Chapter 15
Separating Large Arrays Find the area of this L-shaped field. Use pictures, words, or numbers to show your solution. Lesson 2 11 miles 7 miles 17 miles 8 miles Chapter 15 Book E115
Making a Vertical Record Find the product. 18 18 _ 19 17 _ 23 23 _ Lesson 3 24 22 _ 36 36 _ 37 35 _ 47 47 _ 48 46 _ Solve. Which product is larger? 149 151 or 150 150 Show how you know with words, numbers, or pictures. E116 Book Chapter 15
Multiplying Three-Digit Numbers Use the diagram to help you find the product. 300 30 3 300 Lesson 4 20 4 20 6,000 30 4 12 3 333 24 324 33 100 20 4 200 10 4 40 4 40 4 44 124 44 214 10 5 200 70 3 137 52 15 273 Chapter 15 Book E117
Lesson 5 Multiplication and Division Situations Max had 132 square tiles. Each tile had an area of 1 square foot. He used the tiles to make the floor of a rectangular patio, so that he would use the least amount of fencing to go around it. What is the length and width of Max s patio? Use the space below to show how you solved the problem. E118 Book Chapter 15
Using Arrays for Division There are 126 children going on a field trip. Each van can hold 7 children. How many vans do they need? Lesson 6 But wait! These kids are not old enough to ride in the front seat. Only 6 children can ride in each van. How many vans do they need? The teachers consider using larger vans that can hold 9 children. How many vans of this size will they need? The teachers decide to use buses. Each bus can hold 48 children. How many buses do they need, and how many empty seats will there be? Chapter 15 Book E119
Solving Division Puzzles For each division problem, create and solve a division puzzle using only whole numbers, if possible. Cross out any problems which cannot be solved with only whole numbers. For Example: 144 7 cannot be solved with only whole numbers because 20 7 140 and 21 7 147. 144 2 144 3 Lesson 7 2 3 144 4 144 5 4 144 6 5 Find more puzzles for 144. 6 E120 Book Chapter 15
Division with Remainders Remember that the Marble Club has 185 marbles, and 7 official members. One day, the marbles are shared evenly and there are none left. How many members are at the meeting? Lesson 8 Each member gets more than 28 marbles but fewer than 33. How many members are at the meeting? A new member joins the club and contributes 38 marbles to the club s collection. All members attend the welcome meeting. How many marbles are left over after they are shared evenly? With the new marble collection, how many members are at a meeting when there are 6 marbles left over? Chapter 15 Book E121