Student Work Text. Texas Edition. Lesson Activity Book

Transcription

1 HARCOURT R SCHOOL O PUBLISHE ERS Texas Edition Student Work Text Lesson Activity Book Developed by Education Development Center, Inc. through National Science Foundation Grant No. ESI

2 Copyright 2009 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. Requests for permission to make copies of any part of the work should be addressed to School Permissions and Copyrights, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida Fax: HARCOURT and the Harcourt Logo are trademarks of Harcourt, Inc., registered in the United States of America and/or other jurisdictions. Printed in the United States of America ISBN 13: ISBN 10: If you have received these materials as examination copies free of charge, Harcourt School Publishers 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 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.

3 Principal Investigator E. Paul Goldenberg Curriculum Design and Oversight E. Paul Goldenberg Lynn Goldsmith Nina Shteingold Research Director: Lynn Goldsmith Sabita Chopra Suenita Lawrence Nina Arshavsky Sophia Cohen Katherine Schwinden Cynthia Char Andrea Humez Eugenia Steingold Editorial Director: Francis Fanning Nicholas Bozard Eric Karnowski Writing Director: Eric Karnowski E. Paul Goldenberg Suenita Lawrence Nina Shteingold Abigail Branch Stacy Grossman Debora Rosenfeld Kate Snow Sara Cremer Andrea Humez Paisley Rossetti Julie Zeringue Graphics and Design Directors: Laura Koval Jessica Cummings E. Charles Snow and Korynn Kirchwey Jennifer Cummings Jenny Wong Project Management Director: Eric Karnowski Kim Foster June Mark David O Neil Amy Borowko Alexander Kirchwey Glenn Natali Cynthia Plouff Nannette Feurzeig Helen Lebowitz Kimberly Newson Additional Mathematics Resource Al Cuoco Mathematics Reviewers Richard Askey, Professor of Mathematics, Emeritus University of Wisconsin, Madison, Wisconsin Roger Howe, Professor of Mathematics Yale University, New Haven, Connecticut Sherman Stein, Professor of Mathematics, Emeritus University of California at Davis, Davis, California Harvey Keynes, Professor of Mathematics University of Minnesota, Minneapolis, Minnesota David Singer, Professor of Mathematics Case Western Reserve University, Cleveland, Ohio iii

4 Chapter 1 Name Introducing This Year s Mathematics NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.3A, 5.5A Make an organized list of all possible combinations of dimes, nickels, and pennies that make 25. Use this table for your list. Date Dimes Nickels Pennies What is the total number of different combinations? Explain how you know you have listed all the possible combinations. 1 1 I one 1

5 Make an organized list of the number of coins in each coin combination in Problem 1. Use this table for your list. Dimes 2 Nickels 1 Pennies 0 Number of Coins 3 Do any of the combinations have the same number of coins? Challenge Use the table above to help you answer the following questions. How many different combinations of dimes, nickels, and pennies are worth 24? Explain how you know. How many different combinations of dimes, nickels, and pennies are worth 26? Explain how you know. 2 two II prime

6 Chapter 1 Name Investigating Cross Number Puzzles NCTM Standards 1, 2, 7, 8 TEKS 5.3A, 5.16B As you complete these puzzles, look for shortcuts. Remember that amounts on both sides of a thick line must be the same. Date prime III three 3

7 Put numbers in the shaded boxes to make up your own Cross Number Puzzle. Complete the puzzle. Explain how you know what numbers to write to the right and below the thick lines. For lunch, Kim bought a sandwich for $2.50 and a glass of lemonade for $1.25. Steve bought a salad for $1.25 and a slice of pizza. If they both spent the same amount, how much was the slice of pizza? Explain how you know. Challenge Complete the puzzles. 4 four IV 2 2

8 Name Chapter 1 Investigating Input-Output Tables Complete the tables. NCTM Standards 1, 2, 6, 8 TEKS 5.3A, 5.3B, 5.3C, 5.14A, 5.14B, 5.16B Date Add 3 5 Multiply by 2 10 Subtract 6 4 MACHINE OUTPUT 4 INPUT Multiply by 3 6 Subtract the Input 4 MACHINE OUTPUT 4 INPUT Every week you earn a certain amount of money. You put half in the bank and spend half. If you earned $6 each week, how much money would you have spent by the end of 4 weeks? Show your work. If you earned $8 a week instead, how much money would you have been able to spend after 4 weeks? Show your work. If you have spent $40 after working for 4 weeks, how much money did you earn each week? Explain. prime V five 5

9 Complete the tables. INPUT Multiply by Divide by MACHINE OUTPUT MAKE YOUR OWN. INPUT Multiply by 6 60 Divide by 3 24 MACHINE OUTPUT Find a one-step rule that would give the same outputs for the same inputs as the two-step rule shown in Problem 7. Challenge Complete the table. INPUT Subtract 8 17 Multiply by 2 60 MAKE YOUR OWN. Add 16 MACHINE OUTPUT 6 six VI 2 3

10 Chapter 1 First, complete the Cross Number Puzzle on the left. Then double each of the numbers to complete the puzzle on the right. Check to make sure the new puzzles work. EXAMPLE INPUT Name Connecting Input-Output Machines and Puzzles NCTM Standards 1, 2, 6, 9 TEKS 5.3A, 5.3B, 5.3C, 5.15A, 5.16B MACHINE OUTPUT Date This output puzzle works! Does this output puzzle work? Does this output puzzle work? Emma counted 14 goldfinches and 8 wrens at her birdfeeders on Saturday morning. In the afternoon she counted twice as many of each kind of bird. How many birds did Emma count in all on Saturday? Explain how you know. prime VII seven 7

11 Complete all puzzles by filling in the missing numbers. Remember that the machine doubles the numbers in the Input puzzles. Here you may have to look at the numbers in the Output puzzles to complete the Input puzzles. Explain how you completed the top row of the input puzzle in Problem 5. Challenge 8 eight VIII 2 2 2

12 Chapter 1 Name Date Introducing Negative Outputs NCTM Standards 1, 2, 8, 9, 10 TEKS 5.3A, 5.3B, 5.6, 5.16B Complete the tables. INPUT Add Subtract 8 16 MACHINE OUTPUT 16 Add 3 7 Multiply by 2 14 Subtract the Input 10 Add 6 MACHINE OUTPUT INPUT The temperature in the evening was 7 less than the temperature in the afternoon. Use the table to record some possible afternoon and evening temperatures. Afternoon Evening Suppose the temperature was 0F in the afternoon. What would the new temperature be in the evening after it dropped 7? Explain how you found the answer. 3 3 IX nine 9

13 Use the number lines to complete the tables. Fill in the shorthand rules. INPUT OUTPUT INPUT OUTPUT INPUT OUTPUT For Problem 7, explain how you found the input when the output was 25. Challenge Complete the table and shorthand rule. INPUT OUTPUT ten X 2 5

14 Chapter 1 Name Determining Rules Using Two Operations NCTM Standards 1, 2, 6, 8, 9 TEKS 5.14A, 5.15A, 5.16A Complete the tables and shorthand rules. Date INPUT x OUTPUT x INPUT x OUTPUT x INPUT x OUTPUT x INPUT x OUTPUT One week, Beth charged $5 for each of the 3 days she worked in her neighbor s garden and $8 for mowing the lawn once. How much did she earn? Explain. Tim earned $7 for each of the 4 days he raked leaves in his neighbor s yard. He spent $10 to buy a new rake. How much did he have left? Explain. prime XI eleven 11

15 Complete the tables and write shorthand rules. INPUT x OUTPUT INPUT x OUTPUT INPUT x OUTPUT INPUT x OUTPUT Challenge Complete the table and then describe what a machine might be doing to generate these outputs. Use pictures, numbers, or words to explain the machine s rule. INPUT OUTPUT twelve XII 2 2 3

16 Chapter 1 Name Complete all the puzzles. Multiplying Cross Number Puzzles NCTM Standards 1, 2, 6, 7, 8 TEKS 5.3A, 5.3B, 5.3C, 5.16B Date A small package of charms has 4 silver charms and 2 gold charms. A large package has 3 times as many gold and silver charms. How many charms are in a large package? Explain. prime XIII thirteen 13

17 Complete all the puzzles. To complete the puzzles on the left, you may need to use some of the numbers in the puzzles on the right. For Problem 6, explain how you found the three missing numbers for the light green boxes in Puzzle B. Challenge Divide. 14 fourteen XIV 2 7

18 Chapter 1 Name Problem Solving Strategy Look for a Pattern NCTM Standards 1, 2, 6, 8, 9 TEKS 5.5A, 5.14B, 5.14C, 5.16A, 5.16B The Rockin Rock Candy machine only takes nickels. There is no sign on the machine telling you how many candies you will get for each nickel. Date The table shows the number of candies given for 1 nickel, 2 nickels, and 6 nickels. Complete the table to show the number of candies you will get for 25, 15, and 50. Write the rule. Nickels x Candies Jon and Peter each saved a certain amount of money each week. Complete the tables. How many weeks did it take each boy to save $60? JON Weeks x Dollars Saved weeks PETER Weeks x Dollars Saved Use the toothpick patterns of triangles to complete the table and write the rule. weeks Number of Triangles x Number of Toothpicks XV fifteen 15

19 Problem Solving Test Prep Choose the correct answer. Alice had a collection of 33 baseball cards. She gave 5 cards to her sister. Let c represent the number of cards Alice had left. Which number sentence could be used to find the number of cards Alice had in her collection? A. c 5 33 B. c 5 33 C. 5 c 33 D. 5 c 33 A typical slice of cheese pizza contains 248 calories, 11 grams of protein, 24 grams of carbohydrates, and 12 grams of fat. How many calories are in an eight-slice pizza? A. 1,984 calories B. 1,900 calories C. 1,620 calories D. 1,500 calories Jenny has 2 rooms to carpet. Each room has the same dimensions as the diagram below. What is the area of the 2 rooms combined? A. 38 square feet B. 69 square feet C. 78 square feet D. 138 square feet What rule can you use to find the next number in the number pattern? 1; 10; 100; 1,000; A. Add 9. C. Multiply by 10. B. Add 90. D. Multiply by 100. Solve each problem. Explain your answer. Bret built a brick wall. He began with 1,051 bricks and built the wall that was between 31 and 36 bricks long. There were 31 bricks left over. How many bricks high is the wall Bret built? Explain how you know. Draw what this figure will look like if it is rotated 180 around the point. Explain how you know. 16 sixteen XVI

20 Name Review/Assessment NCTM Standards 1, 2, 6, 7, 8, 9 Date Complete the Cross Number Puzzles. Lesson 2 Complete the Cross Number Puzzle on the left. Then double each of the numbers to complete the puzzle on the right. Lesson 4 Complete both Cross Number Puzzles. Lesson 7 prime XVII seventeen 17

21 Complete the table. Lesson 3 INPUT Multiply by 8 64 Divide by MACHINE OUTPUT Complete the tables and rules. Lessons 5 and 6 INPUT x OUTPUT x INPUT x OUTPUT x 1 INPUT x OUTPUT x Use the tile patterns to complete the table and write the rule. Lesson Pattern Number x Number of Tiles 3 18 eighteen XVIII 2 3 3

22 Chapter 2 Name Finding Patterns in the Multiplication Table NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.3B, 5.3C, 5.16B Fill in the table. Use patterns you know to help you. Date Use facts in the table to complete these number sentences prime XIX nineteen 19

23 There are 27 students in a class. No more than 6 students may ride in each van. How many vans are needed to take all the students on a field trip? Tell or show how you know. Write the fact family that uses the given numbers. 6, 48, 8 7, 9, , 9, 6 7, 56, 8 Challenge 8, 64, 8 14, 126, 9 20 twenty XX 2 2 5

24 Chapter 2 Splitting Area Models Complete the area models and puzzles. Name NCTM Standards 1, 2, 7, 9, 10 TEKS 5.3B Date XXI twenty-one 21

25 Complete the puzzles For 11 and 12, draw lines (one vertical and one horizontal) to split each area model. Write the new factors. Complete puzzles to match Challenge twenty-two XXII 2 11

26 Chapter 2 Name Doubling and Adding NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3B, 5.14A Complete the table. You might want to double or add other numbers in a column to complete it. Date prime XXIII twenty-three 23

27 Complete the table row. Then answer the question All 18 students in the class are supposed to bring a dozen cookies to sell at a bake sale. How many cookies will the class have to sell? Explain. Complete the table row. Then answer the question There were 18 boxes of mini muffins with 16 muffins in a box. If the class sells 14 boxes of muffins at the bake sale, how many muffins will they sell? Explain. Challenge Complete the table row twenty-four XXIV

28 Chapter 2 Name Multiplying by Multiples of 10 NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.3B, 5.15A Complete the area model and puzzles. Date XXV twenty-five 25

29 What is the connection between 2 3 and 20 30? Complete the number sentences Challenge Complete the puzzle twenty-six XXVI 2 13

30 Chapter 2 Name Working with Large Numbers NCTM Standards 1, 2, 7, 9 TEKS 5.1A Write numbers to match the words. Nine hundred ninety-nine billion, nine hundred ninetynine million, nine hundred ninety-nine thousand, nine hundred ninety-nine Date Four hundred five million, seven hundred thousand, five hundred four Eight hundred six billion, three hundred ten million, seventy-two thousand, fifty-eight For each group of numbers, write 1, 2, or 3 in the boxes to rank the numbers in order from greatest to least. 4,203,615 16,710,688, ,403,555,403 4,302,516 16,710,868, ,555,403,403 4,320,615 16,710,688, ,403,403, XXVII twenty-seven 27

31 Complete the number sentences. 4,502,000 (4 1,000,000) (5 ) (2 ) 30,020,008 (3 ) (2 ) (8 ) (4 1,000,000) (8 10,000) (5 1,000) (9 100) (9 10,000,000) (6 100,000) (3 100) Write,, or to complete the number sentences. 351,007, ,070,298 10,000,000, ,000,000 46,644,464,646 46,644,464,446 Challenge Write the number that is forty thousand greater than four hundred twenty billion, three hundred twenty-five million, six hundred sixty-seven thousand, eight hundred ten. 28 twenty-eight XXVIII 2 2 7

32 Chapter 2 Name Round and estimate. Estimating Products NCTM Standards 1, 2, 4, 6, 7, 8, 9 TEKS 5.3B, 5.4, 5.10A Date Estimate: Estimate: Estimate: Estimate: Complete the number sentences prime XXIX twenty-nine 29

33 Figure out how many tickets were bought in a year if people each bought 40 tickets. tickets 30 people each bought 400 tickets. tickets 40 people each bought 300 tickets. tickets Solve the problem. Kim and her mother want to plant a border garden of wildflowers in their backyard. Kim drew this sketch showing the garden s measurements. In order to buy wildflower seeds, Kim and her mother need an estimate of the product (the area of the garden). How can they estimate the product to be certain that they buy enough seeds? Explain your estimate. Estimate: sq in. Challenge Show how you could estimate the number of square feet in Kim s garden. sq ft 30 thirty XXX 2 3 5

34 Chapter 2 Name Estimate the products. Estimating in Various Ways NCTM Standards 1, 2, 7, 8, 9 TEKS 5.4, 5.16B Date Example 1 Example 2 Estimate: Estimate: , , Estimate: Estimate: Estimate: Estimate: Estimate: Estimate: prime XXXI thirty-one 31

35 Show two different ways to estimate the product Estimate 1 Estimate 2 How can you use the fact to estimate ? Estimate: Challenge Jenna estimated the product by using the product Her friend Miccah used the estimate Without calculating the product 42 14, which estimate do you think is closer? Why do you think that? 32 thirty-two XXXII

36 Chapter 2 Name Discovering a Useful Multiplication Pattern NCTM Standards 1, 2, 7, 9, 10 TEKS 5.5A, 5.16A Complete the diagrams and number sentences. Date XXXIII thirty-three 33

37 Complete the related number sentences , , ,808 Complete the tables by filling in the white boxes. Challenge Complete the diagram and related sentence thirty-four XXXIV 2 17

38 Chapter 2 Name Extending the Multiplication Pattern NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.5A, 5.16B Complete the diagrams and tables. Date Steps Away Steps Away Steps Away XXXV thirty-five 35

39 Complete the tables. Steps Away Steps Away Steps Away Steps Away Use these square number facts to complete the number sentences Challenge Would you use square numbers and the patterns of steps away to solve 21 24? Why or why not? 36 thirty-six XXXVI

40 Chapter 2 Name Investigating Why the Pattern Works NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.5A, 5.16B Fill in the missing numbers. Date prime XXXVII thirty-seven 37

41 Solve each problem. You can use ,025 to figure out Explain how this can be done and find the product. James wants to use 1-foot carpet squares to cover a porch floor. The porch is 9 feet by 15 feet. Use to help you figure out how many carpet squares James will need. Challenge Complete the number sentences. 38 thirty-eight XXXVIII 2 19

42 Chapter 2 Name Fill in the missing numbers. Finding Products of Large Factors NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.5A Date Use the product 5 steps away to figure out the square numbers (40 50) (60 70) (30 ) Use simpler multiplications to find the products. You might double and add products, split an area model, or use square numbers XXXIX thirty-nine 39

43 Show two different ways to find the product First Method Second Method Which method do you prefer the first or the second? Explain why. Use the product 5 steps away to figure out the square numbers ( 70 ) ( ) Challenge forty XL

44 Chapter 2 Name Problem Solving Strategy Solve a Simpler Problem NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3B, 5.14A, 5.14B, 5.14C, 5.16B Solve the problem and check ( ) the strategy you used. If you checked OTHER, tell what you did. Show your work. Date Rachel delivered 21 newspapers a week for the last 19 weeks. How many total newspapers did she deliver? newspapers Made an area model or puzzle Used a square number Doubled or added products Other: Twenty-six students in a class each decorated a dozen eggs. The teacher knew she would need to find lots of room to display them all. How many eggs were there? eggs Made an area model or puzzle Doubled or added products Other: prime XLI forty-one 41

45 Problem Solving Test Prep Choose the correct answer. Vicky tosses a small paper cup in the air 50 times. It lands on its side 45 times. From the data what is the probability that the cup will land on its side? A. 4 5 B C. D The volume of the rectangular prism is 64 cubic units. Which are the missing dimensions? A. l 6, w 2 B. l 6, w 3 C. l 8, w 4 D. l 8, w 2 What is the weight of one box labeled e? A. 12 pounds C. 16 pounds B. 14 pounds D. 18 pounds What is the value of w in the puzzle? s 6 10 t v w z ,064 A. 59 C. 450 B. 60 D. 500 Solve each problem. Explain your answer. James brought a plant to class on Monday and it was 8 centimeters tall. On Tuesday, it was 12 centimeters; on Wednesday, 17 centimeters; and on Thursday, 23 centimeters. If the plant s growing pattern continues, how tall will it be on Friday? Explain. The chairs for the school concert were set up in 30 rows with 30 chairs in each row. In order to make an aisle, the chairs are rearranged into 26 rows with 34 chairs in each row. How does the rearrangement change the number of chairs? Explain. 42 forty-two XLII 2 3 7

46 Name Review/Assessment NCTM Standards 1, 2, 6, 7, 9, 10 Date Complete the number sentences for the fact family. Lesson Complete the puzzles. Lesson Complete the table row. Lesson Complete the number sentences. Lesson For each group of numbers, write 1, 2, or 3 in the boxes to rank the numbers in order from greatest to least. Lesson ,468,902 63,890,605, ,872,444,203 21,648,920 63,890,605, ,782,023,444 21,468,092 63,980,605, ,782,203,444 prime XLIII forty-three 43

47 Estimate the products. Lessons 6 and Complete the diagrams. Lessons 8, 9 and 10 Show two different ways to find the product Lesson 11 Solve the problem. Show your work. Chris wants to know how many dozen eggs are closest to 100 eggs. Help him find the answer. dozen eggs Lesson forty-four XLIV 4 11

48 Chapter 3 Name Date Investigating Mystery Number Puzzles NCTM Standards 1, 6, 7, 8, 10 TEKS 5.3A, 5.3B, 5.14C, 5.15A Solve the puzzles. The boxes next to the clues show you the number of digits in the solution. Clues Workspace Puzzle A 25 is one of its 6 factors Sum of the digits is a multiple of 5 Puzzle B Multiple of 8 less than 7 8 Sum of the digits is even Ones digit is 4 more than the tens digit Puzzle C Product of the digits 15 Sum of the digits 8 Puzzle D Multiple of 12 greater than 12 8, but less than Sum of the digits is not 9 Tens digit is double the hundreds digit XLV forty-five 45

49 Clues Workspace Puzzle E Square number greater than 0 0, but less than Even Sum of the digits is even Tens digit is 2 more than the ones digit Puzzle F Write clues for your own Mystery Number Puzzle. Solve your puzzle. Challenge Puzzle G 25 is a factor Less than 250 Multiple of 10 Multiple of 3 46 forty-six XLVI 2 23

50 Chapter 3 Name Factoring NCTM Standards 1, 2, 6, 8, 10 TEKS 5.3B, 5.3C, 5.14A, 5.16A, 5.16B Write all the factors of each product in the diagram. Connect pairs of factors as shown. Date Solve the problem. Lynn baked 24 cookies. How many cookies will each child get if there are 8 children? 4 children? 12 children? 3 children? 6 children? 2 children? Explain a pattern you see in the number of children and the number of cookies. prime XLVII forty-seven 47

51 List as many factors of each product as you can Explain how you found the factors of 42 in Problem 7. Use diagrams, numbers, or words in your explanation. Challenge Solve the puzzle. A factor of 500 A multiple of 20 A multiple of 25 Greater than 400 Explain how you found the answer using diagrams, numbers, or words. 48 forty-eight XLVIII

52 Chapter 3 Name Finding Common Factors NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.3B, 5.3D, 5.14B, 5.14C, 5.15A To solve these puzzles, you may need to make more than one list of numbers. Read all the clues for each puzzle before you begin. The boxes next to the clues show you how many digits the number has. Date Clues Workspace Puzzle A Less than 30 Even Product of the digits does not equal 8 Sum of the digits 3 Puzzle B Odd Factor of 36 Not a factor of 48 A square number Puzzle C Which clue in Puzzle B is unnecessary? Explain why the clue is unnecessary. Sum of the digits 9 Common factor of 54 and XLIX forty-nine 49

53 There may be more than one possible answer to these puzzles. Find as many possibilities as you can. Clues Workspace Puzzle D Common multiple of 6 and 9 less than 90 Tens digit is less than the ones digit Product of the digits is a 1-digit number Puzzle E Common factor of both 66 and 99 Sum of digits is a factor of 12 Product of digits is a square number Julie bakes bread every fourth day. She bakes muffins every fifth day. If she bakes both bread and muffins today, in how many days will she bake both bread and muffins again? Explain how you know. Challenge Puzzle F 3-digit common multiple of 4 and 20 Greater than 10 20, but less than Sum of the digits is even Product of the digits 0 Sum of the digits fifty L 2 5 5

54 Chapter 3 Name Investigating Prime and Composite Numbers NCTM Standards 1, 2, 6, 8, 10 TEKS 5.3B, 5.3C, 5.3D, 5.5B, 5.16B Date List the factors and draw lines to connect factor pairs. Write P for prime, C for composite, or N for neither. Number Factors P, C, or N What is the only even prime number? Use a diagram to explain how you know the number is prime LI fifty-one 51

55 List the factors for each number. Then list any common factors for the two numbers. Circle the greatest common factor. Example Common Factor(s): 1, 3, 9 Common Factor(s): Common Factor(s): Thomas is packaging trading cards to give to his friends. He is going to give away 45 baseball cards and 36 football cards. Each package will have one kind of card and all the packages will have the same number of cards. What different ways can Thomas package the trading cards? Explain how you solved the problem. Challenge Find two composite numbers that do not have any common factors other than fifty-two LII

56 Chapter 3 Name Writing a Number as the Product of Prime Factors NCTM Standards 1, 2, 6, 8, 10 TEKS 5.5B, 5.15A For each problem: A. Draw one factor tree and circle the prime factors. B. Draw a different factor tree by starting with two different factors. C. Write number sentences with the prime factors. D. What do you notice? Date For Problem 3, how do the two number sentences you wrote for 20 compare? prime LIII fifty-three 53

57 For each problem: A. Draw a factor tree and circle the prime factors. B. Write a number sentence with the prime factors Whitney made this factor tree for 48. Describe and correct her error. Challenge Fill in the trees in different ways. Prime factors must be in the circles. 54 fifty-four LIV

58 Chapter 3 Name Investigating Divisibility by 2, 5, and 10 NCTM Standards 1, 2, 7, 8 TEKS 5.3B, 5.3C, 5.14C, 5.16B Solve the Mystery Number Puzzles. Date Clues Workspace Puzzle A Divisible by 10 Less than 300 Multiple of 11 Sum of the digits 4 Puzzle B Divisible by 2 Less than 700, but greater than 680 Not divisible by 10 Sum of the digits 23 Puzzle C Divisible by 5 and 2 Less than 500 Sum of the digits 12 At least one digit is odd Puzzle D Divisible by 5 Multiple of 50 Sum of the digits is a multiple of LV fifty-five 55

59 To solve these puzzles, you may need to think about more than one clue at a time. Clues Workspace Puzzle E Divisible by 10 Greater than 200, but less than 300 Sum of the digits is a multiple of 3 Sum of the digits is even Write a word problem with an answer that is a number divisible by 2, 5, and 10. Show the solution. The number on Tyler s locker is divisible by 2, 5, and 10. Which of these is Tyler s locker? Explain. Challenge Fill in the trees in different ways. Prime factors must be in the circles. 56 fifty-six LVI

60 Chapter 3 Name Investigating Divisibility by 3, 6, and 9 NCTM Standards 1, 2, 7, 8 TEKS 5.3B, 5.3C, 5.14C, 5.16B Solve the Mystery Number Puzzles. Date Clues Workspace Puzzle A Multiple of 5 Divisible by 3 Greater than 495, but less than 525 Puzzle B Divisible by 9 Multiple of 2 Greater than 312, but less than 336 Puzzle C Divisible by 6 Multiple of 7 Greater than 224, but less than 266 Matt says that every number that is divisible by 3 is also divisible by 6. Do you agree or disagree? Explain LVII fifty-seven 57

61 Is the number divisible by 3? Write yes or no ,003 Is the number divisible by 9? Write yes or no ,323 Is the number divisible by 6? Write yes or no Write other numbers that are divisible by 3, 6, and 9. Divisible by 3 Divisible by 6 Divisible by 9 Fill in the trees in different ways. Prime factors must be in the circles. Challenge Write yes or no and tell why. Can 300 paper clips be divided among 3 students? Why? 6 students? Why? 9 students? Why? 58 fifty-eight LVIII 2 29

62 Chapter 3 Name Problem Solving Strategy Guess and Check NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.14B, 5.14C, 5.15A, 5.16B Date Solve. Show your work. Randi wrote clues for a Mystery Number Puzzle. Solve her puzzle. Multiple of 5 Hundreds digit is 1 Even Sum of the digits is greater than 9 There are 150 fifth graders who will participate in fieldday events. All the students can be put on 2-person teams with no student left out. Name all the other sizes of teams that all students can join with no one left out. All the teams must have the same number of students. Write any number that matches the clue. You might list a few other possible numbers in the workspace on the right. 3-digit multiple of 3 and 5 4-digit multiple of 3, but not 6, 5-digit multiple of 9 and 10, prime LIX fifty-nine 59

63 Problem Solving Test Prep Choose the correct answer. What are lines called that are intersecting and form right angles? A. intersecting lines B. perpendicular lines C. rays D. right angles Paulo has 28 shells to display in groups on a table. He wants each group to have the same number of shells. How many different ways can he arrange the shells? The volume of the rectangular prism is 756 cubic meters. What is the measure of the missing dimension? A. 9 meters C. 7 meters B. 7.5 meters D. 6.5 meters Which is the side view of a cube? A. groups of 1, 2, 3, 4, 5, 6, or 7 B. groups of 1, 2, 4, 7, 14, or 28 C. groups of 1, 2, 3, 7, 9, or 27 D. groups of 1, 2, 7, 14, 21, or 28 Solve each problem. Explain your answer. Min is standing in line at the amusement park to ride a roller coaster. He counts 47 people in front of him in line. Each car holds 5 passengers. If each car before his is filled to capacity, in which car will Min ride? Explain how you know. The diagram shows the decorative border Kim glued around the outer edge of each arrangement of tables. Which arrangement needed more border? How much more? Explain. 60 sixty LX

64 Name Review/Assessment NCTM Standards 1, 2, 7, 8, 9, 10 Date Solve the Mystery Number Puzzles. Show your work. Lessons 1 and 3 Puzzle A Common multiple of 3 and 5 Less than 150 Odd Tens digit is even Puzzle B Common factor of 21 and 70 Prime number Odd Tell whether 1005 students can be put into equal groups with these numbers of students. Write yes or no. Lessons 6 and 7 2 students 6 students 3 students 9 students 15 students 10 students List the factors of each number. Then list any common factors. Lessons 2, 3, and , 15 Common factor(s) of 15 and Common factor(s) of 48 and 36 prime LXI sixty-one 61

65 Draw a factor tree and circle the prime factors. Write a number sentence with the prime factors. Lessons 4 and Write 3 prime numbers. Use pictures, numbers, or words to explain how you know the numbers are prime. Lesson 5 Solve the problem. Lesson 8 Alex has 100 trading cards that he wants to put in stacks with the same number of cards in each stack and no cards left over. List all the ways he can stack the cards. Use pictures, numbers, or words to explain your answer. 62 sixty-two LXII 2 31

66 Chapter 4 Name Write the outputs. Investigating the Result of Two Operations NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3B, 5.3C, 5.14A Date Example LXIII sixty-three 63

67 Solve the problems. Show your work. Anne had thirty shells. Tom had three times as many shells. He gave all his shells to his two brothers. Each brother received the same number of shells. How many shells did each brother receive from Tom? Mrs. Maxwell had a half-dozen eggs. She used a third of them in a salad. How many eggs did Mrs. Maxwell have left over? A group of 9 friends together earned Divide seventy-two by four and $36 each afternoon. They divided multiply the result by three. the money evenly among themselves. If they earned this same amount each afternoon for 5 afternoons, how much would each friend receive? Write inputs and outputs for the machines. Challenge Write the missing numbers. 64 sixty-four LXIV

68 Chapter 4 Name Record the outputs. Investigating the Order of Two Operations NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.3B, 5.3C, 5.15A Date Fill in the missing numbers LXV sixty-five 65

69 Shade the bars to show the multiplying and dividing performed by the fraction machines. Challenge Make up an example in which it is more convenient to divide first. Make another in which it is more convenient to multiply first. Why is it more convenient to multiply first in your second example? 66 sixty-six LXVI

70 Chapter 4 Name Finding Equivalent Fractions NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.2A Check ( ) the fraction machines that produce the result shown. Cross out ( ) the fraction machines that do not. Fill in the boxes on the left with the smallest numbers that produce the result shown. Date prime LXVII sixty-seven 67

71 Write the numbers to show the dividing and multiplying. Complete the grids. Example Challenge 68 sixty-eight LXVIII

72 Chapter 4 Name Equivalent Fractions Using Dot Sketches NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.2A Complete the dot sketches and write the fractions. Date Use dot sketches to find equivalent fractions LXIX sixty-nine 69

73 Complete the dot sketches and find equivalent fractions Find any equivalent fraction with a dot sketch Challenge Show each number s location on the number line seventy LXX 2 5 7

74 Chapter 4 Name Strategies for Comparing Fractions NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.2C, 5.16B Compare the fractions. Write,, or. Date How did you figure it out? Choose one or more. Compared each fraction to 1_ 2. Figured out which fraction is closer to 1. Recognized equivalent fractions. Something else: Same denominators compared the numerators. Same numerators compared the denominators How did you figure it out? Choose one or more. Compared each fraction to 1_ 2. Figured out which fraction is closer to 1. Recognized equivalent fractions. Something else: Same denominators compared the numerators. Same numerators compared the denominators How did you figure it out? Choose one or more. Compared each fraction to 1_ 2. Figured out which fraction is closer to 1. Recognized equivalent fractions. Something else: Same denominators compared the numerators. Same numerators compared the denominators. prime LXXI seventy-one 71

75 Casey and Caitlin disagreed over whether the fractions 2_ and 3_ 6 9 are equal. Are the fractions equal? Tell or show how you know. For 5 6, write,, or. Tell or show how you know Alberto used 2_ cup of peanuts, 3_ cup almonds, and 3 4 3_ cup raisins to make a trail mix for his hiking trip. 5 Did he use more almonds or raisins? Explain how you know. Did he use more peanuts or almonds? Explain how you know. Challenge Write two new fractions that have the same denominator and that make these sentences true Which fraction is greater: 5 6 or 3? How much greater is it? 4 72 seventy-two LXXII

76 Chapter 4 Name Comparing Fractions Using Common Denominators NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.2C, 5.16B Date For each pair of fractions: Write an equivalent pair of fractions, but with a common denominator. Use dot sketches to make equivalent fractions, if you wish. Write,, or between the fractions. Example 1 Example _ _ prime LXXIII seventy-three 73

77 Write the fractions with a common denominator in order to solve the problems. Scott ate 4_ of a pizza and Todd 5 ate 3_ of a pizza. 4 In Sam s class, 1_ of the students 8 chose strawberry, 1_ chose chocolate, 2 and 3_ chose vanilla as their favorite 8 ice cream flavor. Who ate more pizza? Which flavor was most popular? Twin sisters Bethany and Britney receive the same allowance. Bethany saves 2_ of hers each week, and 3 Britney saves 1_ of hers. 2 Aki ran 5_ of the route to school. 6 His brother, Yoshi, ran 6_ of the 8 same route. Who saves less each week? Challenge Drew spent 3_ 4 of his lunch hour eating and he spent the rest of the time talking. Meg spent 1_ of her 6 lunch hour talking and the rest of the time eating. Who was closer to school when he stopped running? If they have the same amount of time for lunch, who spends more time talking? How do you know? 74 seventy-four LXXIV 2 37

78 Chapter 4 Name Area Models and Number Lines NCTM Standards 1, 2, 7, 9, 10 TEKS 5.2A Write the fractions for the shaded shapes. The denominators must show the total number of pieces. Date 3 Write the fractions from Problems 1 8 as pairs of equivalent fractions. 4_ LXXV seventy-five 75

79 Shade the sketches for the fractions. You may need to draw lines to split up some of the pieces. 2_ Write the fractions from Problems at their locations on the number line. Challenge Write four equivalent fractions to match the sketch. 76 seventy-six LXXVI

80 Chapter 4 Name Numbers Greater Than 1 NCTM Standards 1, 2, 6, 7, 8, 9, 10 Write the numbers at their locations on the number line. If two numbers label the same point, write one above the line and the other below TEKS 5.2B, 5.2C, 5.14A, 5.16B Date 6 8 Solve the problems. Alex s family likes to celebrate half-birthdays every half year. Alex had his first when he was 1_ year old, 2 his second at 1, his third at 1 1_, and so on. He just 2 celebrated his 19th half-birthday. How old is he? Explain how you know. Lauren walks 2 1_ miles each day. Write the number 4 of miles as an improper fraction. Explain LXXVII seventy-seven 77

81 Ryan had only a 1_ -cup measuring cup to measure the flour 3 for a cake recipe. He filled the measuring cup seven times. How much flour did Ryan measure? Tifani had 3 1_ meters of rope. Her sister had 7 halfmeter pieces, and thought that was more than 2 Tifani had. Who had more rope? Tell or show how you know. Mr. Lopez had seven pieces of paper and cut each one into fourths. Does he have enough paper to give a fourth of a piece of paper to each of his 26 students? Tell or show how you know. Challenge The bus traveled 7 2_ miles before 3 stopping for gas. It then traveled another 4 2_ 3 miles to the bus station. How far did the bus travel? 78 seventy-eight LXXVIII

82 Chapter 4 Equivalent Fractions Greater Than 1 Draw lines to match the equivalent numbers Name NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.2B, 5.2C, 5.16B Date Write three equivalent fractions or mixed numbers for each prime LXXIX seventy-nine 79

83 Solve the problem. Anh and Maya were both braiding chains out of yarn. Anh s measured 4 3_ feet long, and Maya s 8 measured 4 9_ feet long. 16 Whose chain is longer? Tell or show how you know. Challenge Which is bigger: (9 7 4 ) or ( )? How much bigger? 80 eighty LXXX

84 Chapter 4 Name Problem Solving Strategy Draw a Picture NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.14B, 5.14C The class sold 2 dozen brownies at their bake sale. Kelly sold 1_ of them, Alima sold 3_ of them, and Jake 2_ of them How many brownies did each person sell? Date Kelly: Alima: Jake: What fraction of the brownies were sold by others? How many brownies were sold by others? A pizza is cut into 12 equal pieces. Shayne serves 2_ of the pizza, 6 Bryanna serves 2_ of the pizza, and Patrick serves 1_ of it What fraction of the pizza is left? How many pieces are left? Find at least one way to completely cover a yellow hexagonal pattern block with other pattern blocks that are not all the same shape. Tell or show the fraction of the hexagon that each shape you used represents LXXXI eighty-one 81

85 Problem Solving Test Prep Choose the correct answer. What is the value of M on the number line? A. 5 C. 7 B. 6 D. 9 A factor tree for 72 has been started. What are the prime factors of 72? A. 3, 3, 4, 4 C. 3, 3, 4, 2 B. 3, 3, 4 D. 3, 3, 2, 2, 2 What is the least whole number that is described below? It is divisible by 2, 3, 4, 6, and 8, but not by 5. The sum of its digits is a 2-digit number. A. 12 B. 24 C. 48 D. 96 Which number sentence is NOT equivalent to the one below? (23 23) 16 A. (23 23) (4 4) B. (19 27) (4 4) C D. (18 28) (3 3) Solve each problem. Explain your answer. In a 24-mile relay race, Edward ran 1_ 4 of the distance, Carlos ran 1_ of the 8 distance, Armand ran 1_, and Ronnie 3 ran the rest. How many miles did Ronnie run? Explain. The sum of the Magic Square is 45. How could the numbers be changed so that the sum would be 51? Explain. 82 eighty-two LXXXII 2 41

86 Name Review/Assessment NCTM Standards 1, 2, 6, 7, 8, 9, 10 Date Record the outputs. Lessons 1 and 2 Write a fraction equivalent to each. Draw dot sketches, if you wish. Lessons 3 and 4 3_ 4 2 _ 8 2 _ 5 8 _ 16 Solve. Lessons 5 and 6 Melinda uses a recipe that calls Drew ran 7_ of the route to the 8 for 1_ cup of sugar, 3_ cup of flour, baseball field. Scott ran 4_ 2 4 of the 6 1_ cup of nuts and 1_ cup of oil. 4 3 same route. Who was closer to the List the ingredients in order from baseball field when he stopped greatest to least amount. running? For each pair of fractions: Lesson 6 Write an equivalent pair of fractions with a common denominator. Make dot sketches, if you wish. Write,, or between the fractions prime LXXXIII eighty-three 83

87 For 13 15, write a fraction equivalent to each fraction labeled on the number line. Lesson 7 Write the numbers at their locations on the number line. 1 3 _ 4 7_ 3 2_ _ _ 3 7_ 4 Write equivalent fractions. Write one in simplest form and circle it. Lesson 9 3_ 6 2 _ 6 Solve the problem. Show your work. Lesson 10 Maria was shopping for a jump rope. One store sold ropes that were 10 3_ feet long 8 and another had ropes that were 10 1_ 2 feet long. Which is longer? 84 eighty-four LXXXIV

88 Chapter 5 Complete the multiplication sentences. You may split and complete an area model or complete a puzzle Name Multiplying Multi-Digit Numbers NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.4, 5.14A, 5.16B Date LXXXV eighty-five 85

89 Make up your own 2-digit by 2-digit multiplication sentences. Split and complete area models as checks. The product is between 3,000 and 5,000. Neither factor has a zero in the ones place. 5 2 The product is between 4,000 and 7,000. Neither factor has a zero in the ones place. Tyler s goal is to read between 500 and 750 pages in January. There are 31 days in January. How many pages could he read each day and meet this goal? Explain how you found your answer. Challenge Make up your own 3-digit by 2-digit multiplication sentence. Split and complete an area model as a check. The product is between 6,000 and 12,000. Neither factor has a zero in the ones place. 86 eighty-six LXXXVI 2 43

90 Chapter 5 Name Writing Vertical Records NCTM Standards 1, 2, 8, 9, 10 TEKS 5.16B Fill in the puzzles. Then complete the multiplication records. Date , Write the partial products on the area models. Then complete the multiplication records LXXXVII eighty-seven 87

91 Complete the multiplication records Challenge How can you find this product in an easy way? Describe your method: 88 eighty-eight LXXXVIII

92 Chapter 5 Name Writing Shorter Records NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.14C, 5.16B Use numbers from the puzzle in the records. Date , , ,100 Complete the area models. Then complete the puzzles and records prime LXXXIX eighty-nine 89

93 Complete the record. Draw an area model, if you wish Solve the problem. Each of the 28 students in Mrs. Farrell s class baked 2 dozen cookies for a cookie exchange. What is the total number of cookies? Explain how you solved the problem. Show your work. Challenge Complete the puzzle and record ninety XC

94 Chapter 5 Name Complete the tables. Using Square Number Differences NCTM Standards 1, 2, 6, 8 TEKS 5.16B Date a 2 4 a a 1 12 a 1 24 (a 1) (a 1) 899 b b ,600 (b 1) (b 1) 143 b 2 1 2,499 Write an expression equivalent to (n 1) (n 1). Alex knows that he needs 625 one-foot tiles to cover a floor that is 25 feet by 25 feet. How many one-foot tiles does he need to cover a floor that is 24 feet by 26 feet? Explain how you can use a pattern to solve XCI ninety-one 91

95 Complete the tables. c 5 c c 3 11 (c 3) (c 3) 2,491 c d d 2 11 d 2 9 d ,096 (d 2) (d 2) 3,596 Abby drew this sketch of the square floor she wants to tile. The s stands for the length of each side in feet. She said she can use the expression s 2 to find the number of one-foot tiles she needs. Blake says she should use the expression s s to find the number of tiles she needs. Who is correct? Explain. Challenge Fill in the beginning of each row and complete the table ninety-two XCII

96 Chapter 5 Name Multiplying Large Numbers NCTM Standards 1, 2, 9, 10 TEKS 5.3B, 5.16B Complete the area model, puzzles, and records. Date XCIII ninety-three 93

97 Use numbers from the puzzles in the records. Use an area model if you wish There are 24 hours in a day, 7 days in a week, and 365 days in most years. How many hours are there in most years? Explain. Challenge For each partial product, write the factors that produce it , ninety-four XCIV 2 47

98 Chapter 5 Name Problem Solving Strategy Make a Table NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3A, 5.3B, 5.5B, 5.15B, 5.16A, 5.16B Jenny made these designs with square tiles. Each design has a square of green tiles and a border of white tiles. Date Circle the expressions that give the number of white tiles needed for a design with an n n green square. 4n 4 4 (n 1) 2 (n 2) 2n Here is a pattern of columns of tiles. Here are some expressions. 2 (n 1) 2n 2 2n 2 If n is the number of orange tiles, which expressions give the number of white tiles? 5 19 XCV ninety-five 95

99 Problem Solving Test Prep Choose the correct answer. Which expression is equivalent to the one below? a 2 4 A. (a 4) (a 4) B. (a 2) (a 2) C. (a 16) (a 16) D. (a 2 2) 2 Which is the only number of juice boxes that cannot be packed in each of the following ways? groups of 3 packages of 6 cartons of 10 A. 60 C. 90 B. 70 D. 120 Ricardo made this area model to multiply 347 and 56. Which partial product is missing from the model? A. 20 C. 2,000 B. 200 D. 20,000 Which is the set of prime factors of 72? A. 2, 2, 2, 3, 3 C. 2, 3, 3, 3 B. 2, 2, 3, 3, 3 D. 2, 3, 3, 4 Solve each problem. Explain your answer. The school library received a shipment of books. There were 27 cartons of 12 books and 19 cartons of 17 books. How many books were in the shipment? Explain. Jade has four unmarked rods that are 1 inch, 4 inches, 7 inches, and 9 inches long. How many different whole-number lengths up to 21 inches can she measure if she uses a rod only once to measure a length? Explain. 96 ninety-six XCVI

100 Name Review/Assessment NCTM Standards 1, 2, 6, 7, 9 Date Write the partial products in the area models and complete the records. Lesson Make up your own 2-digit by 2-digit multiplication sentences. Lesson 1 The product is between 2,000 and The product is between 5,000 and 3,000. Neither factor has a zero in 6,000. Neither factor has a zero in the ones place. the ones place. Complete the puzzles and the records. Lessons 2, 3 and prime XCVII ninety-seven 97

101 Complete the table. Lesson 4 d 3 5 d d d (d 1) (d 1) 2,499 Solve the problem. Show your work. Lesson 6 Brad used toothpicks to make a pattern of squares. Circle the expressions that give the number of toothpicks needed to make n squares? 2n 1 3n 1 2n n 1 4n 98 ninety-eight XCVIII 2 7 7

102 Chapter 6 Name Making Figures on a Coordinate Grid NCTM Standards 2, 3, 7, 9, 10 TEKS 5.9 Date Plot each point, label it, and then connect A B C D A. Name A B C D Coordinates (1,1) (2,5) (3,3) (5,2) Complete the table using the rule given. Name A B C D Coordinates (x,y) (1,1) (2,5) (3,3) (5,2) New Ordered Pairs: Double Each Coordinate (2x,2y) Plot the points that have the new coordinates. Connect the new points the same way: A B C D A XCIX ninety-nine 99

103 For 4 and 5, use the grid. Use the table to record the coordinates of the vertices of the figure shown on the grid. Then follow the rule to produce five new ordered pairs. Name A B C D E Coordinates (x,y) New Ordered Pairs: Add 4 to each coordinate (x 4, y 4) Plot the points for the new coordinates. Connect the points in the same way the original points were connected. Challenge Find a rule and complete the table. Then write the rule using shorthand notation. Original Ordered Pairs (x,y) (4,4) (4,7) (6,8) (6,6) (5,6) (5,7) New Ordered Pairs (6,1) (6,4) (8,5) (8,3) Rule:, 100 one hundred C

104 Chapter 6 Name Date Translating Figures on a Grid NCTM Standards 2, 3, 7, 8, 10 TEKS 5.8A, 5.9 Record the coordinates of the vertices of the original trapezoid. A B C D Translate the trapezoid 6 spaces to the right (east) and draw the result. Record the new coordinates. A B C D What is the rule? Rule: (x,y) becomes (, ). prime CI one hundred one 101

105 On the grid above, draw and label these points. L M N O (6,10) (8,8) (6,6) (4,8) Then draw these line segments. LM, MN, NO, OL Translate the figure 5 spaces to the right (east), and then 4 spaces down (south). Draw the new figure. L M N O What is the rule for this translation? Rule: (x,y) becomes (, ). Challenge Describe how a figure moves if the coordinates of every vertex (x,y) change to (x 3, y 4). 102 one hundred two CII

106 Chapter 6 Name Date Reflecting Figures on a Grid NCTM Standards 3, 7, 8, 9, 10 TEKS 5.8A, 5.9, 5.15A Complete the table below for the figure and its reflection. Record the coordinates of each vertex of the original figure. Reflect the figure over the dotted horizontal line. Record the coordinates of the corresponding vertices of the reflected image. Vertices Original Figure Reflected Image A B C D Complete the table below for the figure and its reflection. Record the coordinates for each vertex of the original figure. Reflect the figure over the dotted vertical line. Record the coordinates of each vertex of the reflected image. Vertices A B C D E Original Figure Reflected Image prime CIII one hundred three 103

107 For 7 12, use the table and the grid to help you draw and reflect the figures. Vertices Figure 1 Figure 2 Figure 3 A (1,4) B (1,7) C (2,7) D (2,5) E (4,5) F (4,4) Plot the vertices of Figure 1. Label each vertex with its letter. Use a straightedge to connect the vertices. A B C D E F A. Label Figure 1. Reflect Figure 1 over the dotted vertical line and draw the result. Label this Figure 2. Record the coordinates of each vertex for Figure 2 in the table. List each reflected vertex next to the original vertex of Figure 1. Reflect Figure 2 over the dotted horizontal line, draw the result, and label it Figure 3. Then write the coordinates of each reflected vertex of Figure 3 next to the original vertex in Figure 2. Challenge Predict the result of first reflecting Figure 3 over the dotted vertical line, and then reflecting that image over the dotted horizontal line. 104 one hundred four CIV

108 Chapter 6 Name Rotating Figures on a Grid NCTM Standards 3, 7, 10 TEKS 5.8A, 5.9 Rotate the triangle 180 counterclockwise around the point (4,5). Draw the result. Date Rotate the trapezoid 90 counterclockwise around the point (4,4). Draw the result CV one hundred five 105

109 Rotate Figure F 180 around the point (4,3). Label the rotated image Figure G. Reflect Figure G over the dotted vertical line. Label the reflected image Figure H. Record the coordinates of each vertex of Figure F and the corresponding points on Figures G and H. A (2,6) B C D E F G H Rotate Figure R 270 counterclockwise around point (5,3). (Note that this point is not part of Figure R!) Label the rotated image Figure S. Challenge Look at Problem 6. What other rotation around the point (5,3) could produce Figure S? (Hint: Reverse the direction of rotation.) 106 one hundred six CVI 2 53

110 Chapter 6 Name Date More About Transformations NCTM Standards 3, 7, 8, 10 TEKS 5.8A, 5.8B, 5.9 List the vertices of Figure A. Draw and label Figures B and C, and fill in the tables of corresponding vertices. Figure A: A (10,8) Figure B: Reflect Figure A across the horizontal dotted line. Figure C: Reflect Figure B across the vertical dotted line. B C Describe a single transformation to turn Figure A into Figure C. prime CVII one hundred seven 107

111 This is a tessellation of a quadrilateral. All of the figures in it are congruent to Figure P. List the coordinates of each vertex of Figure P in the table. Find as many examples of a translation of Figure P as you can, and label each of them S (for slide). Choose one of them and record the coordinates of its vertices in the table. P S R T Find as many examples of a reflection of Figure P as you can, and label each of them R. Choose one and fill in the table. Find as many examples of a rotation for Figure P as you can, and label each of them T (for turn). Choose one and fill in the table. Challenge Find one of the quadrilaterals that you have not marked, and label it Q. Describe a transformation or a combination of at most two transformations that transform Figure P to Figure Q. Describe what you did. 108 one hundred eight CVIII

112 Chapter 6 Name Graphing with Negative Numbers NCTM Standards 3, 7, 8, 10 TEKS 5.9, 5.16A Write the coordinates for each labeled point, or locate and label the point. Date A F K P Find (2,6) and label it P. B G L Q Find (4, 4) and label it Q. C H M R Find ( 5, 2) and label it R. D I N S Find ( 1,4) and label it S. E J O prime CIX one hundred nine 109

113 Graph the points in each list. Use the pattern that you see to find the missing coordinates, and graph those points too. A (4, 3), (3, 1), (2, ), (1, ), (0, ), ( 1, ), (,9) B (6,3), (4,2), (2,1), (0, ), (, 1), ( 4, ), (, ) Which point is in both sets of points? Challenge Choose the phrase that correctly completes the statement. When two different points have the same x-coordinate, the line that connects them... A. must be vertical. C. cannot be either vertical or horizontal. B. must be horizontal. D. can go in any direction. When two different points have the same y-coordinate, the line that connects them... A. must be vertical. C. cannot be either vertical or horizontal. B. must be horizontal. D. can go in any direction. 110 one hundred ten CX

114 Chapter 6 Name Moving on a Coordinate Grid NCTM Standards 3, 7, 8, 10 TEKS 5.9 Follow the directions to locate and label each point on the grid. Date Find (6, 5) on the graph and label it A. Translate (slide) A left two spaces and up one space. Label the new point B. What are the coordinates of B? Translate B left two spaces and up one space. Label this point C. What are the coordinates of C? Translate C left two spaces and up one space. Label this point D. What are the coordinates of D? Translate D left two spaces and up one space. Label this point E. What are the coordinates of E? Translate E left two spaces and up one space. Label this point F. What are the coordinates of F? Translate F left two spaces and up one space. Label this point G. What are the coordinates of G? 3 37 CXI one hundred eleven 111

115 Find as many points as you can for which the sum of the horizontal and vertical coordinates is 5. Label each point with its coordinates. Challenge Find as many points as you can for which the product of the horizontal and vertical coordinates is 24. Label each point with its coordinates. Describe the graph of all the points with a horizontal coordinate equal to zero. Points on 112 one hundred twelve CXII

116 Chapter 6 Name Graphing Data NCTM Standards 5, 6, 7, 9, 10 TEKS 5.13B, 5.13C This pictograph shows the number of hits in one season for the starting players on the Anytown Aardvarks. Date How many hits did Abbot get? How many hits did Axe get? Which player(s) had exactly 50 hits for the season? How many players had more than 30 hits? Who had the most hits? How many? This is the maximum for the set of data. Who had the fewest hits? How many? This is the minimum for the set of data. What is the difference between the maximum number of hits and the minimum number of hits? This is the range for the set of data. prime CXIII one hundred thirteen 113

117 This list of data shows the number of home runs in one season for all of the players on the Anytown Aardvarks team. 10, 21, 9, 20, 13, 34, 12, 7, 12, 7, 2, 1, 8, 4, 10, 0, 0, 2, 1, 1, 4 Make a graph of this set of data. Write a title and any necessary labels. Challenge Complete the sentence. Ten of the Anytown Aardvarks got more than home runs. 114 one hundred fourteen CXIV

118 Chapter 6 Name What is Typical? NCTM Standards 1, 5, 6, 7, 8, 9, 10 TEKS 5.13, 5.13B Date Before opening a restaurant, Charlie conducted a survey to determine what type of food to serve, and to what age group of the population. Use the results of his survey to complete the graph. FOOD PREFERENCES Age Preference 10 Burger 21 Pizza 8 Wrap 18 Pizza 25 Salad 37 Salad 51 Wrap 15 Salad 28 Salad 49 Burger 12 Burger 8 Burger 14 Salad Which food item is the mode? Arrange the ages in order from least to greatest. What is the median age of respondents? Charlie only wants to offer three items on his menu. Which item do you think he should not include? 5 23 CXV one hundred fifteen 115

119 Use the graphs to answer the questions. What is the minimum number of hours of sleep reported? What is the maximum number of hours of sleep reported? What is the range of hours of sleep for these students? What is the mode? What is the median? A new graph was made to be more specific about the amount of time students spent sleeping. What is the range of hours of sleep now? What is the mode? What is the median? Challenge Explain whether the old or new mode or median is more accurate. 116 one hundred sixteen CXVI

120 Chapter 6 Name Another Way of Describing What s Typical NCTM Standards 1, 5, 6, 7, 8, 9, 10 TEKS 5.13B, 5.16B The table shows the populations of the nine states in the United States that have the greatest populations. Use the table to answer the questions below. You may use a calculator to help you. The Nine States with Greatest Population from the 2004 U.S. Census Estimated Total Population of These Nine States on July 1, 2004: 150,529,014 State Population State Population California 35,893,799 New York 19,227,088 Florida 17,397,161 Ohio 11,459,011 Georgia 8,829,383 Pennsylvania 12,406,292 Illinois 12,713,634 Texas 22,490,022 Michigan 10,112,620 Which state has the greatest population? Date What is the population of that state? Which of these states has the least population? What is the population of that state? What is the range of populations for these states? Which state has the median population for these states? About what is the mean population for these states? (Hint: The addition has already been done for you!) If you were to survey all the people who live in these states about which state they live in, what would be the mode? CXVII one hundred seventeen 117

121 Surprisingly, Mario and Marsy had the same four test scores: 85, 90, 80, 100. Their teacher told them that these four scores and a score for homework would be used to determine their report card marks. Mario s homework score was 70 and Marsy s was 45. If Mario and Marsy s teacher uses the median score to determine their grades, what will each student s score be? Mario: Marsy: If their teacher uses the mean score to determine their grades, what will each student s score be? Mario: Marsy: Do you think the median or mean best reflects their performances? Explain. Challenge Find nine numbers that have: a mean of 5, but not a median of 5. a median of 5, but not a mean of one hundred eighteen CXVIII 2 59

122 Chapter 6 Name Reading Graphs and Tables NCTM Standards 5, 6, 8, 9, 10 TEKS 5.13B, 5.16B For each graph, answer as many questions as you can. If the graph does not provide a way to figure out the answer, write cannot tell. Some fifth graders in Canada were surveyed about their favorite winter sport. Date How many students were surveyed? What choice is the mode? The Sports Federation wanted to know how much more popular the most popular sport is than the least popular sport. What is the range of the number of votes? Some fifth graders compared the number of letters in their first names. How many names are names of girls? What is the median number of letters? How many students names were used? The mean number of letters is between letters and letters. What number of letters is the mode? 7 17 CXIX one hundred nineteen 119

123 Match each table to its corresponding graph. A 12 B 8 C 7 D 10 E 5 A B C D E A 1 7 B 2 4 C 3 4 D 4 8 E 5 7 Challenge A city is adding lanes to their main highway. They found that there is mean of 1,075 cars per day on that highway, the median car passes through town at 3 P.M., and that the mode travel time is 5 P.M. Which piece of information will be most useful for deciding when to do construction? 120 one hundred twenty CXX

124 Chapter 6 Problem Solving Strategy Act It Out Katy is writing a computer game about flying a spacecraft. How could she get the spacecraft from the starting position to its ending position using only 2 transformations? Name NCTM Standards 3, 6, 8, 9, 10 TEKS 5.14B, 5.14C, 5.14D Date Transformation 1: Transformation 2: CXXI one hundred twenty-one 121

125 Problem Solving Test Prep Choose the correct answer. The population of a large city is 1,593,482. What will the population be when there are 10,000 more people? A. 1,693,482 B. 1,613,482 C. 1,603,482 D. 1,594,482 Diagonals drawn from the same vertex cut a polygon into triangles. How many triangles can be made this way from a 20-sided polygon? A. 15 C. 17 B. 16 D. 18 Solve each problem. Explain your answer. Draw the results of rotating the triangle 90 counterclockwise around the point (6,2). Then translate the result 5 units left. What are the coordinates of Point A in the final image? William is making packages of pens and pencils for the school store. He has 48 pens and 60 pencils. Each package will have the same number of items and will have either pens or pencils, but never both. A In how many different ways can he make the packages? B If he puts the largest number of pens or pencils in each package, how many packages will he have made in all? Explain. 122 one hundred twenty-two CXXII 2 61

126 Name Review/Assessment NCTM Standards 3, 5, 6, 7, 9, 10 Date For 1 4, list the vertices of each figure. F G H I (1,3) Lessons 2 5 Which figure is a translation of Figure F? Which figure is a reflection of Figure F? Which figure is a rotation of Figure F? Translate Figure G two spaces to the right and one space up, draw the result, and label it Q. Reflect Figure I over a vertical line that goes through point (3,0). Draw the result and label it R. For 10 16, use the grid. Lessons 1 7 Write the coordinates for each labeled point. Point A Point B Point C Plot each point on the grid. Find (3, 2) and label it D. Find ( 2,4) and label it E. Find ( 4,0) and label it F. Find four points where the horizontal coordinate is double the vertical coordinate. Label each of these points with its coordinate pair CXXIII one hundred twenty-three 123

127 For 17 20, use the graph. How many books were read? How many books did Sam read? What is the range of books read? What is the median number of books read? The table shows Morgan s spelling scores for 8 weeks. MORGAN S SPELLING SCORES Week Score Make a frequency graph of her scores. Find these data measures. range: median: mode: mean: Solve the problem. Lesson 12 Beth made a design to use as a border around the ceiling of her bedroom. To make the design she started with the figure on the grid. She reflected the figure over the vertical dotted line. A Draw the new figure on the grid. B Which vertex on the new figure corresponds to the vertex at (1,1) on the original figure? 124 one hundred twenty-four CXXIV

128 Name Chapter 7 Investigating Decimals NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.1B, 5.15A, 5.16B Locate each decimal on the number line. Date Write any number between the two numbers Write the decimal that is halfway between the two decimals CXXV one hundred twenty-five 125

129 Write any number that is between the two numbers Explain how you know that the number you wrote for Problem 10 is correct. Use pictures, numbers, or words to explain your answer. Circle the smaller number in each pair Challenge Put dots on the number line to show the approximate locations of 2.93 and Write the numbers next to the dots. Tell why you put them where you did. 126 one hundred twenty-six CXXVI

130 Chapter 7 Name Comparing and Ordering Decimals NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.1B, 5.3A, 5.16B Write the numbers in order from least to greatest. Date Write,, or to complete the number sentence prime CXXVII one hundred twenty-seven 127

131 Write the numbers in order from least to greatest Circle the smallest number in each set Keith said that is larger than 7.45 because has more digits to the right of the decimal point. Is he correct? Explain. Challenge Terrell ran the 40-yard dash in 4.6 seconds. His teammate Troy ran it in 4.39 seconds. Who was faster? Explain how you know. What is the difference between the two times? 128 one hundred twenty-eight CXXVIII

132 Name Chapter 7 Large and Small Numbers NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.1A, 5.1B, 5.16B Write the numbers in order from greatest to least. Date 1,560,700 1,067,500 1,506,700 1,076,500 1,065,700 1,506, Write the numbers in order from least to greatest. 6,356,406,132 6,365,132,406 6,455,406,132 6,365,132, Solve the problem. Max said that 0.16 is greater than 0.5. Is Max correct? How do you know? 3 43 CXXIX one hundred twenty-nine 129

133 Complete the table without using a calculator , , Explain how you knew what numbers to write in the column for 6 in Problem 6. Challenge Complete the table one hundred thirty CXXX

134 Chapter 7 Name Connecting Decimals to Fractions NCTM Standards 1, 2, 7, 8, 9, 10 TEKS 5.1B, 5.2D Date Fill in the fraction notation (above the picture) and decimal notation (below the picture) to match the blocks. Example prime CXXXI one hundred thirty-one 131

135 Write the mixed number that matches the decimal. Example Write the decimal that matches the mixed number. Example Challenge Which decimal has the same value as 72.9: or 72.90? Tell or show how you know one hundred thirty-two CXXXII

136 Chapter 7 Name Connecting Decimals to Other Fractions NCTM Standards 1, 2, 6, 7, 8, 10 TEKS 5.2D, 5.16B Use the grid to help you write the equivalent decimal for each fraction. Date Write the mixed numbers above the number line and the matching decimals below. Write equivalent fractions and decimals. Example Jordan ran 4_ mile. Kelley ran 0.75 mile. 5 Who ran farther? Explain how you know CXXXIII one hundred thirty-three 133

137 Simplify each fraction. Then write the equivalent decimal. Example Explain how you simplified the fraction in Problem 16. Challenge This square represents Imagine splitting it into 10 equal pieces. Write the fraction for 1 piece. Write the decimal for 1 piece. Write one fraction for 5 pieces. Write a different fraction for 5 pieces. Write the decimal for 5 pieces. 134 one hundred thirty-four CXXXIV 2 67

138 Chapter 7 Name Estimating Decimals Using Familiar Fractions NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.2D, 5.16B Write a decimal for each fraction. Date Circle the number that is closer to each decimal or 5 12 or or or or or CXXXV one hundred thirty-five 135

139 Find pairs of numbers that have approximately the same value _ _ _ _ 4 For each decimal, write a mixed number that has approximately the same value Jessica needs 2 pounds of ground meat to make chili. She has one package with 2.42 pounds of ground meat and another package with 2.08 pounds of ground meat. Which amount is closer to 2 pounds? Explain how you know. Challenge Write,, or to complete the number sentences one hundred thirty-six CXXXVI

140 Chapter 7 Name Estimating Decimals Using Rounding NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.4, 5.16B Round each number to the nearest whole number. Date Example ,080.4 Round each number to the nearest tenth. Example Round each number to the nearest hundredth. Example prime CXXXVII one hundred thirty-seven 137

141 Write reasonable estimates. Nick wanted to add the following prices in his head, so he rounded them to the nearest dollar: $19.99, $4.69, and $3.29. He added to get an estimate of. Mr. Brown saw when he stepped on the scale. He weighed close to pounds. Ralph s mother took his temperature and it was It was close to degrees. For 19 and 20, use these items and prices. Ross has $8.00. He wants to buy all four items. Does he have enough money? Explain how you can use rounding to find out if he has enough money. Rebecca has $5.00. She wants to buy the pen and one other item. Which other item can she buy? Explain how you can use rounding to find another item. Challenge Round to the nearest whole number tenth hundredth Explain how you rounded to the nearest hundredth. 138 one hundred thirty-eight CXXXVIII

142 Chapter 7 Adding with Decimals Complete. Name NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3A, 5.14B, 5.14D, 5.16B Date _ _ _ Use the map to answer the questions below. The number along each route shows the distance in miles. On her way home from school, Alane went to the library, and then to the gas station. How many miles did she travel to get from school to the gas station? Ms. Ashe rode her bicycle from school to the grocery store, and then to the gas station to pump up her tires. How far did she ride? Explain your answer. prime CXXXIX one hundred thirty-nine 139

143 The number along each route shows the distance in miles. Which town is closer to Dunesville: Oceantown or Inland? Tell or show how you know. What is the distance along the shortest route from Inland to Sharksville? Show your computation. Challenge Which town or towns do you pass through along the shortest route from Sharksville to Dunesville? Show how you know. 140 one hundred forty CXL

144 Chapter 7 Name Subtracting with Decimals NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.1B, 5.3A, 5.14A, 5.14B, 5.14D Complete. Use base-ten blocks, if you wish. Date _ _ _ Carla set the trip meter in her van to 0 before she started her trip. She drove 4.6 miles from home to school using Route A. The trip meter showed: miles traveled miles traveled Then she drove back home using Route B. She did not reset the meter. At the end of the trip, the trip meter showed this. miles traveled How long was Route B? Explain how you know. Write a word problem that involves subtracting decimals, and then show how to solve it. You might use a trip meter in your problem CXLI one hundred forty-one 141

145 The family set the trip meter to 0 before the trip began. Write the number of miles between each town and the next. The shortest distance between two towns was miles. The longest distance between two towns was miles. Write the distance in miles between these cities. Malta and Dover Dover and Lee City Olan and Knox and A trip from Olan to Benton and back again is miles. Challenge The family drove from Knox back to Lee City to pick up a forgotten suitcase. What did the trip meter show when they arrived back in Knox? Show your work one hundred forty-two CXLII 2 71

146 Chapter 7 Name Adding and Subtracting Decimals NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.3A, 5.4 Three of these problems are answered incorrectly. As quickly as you can, and without writing anything, use rounding and compatible numbers to find the incorrect answers. If a problem is incorrect, put a check in the box. Date INCORRECT? INCORRECT? INCORRECT? INCORRECT? INCORRECT? INCORRECT? INCORRECT? INCORRECT? INCORRECT? INCORRECT? For each problem above with an incorrect answer, explain how you used rounding or compatible numbers to find the ones that were wrong. Then find the correct answer CXLIII one hundred forty-three 143

147 Nicholas earned twenty dollars doing yard work for his neighbor. He spent $9.45 of the money he earned on a ticket to a baseball game and $3.40 on snacks. How much of the twenty dollars does he have left? Explain. Here are more student responses. All of these are incorrect. Describe what the student may have done wrong, and then correct the problem. ROLANDO STACEY CARMEN Challenge DANTE one hundred forty-four CXLIV

148 Chapter 7 Name Multiplying with Decimals NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.4, 5.14A, 5.14B First circle the best estimate for each problem. Then multiply. Finally place the decimal point. Date 7. 4 closer to closer to closer to 5 _ closer to closer to 1. 8 closer to closer to closer to closer to Solve each problem. Each juice bottle contains 67.6 fluid ounces of liquid. You buy 3 bottles. A Is the total number of ounces closer to 2, 20, 200, or 2,000? B What is the total number of ounces? Show your work. fluid ounces Petunia plants are on sale for $0.88 each. Jon has $15. Does he have enough money to buy 15 plants? Explain how you can use estimation to solve the problem CXLV one hundred forty-five 145

149 Multiply and then place the decimal point _ 5 _ _ 3 _ Challenge Mr. Walker travels 45.8 miles a day to work. He rounded 45.8 miles to 46 miles to figure out that he travels about 184 miles a week to work. A How many days a week does he travel to work? B How many miles does he travel each week? Show your work. miles 146 one hundred forty-six CXLVI 2 73

150 Chapter 7 Name Solve. Show your work. Problem Solving Strategy Act It Out Make a Model NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3A, 5.3B, 5.14B, 5.14C, 5.14D, 5.16B Date Rori insisted that the number 4.85 is four and eighty-five hundredths. Her friend Maria was sure that it was four and eight tenths and five hundredths. How can you show who is correct? Can you think of another way to describe 4.85? The directions that Mr. Di Marzio will follow for this trip say that he will travel 16.8 miles before turning right onto Route 140. He will then drive another 24.9 miles to his destination. Mr. Di Marzio set his car s trip meter to 0.0 before he began the trip. What will the meter read when he arrives at his destination? Nikki had to measure chemicals very carefully for a science experiment. She measured out 1.92 grams of one chemical and 3.86 grams of another. What is the difference between these two measures? 3 49 CXLVII one hundred forty-seven 147

151 Problem Solving Test Prep Choose the correct answer. There are 96 members of the Lincoln School marching band. Which of the following arrangements will not include all of the band members? A. 8 rows of 12 B. 7 rows of 12 and 2 rows of 6 C. 5 rows of 15 and 1 row of 12 D. 3 rows of 16 and 6 rows of 8 Each of 8 students is standing on one vertex of an 8-sided polygon. They are modeling a telephone network by connecting each person to every other person with strings. How many strings do they use in all? A. 64 B. 56 C. 49 D. 28 Solve each problem. Explain your answer. Rachel has 25 plants in her garden. She has a row of 6 tomato plants, a row of 14 carrots, and a row of 5 bean plants. The bean plants are in the back. The tomato plants are behind the carrots. Which plants are in the front? Explain how you know your answer is correct. Mr. Yu s class is comparing the types of snacks they have in their backpacks. There are 20 students, and each student has at least one snack. Twelve of them have a piece of fruit, and 10 have some type of chips. How many students have both fruit and chips? Explain how you know your answer is correct. 148 one hundred forty-eight CXLVIII

152 Name Review/Assessment NCTM Standards 1, 2, 6, 7, 9 Date Write two numbers that come between the two given numbers. Lessons Write,, or to complete the number sentences. Lessons 2 and Write the numbers in order from least to greatest. Lessons 2 and ,495,704,123 8,459,123,704 8,594,704,123 8,459,123,407 Write equivalent fractions and decimals Lessons 4 and prime CXLIX one hundred forty-nine 149

153 Circle the number that is closest to each decimal. Lesson or or or Round to the nearest whole number. Lesson Round to the nearest tenth. Lesson Round to the nearest hundredth. Lesson Complete the number sentences. Lessons 8 and Solve. Lessons _ _ _ Solve the problem. Show your work. Lesson 11 On Monday, Heather drove 8.4 miles from her home to work. On her way home, she drove 2.5 miles from work to the book store. After buying a book, she drove another 7.3 miles straight home. How many miles did she drive that Monday? miles 150 one hundred fifty CL

154 Chapter 8 Name Exploring Missing Factors NCTM Standards 1, 2, 6, 9, 10 TEKS 5.3B Sheila s Shipping Company uses these special shipping stamps for postage. Date Complete the puzzles and number sentences to show the postage for each package. Use one stamp from Group A and one from Group B. Example A B A 10 B A B A B A B A B prime CLI one hundred fifty-one 151

155 Use these puzzles to show the postage for each package for larger shipments. Complete the number sentences. A B A B A B A B Challenge A B , ,249 Challenge A B 103 1, , , , one hundred fifty-two CLII

156 Chapter 8 Name Find the missing number. Connecting Multiplication and Division NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3B, 5.3C, 5.16B Date Find the missing product or factor , , CLIII one hundred fifty-three 153

157 Solve one problem in each pair to help you solve the other Pick one of the pairs above. Explain how you used one problem to help you solve the other. Whenever possible, use solutions to earlier problems to help you solve new ones Challenge A piece of halfinch graph paper has 22 rows of squares with 17 squares in each row. How many squares does it have? Challenge Kristina s mom used 861 one-inch square tiles to tile the top of Kristina s dresser. There were 21 rows of tiles. How many tiles are in each row? 154 one hundred fifty-four CLIV

158 Chapter 8 Name Dividing Using Multiplication and the Area Model NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3C, 5.16B Cut the area model in any way that helps you solve the problem. There are twenty-five rows. How many squares per row are there? Date Total 625 squares Total 875 squares Total 2,575 squares 25 2, , Total 8,825 squares 5 31 CLV one hundred fifty-five 155

159 Use estimates or list some convenient multiples of 23 to help you. This time there are only twenty-three rows. How many squares are there per row? , Challenge Miss Tanaka s 23 fifth graders lay down head to toe in the yard and measured their combined height. From the toe of the first child to the top of the last child s head, they measured just over 109 feet and 3 inches. About how many inches tall was each child? Explain how you found your answer. 156 one hundred fifty-six CLVI

160 Chapter 8 Name Recording the Steps in Division NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3C, 5.15A Complete the table of multiples of 21. Date Complete the area models and division records. Solve these on a separate piece of paper , , prime CLVII one hundred fifty-seven 157

161 Complete this table Complete. Solve these on a separate piece of paper , , , , How many 5th grade classes are in your school? About how many 5th graders does your school have? If there are about the same number of students in each grade, estimate the number of students in your school. Challenge Many new students enrolled in Sam Houston Elementary School. There are now 1,048 children enrolled. All classes except one have 25 children. To have one teacher for every class, how many teachers does the school need? 158 one hundred fifty-eight CLVIII 2 79

162 Chapter 8 Name Dividing and Recording Division Efficiently NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3C, 5.15A, 5.16B Complete the table of multiples of 37. Date Complete the area models and division records. Solve these on a separate piece of paper , , CLIX one hundred fifty-nine 159

163 Use the table of multiples of 37 that you made earlier to solve this problem. Make a table of multiples of 17 and solve the division problems below , Challenge Quick estimate: Are there more than three thousand 37s in 123,321? Explain how you solved this problem. 160 one hundred sixty CLX

164 Chapter 8 Name Using Multiplication to Check Division NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3C Complete the table of multiples of 28. Date Divide, and then check the division with multiplication. Show all your work Check: These division problems were done on a calculator. Check the results by multiplying. If there was an error, please correct it , Check: , Check: Is the quotient correct? If not, what is the correct quotient? Is the quotient correct? If not, what is the correct quotient? 7 23 CLXI one hundred sixty-one 161

165 Divide and check. Use the table of multiples on LAB page 161, if you wish. Check: 28 2, Check: 28 6, Challenge The division record shows a quotient with a remainder. Check the division. 56 2, , Check: 162 one hundred sixty-two CLXII

166 Chapter 8 Name Investigating Remainders NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.15A Find the whole-number quotient and, if present, the remainder. Then write a number sentence that checks the division. You can use a grid to help you. Date Number sentence: Number sentence: Number sentence: Number sentence: Show quotients with fractions, if needed. Then write a number sentence that checks the division. You can use a grid to help you Number sentence: Number sentence: prime CLXIII one hundred sixty-three 163

167 Write the answers using whole numbers and remainders, or using fractions if you prefer. 24 3, , , Challenge Show a way to check that your answer for Problem 9 is correct. 164 one hundred sixty-four CLXIV

168 Chapter 8 Interpreting Remainders in Word Problems Decide what to do when there is a remainder ignore it or include it as a fraction or a decimal. How many 24-foot jump ropes can be made from a rope that is 100 feet long? Solution: Name NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3C, 5.15A What should you do about the remainder? Date Nathan used lots of tennis balls when practicing his serve. At the end of practice, he gathered up 59 tennis balls and put them back into cans. If each can holds 3 tennis balls, how many cans will he fill? Solution: What should you do about the remainder? Altogether, the 32 students in Ms. Rosenfeld s class raised $456 at the bake sale. The money will be divided up to pay for each student s admission and snack for a field trip. How much money is available for each student? Solution: What should you do about the remainder? CLXV one hundred sixty-five 165

169 My large plastic bottle holds 196 ounces of water. How many cups of water is that? (1 cup 8 oz) Solution: What should you do about the remainder? The bagel bakery advertised a Baker s Dozen Sale : buy a dozen bagels and get an extra bagel free. The first batch they made was 20 dozen bagels. How many bags of 13 bagels will that make? Solution: What should you do about the remainder? Challenge A rope is 408 ft long. If it is cut into 32 shorter pieces, what is the length of each piece? Write your answer in feet and inches. Solution: What should you do about the remainder? 166 one hundred sixty-six CLXVI 2 83

170 Chapter 8 Another Option for Interpreting Remainders Decide what to do when there is a remainder ignore it (round down), include it as a fraction or a decimal, or round up. Four classes of fifth graders a total of 107 students and adults will travel by bus to Colonial Jamestown for a field trip. Forty-four people may ride on one bus. How many buses will be needed? Solution: Name NCTM Standards 1, 2, 6, 7, 9 TEKS 5.3C What should you do about the remainder? Date 180 people bought tickets to see a play. 22 people can fit in each row of seats. If the people fill in as many rows as possible, how many rows will have people seated in them? Solution: What should you do about the remainder? The Cape Cod ferry can take 30 cars at a time. How many trips must the ferry make to take 366 cars? Solution: What should you do about the remainder? prime CLXVII one hundred sixty-seven 167

171 Ms. Lawrence wants to give some special pencils to her 26 students. If she orders 11 dozen pencils and wants to give each student the same number of pencils, how many pencils will each student get? Solution: What should you do about the remainder? Marya was surprised when she saw on her pedometer that she had walked 135 miles in the last 30 days. If she walked about the same distance every day, about how many miles did she walk each day? Solution: What should you do about the remainder? Challenge We laid pencils side by side until the total width was a whole number of inches. We found that 24 pencils, side by side, measured 7 inches. We found some boxes that were 3 1_ inches wide and 2 held only one layer of pencils. How many of the smaller boxes would we need to hold 100 pencils? Explain. Solution: What should you do about the remainder? 168 one hundred sixty-eight CLXVIII

172 Chapter 8 Name Solve. Show your work. Problem Solving Strategy Draw a Picture NCTM Standards 1, 2, 6, 7, 8, 9, 10 TEKS 5.3C, 5.14B, 5.14C Date Juan s father baked 6 dozen cookies for Juan s birthday party. If Juan and his ten friends share the cookies equally, how many cookies will be left for Juan s father? Tia loves celebrating her birthday. One day she said she was 10 years and 135 days old. That means there were 230 days until her next birthday. How many full weeks were there until her next birthday? How many extra days were left? Three friends want to share two candy bars equally. How much will each friend get? Draw a picture that might help you explain why your solution is correct CLXIX one hundred sixty-nine 169

173 Problem Solving Test Prep Choose the correct answer. Ryan divides his model car collection into groups of 8 cars. There are 3 cars left over. How many cars would be left over if he divided his collection into groups of 4? A. 8 B. 6 C. 3 D. 2 Jada stacks boxes to make a pyramid display in a store window. Each row has one fewer box than the row below it. If the bottom row has 9 boxes, how many boxes are in the display? A. 35 B. 45 C. 55 D. 72 Solve each problem. Explain your answer. The streets in Morgan s town run north-south and east-west. She leaves her house on her bike, rides 5 blocks north, 4 blocks east, 6 blocks south, and 1 block west. What is the least number of blocks she must ride to get home? Albert, Carlo, Jamie, and Steve do odd jobs on the weekends. One Saturday, Albert earned more than Carlo but less than Jamie. Steve earned more than Jamie. Using this information, is it possible to put the boys in order from greatest to least earnings? If so, put them in order, and explain your answer. If not, explain what other information you would need. 170 one hundred seventy CLXX

174 Name Review/Assessment NCTM Standards 1, 2, 6, 7, 8, 9, 10 Date Find the missing product or factor Lessons 1 and Use this table of multiples of 23 to help you with Problems 7 and Complete the area model or the division record to find (You don t have to complete both.) Lesson 2 Divide, and then check your division with multiplication. Show all your work. Lessons 3 and 6 Check CLXXI one hundred seventy-one 171

175 Find the answers to the following problems. Lessons 3 and 7 Write the answer using whole numbers. Divide. Write the remainder as a fraction Theresa created a card game that used 102 cards. She could fit 8 cards on a sheet of paper. How many sheets of paper did she need to make the cards? Lessons 3, 8, and 9 Solution: What should you do about the remainder? Solve the problem. Show your work. A painting is 17 inches tall. Its area is 374 square inches. It hangs in the center of a wall that is 98 inches wide. How far is each side the painting from the ends of the wall? Lesson 10 Explain how you solved the problem. 172 one hundred seventy-two CLXXII

176 Chapter 9 Name Investigating Angles NCTM Standards 3, 4, 7, 8 TEKS 5.15A, 5.16B Tell whether each marked angle looks acute, right, or obtuse. Date prime CLXXIII one hundred seventy-three 173

177 For each pair of angles, identify which is bigger and explain your choice. Which angle is bigger: U or V? Explain: Which angle is bigger: W or X? Explain: Which angle is bigger: Y or Z? Explain: Challenge Can a triangle have two right angles? Explain your thinking with words and pictures. 174 one hundred seventy-four CLXXIV

178 Chapter 9 Name Classifying Angles and Triangles NCTM Standards 3, 4, 7, 9 TEKS 5.7, 5.14D, 5.16A Complete the table below. Identify each angle as acute, right, or obtuse. Then measure it to the nearest 5. Date Angle C D E F G H J K acute, right, or obtuse Measure acute CLXXV one hundred seventy-five 175

179 Use a ruler and a protractor to measure the sides and angles of XYZ. Angle Measure Side Length X about XY about cm Y about YZ about cm Z about XZ about cm Circle all of the following that apply to XYZ. Scalene Isosceles Equilateral Acute Right Obtuse Use a ruler and a protractor to measure the sides and angles of UVW. Angle U Measure about Side Length UV about cm V about VW about cm W about UW about cm Circle all of the following that apply to UVW. Scalene Isosceles Equilateral Acute Right Obtuse Challenge Can a triangle be both isosceles and right? Can a triangle be both equilateral and right? What other combination of the two classes of triangles is not possible? 176 one hundred seventy-six CLXXVI

180 Chapter 9 Name Constructing Triangles NCTM Standards 3, 4, 8, 10 TEKS 5.7, 5.10C, 5.14D, 5.15A On a separate piece of paper, construct XYZ so that: Date Length of YZ Length of XZ 6 cm 3 cm Measure of Z 60 Now measure the triangle you have drawn. Length of XY about cm Measure of X about Measure of Y about Cut out XYZ and compare it with the others in your class. What do you notice? Attach your copy of XYZ below CLXXVII one hundred seventy-seven 177

181 Here is a triangle. Choose two of its angles to measure. Also measure the side of the triangle shared by those two angles. In the table, write the names and measures of the angles and side you chose. Name Measure cm Use those measures to draw a triangle on your own paper. Draw the side first, and make sure it is between the angles that you measured. Cut out your triangle and compare it with the one above, and with others in your class. What do you notice? Tape your triangle below. 178 one hundred seventy-eight CLXXVIII 2 89

182 Chapter 9 Name Constructing Similar Triangles NCTM Standards 3, 4 TEKS 5.7, 5.10C, 5.14D Use a straightedge to draw a line to make the angles. Date measure of A: 60 measure of B: 45 Use a protractor and straightedge to draw the angles. X measures 30. Y measures 120. Draw lines to match similar figures. prime CLXXIX one hundred seventy-nine 179

183 Use a ruler with this triangle to do the following. Find the midpoint of UV. Label it X. Find the midpoint of VW. Label it Y. Connect the midpoints to form XY. Label the angles in XVY as angles 3, 4 and 5. Use the triangles above to answer the following. What angle is congruent to 1? What angle is congruent to 2? Identify a triangle similar to UVW. Add two more line segments so that there are four triangles all congruent to XVY inside UVW. Challenge Draw BDA with the following measures: Name BA BD Measure about 10 cm about 7 cm B about one hundred eighty CLXXX

184 Chapter 9 Name Angles Formed by Intersecting Lines NCTM Standards 3, 4, 7, 9 TEKS 5.7, 5.14D, 5.15A, 5.16A Use your knowledge of straight angles and opposite angles to figure out the missing angle measures. (No protractors, please!) Date prime CLXXXI one hundred eighty-one 181

185 Fill in letters to make the number sentences true. No protractors, please! Complete the table. m m 180 m m m 180 Angle Measure C F G H A Find eight angles that measure 80. You may use a protractor if you wish. Angle B Measure Challenge Without a protractor, figure out the angle measures and complete the table. Angle P Q R S T Measure U 182 one hundred eighty-two CLXXXII

186 Chapter 9 Name Angles Formed by a Line Intersecting Parallel Lines NCTM Standards 1, 3, 4, 7, 8, 9 TEKS 5.16B Trace over a Z in each group of intersecting lines. Date a b c d Use the Zs to figure out the missing angle measures. e f g h i j l m 3 61 CLXXXIII one hundred eighty-three 183

187 Without a protractor, use your knowledge about Zs, straight angles, and opposite angles to figure out the missing angle measures. r t g h Use a protractor to measure at least one angle. See how few you need to measure! m n d e Challenge Explain how you would use this picture to show why angles in Zs have the same measure. m n 184 one hundred eighty-four CLXXXIV

188 Chapter 9 Name Comparing and Classifying Quadrilaterals NCTM Standards 3, 7, 9 TEKS 5.7 Circle the names of all the quadrilaterals for which the sentence is correct. This shape has 4 sides. Date trapezoid rhombus square parallelogram rectangle kite This shape has 4 congruent angles. trapezoid rhombus square parallelogram rectangle kite This shape has 4 congruent sides. trapezoid rhombus square parallelogram rectangle kite This shape has two pairs of parallel sides. trapezoid rhombus square parallelogram rectangle kite This shape has two pairs of congruent sides. trapezoid rhombus square parallelogram rectangle kite This shape always includes a right angle. trapezoid rhombus square parallelogram rectangle kite 5 37 CLXXXV one hundred eighty-five 185

189 Answer the questions about the attributes of these quadrilaterals. To find all the lines of symmetry, trace the figures and fold the copies. Quadrilateral EFGH Quadrilateral ABCD Draw all lines of symmetry on the figure. Number of pairs of congruent sides: Number of pairs of congruent angles: Quadrilateral MNOP Draw all lines of symmetry on the figure. Number of pairs of parallel sides: Number of pairs of congruent angles: Quadrilateral QRST Draw all lines of symmetry on the figure. Number of congruent sides: Draw all lines of symmetry on the figure. Number of pairs of congruent sides: Number of pairs of Number of pairs of congruent angles: perpendicular sides: Challenge Quadrilateral UVWX Draw all lines of symmetry on the figure. Number of congruent sides: Number of pairs of perpendicular sides: 186 one hundred eighty-six CLXXXVI

190 Chapter 9 Name Investigating Quadrilaterals NCTM Standards 3, 4, 6, 7, 9 TEKS 5.7, 5.16B Without using a protractor, find the missing angle measures. (Hint: Use what you know about triangles first, then use what you know about quadrilaterals.) Date Angle AYX B YZX XZC CXZ Measure DXY D Without using a protractor, find the missing angle measures in these special quadrilaterals. Use what you know about the quadrilaterals and about angle measures in Z s. For each, you need to find one angle measure outside the quadrilateral. Parallelogram Trapezoid Angle E F G Measure Angle I J Measure H K CLXXXVII one hundred eighty-seven 187

191 Without a protractor, use your knowledge about Zs, straight angles, opposite angles, and angles in quadrilaterals to figure out the missing angle measures. (There may be other angles you want to find, as well!) PR SV PV RS WT RS Angle Measure VWT SWT PRS RSW TSW WTU PVW Challenge When Jonah said, Quadrilateral STUV in the figure above is a trapezoid, Nina disagreed. It does look like a trapezoid, she said, but it can t be. Look at all the angle measures. Nina is correct! Why isn t Quadrilateral STUV a trapezoid? 188 one hundred eighty-eight CLXXXVIII

192 Chapter 9 Name Problem Solving Strategy Look for a Pattern NCTM Standards 2, 3, 4, 6, 8, 10 TEKS 5.3A, 5.3B, 5.5B, 5.8A, 5.14B, 5.14C, 5.16B Kurt used green and white triangles to make this figure. There are 24 rows in the figure. Date A How many small triangles (green and white) did he need? B How many small triangles (green and white) would be in a figure with n rows? The heptagon (seven-sided polygon) on the left can be cut into eight congruent triangles, as shown on the right. The triangles are right triangles, and one angle measures 20. A What is the sum of the angle measures at the vertices of the heptagon? B Explain how you found your answer CLXXXIX one hundred eighty-nine 189

193 Problem Solving Test Prep Choose the correct answer. Alex moves point A right 3 spaces and down 2 spaces. What is the location of point A after the translation? A. (5,8) C. (1,8) B. (6,4) D. (6,2) Which fraction is greater than 5 _ 16? A. 3 _ 8 B. 2 _ 9 C. 1 _ 4 D. 6_ 20 Which numbers complete the factor tree for the prime factors of 40? A. 2, 4, 5 B. 2, 2, 5, 5 C. 2, 2, 2, 2, 5 D. 2, 2, 2, 5 Which is a true statement for this set of data? 3, 3, 3, 5, 6, 7, 9, 10, 11, 11, 12 A. mode median B. median mean C. mean median D. mode mean Solve each problem. Explain your answer. If you use beans to represent the numbers in the pattern below, how many beans will you use for the first 7 numbers? Explain. 1, 3, 7, 15, 31,... Pablo folds a paper in half, then in half again, and so on. The first two folds are shown below. After how many folds will he have 32 congruent sections? Explain. 190 one hundred ninety CXC

194 Name Review/Assessment NCTM Standards 1, 2, 3, 4, 6, 7, 9, 10 Date Complete the table. Identify each angle as acute, right, or obtuse. Then measure to the nearest 5. Lessons 1 and 2 Angle acute, right, or obtuse? Measure B C D E For 5 6, use the information in the drawing (not protractors or rulers). Lesson 2 The measure of P is. Circle all that apply. PQR is... acute obtuse right scalene isosceles equilateral Use a straightedge to draw an Without using a protractor, find the angle that is 35. Lesson 3 missing angle measures. Lessons 5 and A measure of A: 35 q r prime CXCI one hundred ninety-one 191

195 Use a ruler and a protractor. Draw a triangle with these measures. Length of AB : 8 cm Measure of A: 45 Measure of B: 30 Lesson 3 Notice the congruent sides and angles. Circle all the names that match each quadrilateral. Lessons 7 and 8 square rhombus rectangle parallelogram rectangle parallelogram trapezoid rhombus For 10 11, sketch in any lines of symmetry in the quadrilaterals. Lesson 7 Without using a protractor, find the measure of D. Lesson 8 The measure of D is. Solve the problem. Lesson 9 Anthony used pattern block rhombuses to make the first three similar figures in this pattern. How many pattern block rhombuses will he need to make the fifth figure in the pattern? 192 one hundred ninety-two CXCII

196 Chapter 10 Length and Perimeter Measure the sides of each figure to the nearest cm. Record the perimeter in cm. Name NCTM Standards 1, 4, 6 TEKS 5.10C, 5.14D Date AB BC CA DE FG EF GD Perimeter Perimeter HI JK IJ KH LM MN NO OL Perimeter Perimeter Measure the sides of each figure to the nearest 1 _ 2 inch. Record the perimeter in inches. PQ QR RP VS TU ST UV Perimeter Perimeter prime CXCIII one hundred ninety-three 193

197 Use the map and a ruler to measure and answer the questions below. Tanya walks from home directly to school in the morning. After school, she walks to the edge of the park and then back home. How far does she walk? miles On Saturday, Tanya walks to the lake, and then jogs the path around the lake. What is the distance she jogs? miles When Tanya feels like taking a long walk, she walks around the park. How long is the walk around the park? Challenge How many miles does Tanya travel if she walks directly from her home, around the park, and back home again? How many miles does she travel if she walks directly from her home, around the lake, and back home again? miles miles miles 194 one hundred ninety-four CXCIV 2 97

198 Chapter 10 Perimeter Formulas Find the perimeter of each parallelogram. Name NCTM Standards 1, 3, 4, 7, 8 TEKS 5.10C, 5.16B Date Perimeter: units Perimeter: units Perimeter: units Perimeter: units Perimeter: units Perimeter: units Perimeter: units Perimeter: units CXCV one hundred ninety-five 195

199 Solve the problems. Why can t you use a formula for finding the perimeter of a parallelogram to find the perimeter of the figure above? How can you find the perimeter? Challenge Does the formula for finding the perimeter of a rectangle work for finding the perimeter of a square? Tell how you know. 196 one hundred ninety-six CXCVI

200 Chapter 10 Name Area of Parallelograms NCTM Standards 1, 3, 4, 7, 9 TEKS 5.10C, 5.15A Record the area of each parallelogram (A F) in square centimeters (sq cm). Date Base 3 cm Height 3 cm Base 3 cm Height 3 cm Area Area Base 3 cm Base 3 cm Height 2 cm Height 3 cm Area Area Base 2 cm Height 3 cm Base 4 cm Height 2 cm Area Area Complete the sentences. Parallelograms,, and look different but have the same area. Explain why. Parallelograms and have different base and height measurements, but they have the same area. Explain why. prime CXCVII one hundred ninety-seven 197

201 Use a centimeter ruler to find the area and perimeter of each parallelogram. Measure to the nearest cm. Record the area in sq cm and the perimeter in cm. Base DC Height Area Perimeter Base FG Height Area Perimeter Base JK Height Area Perimeter Challenge Use an inch ruler to find the area and perimeter of this parallelogram. Measure to the nearest 1_ inch. Record the area in sq. in. and the 2 perimeter in inches (in.). Base QR Height Area Perimeter 198 one hundred ninety-eight CXCVIII

202 Chapter 10 Name Measuring to Find Areas of Parallelograms NCTM Standards 1, 3, 4, 6, 7, 9, 10 TEKS 5.10C Measure the sides of each parallelogram to the nearest cm. Draw in the height and measure it to the nearest cm. Record the area and perimeter. Date Base BC Area Base FG Area Height 3 cm Perimeter Height Perimeter Base JK Area Base NO Area Height Perimeter Height Perimeter prime CXCIX one hundred ninety-nine 199

203 Solve the problems. The fence around a rectangular-shaped park is 240 yards long. A Draw a rectangle to represent the park, and label the lengths of the sides. B What is the area of a park with these measurements? C Draw a different rectangle to represent the park. D What is the area of a park with these measurements? Challenge A quilt is made up of square patches, each of which measure 16 inches by 16 inches. Each patch is made up of 16 small squares. What is the area of each small square? Draw a sketch if you wish. 200 two hundred CC

204 Chapter 10 Area of Triangles and Trapezoids Find the area and perimeter of each triangle. The given measures are approximate. Name NCTM Standards 1, 3, 4, 6, 7, 9 TEKS 5.10C Date Base BC 3 cm Height 2 cm Side AB 2.1 cm Side AC 3 cm Base DE 4 cm Height 2 cm Side FD 3 cm Side FE 3 cm Base GH 3 cm Height 2 cm Side GI 3 cm Side IH 3 cm Area Area Area Perimeter Perimeter Perimeter Base KL 5 cm Height 3 cm Side JK 4 cm Side LJ 4 cm Area Perimeter Find the area and perimeter of each trapezoid. The given measures are approximate. Base AD 3 cm Side DC 3 cm Base BC 6 cm Side Base EH 1 cm Side EF 2.2 cm AB 2.3 cm Base FG 2 cm Side GH 3 cm Height 2 cm Height 2 cm Area Perimeter Area Perimeter 3 67 CCI two hundred one 201

205 Measure the dimensions and then find the area of each figure in square inches. Draw in the height. Measure to the nearest half inch. Base Base AB Base Height Height 1 in. Area Area Base Base Height Area Challenge Use this diagram and scale to help you answer the questions. Measure to the nearest centimeter. A Approximately how many yards of fencing surround the pool and patio? B How many square yards make up the approximate area inside the fence? 202 two hundred two CCII 2 101

206 Chapter 10 Area and Perimeter of Other Polygons Use the measurements given to find the area and perimeter. Name NCTM Standards 1, 3, 7, 9 TEKS 5.3A, 5.3B, 5.10C, 5.16B Date Area Perimeter Area Perimeter 7 29 CCIII two hundred three 203

207 Find pairs of polygons that have the same area. A B C D E F Same area: Same area: Same area: Challenge Pick 2 figures above that have the same area but look like they have different perimeters. Without measuring, decide which one has a greater perimeter. Figure has a greater perimeter than figure. Why do you think so? 204 two hundred four CCIV

208 Chapter 10 Name Solve each problem. Date Problem Solving Strategy Solve a Simpler Problem NCTM Standards 1, 3, 4, 6, 7, 8, 9 TEKS 5.1A, 5.3A, 5.3B, 5.3C, 5.5A, 5.7, 5.10B, 5.10C, 5.14B, 5.14C, 5.16B Here is a sketch of a cover for a hexagonal swimming pool. AF, BE, and CD are parallel. Use measurements to the nearest cm and use the scale to find the area of the cover. Area Find the perimeter of the outside edge of the pool. Perimeter Mr. Reynolds needed to order carpeting for a room. He made approximate measurements and drew this sketch to show the information he had. Find the area of the rug. Area Find the perimeter of the edge of the rug. Perimeter 5 41 CCV two hundred five 205

209 Problem Solving Test Prep Choose the correct answer. What is the rule for the table? Input Output Which number is NOT between the two given ones when the numbers are written in order? 999,809 and 1,001,034 A. 1,001,019 C. 999,900 B. 1,001,101 D. 999,810 Which is NOT a correct name for all the figures? A. x 10 C. 2x 6 B. 4x 2 D. 3x 2 Which is the only number of juice boxes that can be packed in cartons of 2, 3, 5, 6, or 9 with no boxes left over? A. 800 C. 1,100 B. 900 D. 1,400 A. polygons B. quadrilaterals C. parallelograms D. simple closed figures Solve each problem. Explain your answer. What is the area of the figure? What is the area of the shaded frame around the picture? 206 two hundred six CCVI 2 103

210 Name Review/Assessment NCTM Standards 1, 3, 4, 6, 7, 9, 10 Date Measure the sides of each figure to the nearest centimeter. Record the perimeter in cm. Draw in a height. Lesson 1 AB DC EF GH BC DA FG HE Perimeter Perimeter Find the perimeter of each parallelogram. Lesson 2 Perimeter Perimeter units units Measure the sides and height of the parallelogram to the nearest cm. Record the area and perimeter. Lessons 3 and 4 Base AB Height Area Perimeter CCVII two hundred seven 207

211 Use the approximate measures to find the area and perimeter of each polygon. Lesson 5 Base BC: 6 cm Height: 2 cm Side AB : 3 cm Side AC : 4 cm Area Perimeter Base EF : 2 cm Base DG : 4 cm Height: 2 cm Side DE : 2.5 cm Side FG : 2.5 cm Area Perimeter Use the measurements given to find the area and perimeter. Lesson 6 Area Perimeter Mason needs to calculate the number of square feet of siding needed to cover the back side of his storage shed. He knows that some of the sides are perpendicular and that the line segments AF, BE, and CD in the sketch are parallel. Lesson 7 Use a cm ruler, the sketch, and the scale to find the area. 1 cm 3 ft Area 208 two hundred eight CCVIII

212 Chapter 11 Name Date Adding and Subtracting Fractions with Like Denominators NCTM Standards 1, 2, 7, 10 Complete the sentences with number words. twelve apples eight apples eight-eighths three-eighths seven-fourths four-fourths Shade the bars to show the sums. Complete the number sentences. Change improper fractions to mixed numbers. 1 Use the pictures to complete the number sentences CCIX two hundred nine 209

213 Complete the number sentences., or 1 Choose one of the number sentences above. Write it and three related addition and subtraction sentences. Challenge Write an equivalent fraction for the sum. _ 210 two hundred ten CCX

214 Chapter 11 Name More Adding and Subtracting Fractions with Like Denominators NCTM Standards 1, 2, 6, 7, 9 TEKS 5.2C, 5.3E Write fractions to complete the number sentences. Date Draw and use a picture to solve the problem. Write a number sentence to show the solution. Ben walks 2 1_ miles along a straight road to go from 4 his house to school. He passes Molly s house 3_ 4 of a mile after he starts his walk and usually walks the rest of the way with her. How far does Molly walk to get to school? prime CCXI two hundred eleven 211

215 Complete the number sentences. If the sum or difference is an improper fraction, change it to a mixed number or a whole number. Example 29_ 8 _ 10 8 _ 39 47_ 8 8 Challenge List the sums and differences from Problems 8 13 in order from least to greatest. 212 two hundred twelve CCXII

216 Chapter 11 Name Stories About Adding and Subtracting Fractions NCTM Standards 1, 6, 7, 9, 10 TEKS 5.3E, 5.10C Solve the problems using the pictures. Write number sentences to match the solutions. Carin ate 3_ of a whole pizza. If her brother 8 ate the rest of the pizza, what fraction of the pizza did he eat? Date Number sentence(s): Ms. Liang cut a square cake into twelve equal-sized pieces. If her husband ate 3_ 12 of the cake and her son ate 3_, what fraction 12 of the cake might she share with her daughter? Number sentence(s): T.J. ran as fast as he could for 6_ 10 of a mile, then jogged the rest of the mile. What fraction of the mile did he jog? Number sentence(s): 3 71 CCXIII two hundred thirteen 213

217 You may use the picture to help you solve both Problems 4 and 5. Write number sentences and draw pictures to match the solutions. Mrs. Benson s class is making a quilt of 24 patches. The class completed 7_ of the quilt the first week 24 and _ 11 more the second week. What fraction of 24 the quilt remains to be finished? Number sentences and pictures: There are 24 students in Mr. Cohen s class. There are 10 boys in the class. What fraction of the students are girls? Number sentences and pictures: Challenge A square-shaped field measures 60 feet by 60 feet. If John mows 1_ of the field, 4 how many square feet does John mow? Show your work. sq ft 214 two hundred fourteen CCXIV 2 107

218 Chapter 11 Name Adding and Subtracting Unlike Things NCTM Standards 1, 2, 4, 6, 7, 9 TEKS 5.3E, 5.10A, 5.16B Complete the sentences with number words. Date eight-tenths three feet twelve inches four feet -tenths fifteenth-tenths feet inches fifty-six inches Complete the number sentences. Use the conversion key. Conversion Key 1 lb 16 oz 1 hr 60 min 1 L 1,000 ml 1 m 100 cm 1 yd 3 ft 1 min 60 sec 1 km 1,000 m 1 cm 10 mm min 2 hr 135 min 4 ft 26 in. in. 2 L 400 ml ml 3 m cm 462 cm 5 43 CCXV two hundred fifteen 215

219 Decide which unit to use for your answer and circle it. Complete each number sentence. 120 sec 4 min sec min 4 lb 32 oz oz lb 4 m 3,000 cm m cm 5 ft 48 in. ft in. Complete the number sentences. 12 yd 12 ft yd 1,300 m 1_ km m 2 mm 12 cm 17 cm 15 min 1_ hr hr 2 Challenge Ali told Chandra that 2 1_ 2 Chandra disagreed. Who was right? 13_ 34_ 4 6. Draw sketches and explain your answer in words. 216 two hundred sixteen CCXVI

220 Chapter 11 Name Adding and Subtracting Fractions with Unlike Denominators NCTM Standards 1, 2, 4, 6, 7, 8, 9 TEKS 5.2A, 5.16B Add or subtract fractions of an hour and find the number of minutes. Date 7 31 CCXVII two hundred seventeen 217

221 For each problem below: A Find a common denominator for the fractions. B Write equivalent fractions using that denominator. C Add or subtract. Drew bought 7_ of a yard of fabric to make a belt for 8 his costume. He used 2_ of a yard for the belt. How 3 much fabric does he have left? Explain. Challenge 218 two hundred eighteen CCXVIII 2 109

222 Chapter 11 Name Stories with Fractions NCTM Standards 1, 2, 4, 6, 7, 9 TEKS 5.2A, 5.2B, 5.2C, 5.3E Date Keffie and Danny were painting a mural at school. They need to make a special color, so they mixed 4 1_ 2 pints of blue paint, 2 1_ pints of white 6 paint, and 2_ of a pint of green paint. 3 Write a number sentence to show how many pints of their special color they had. Jake ran five-sixths of a mile. Shayne ran three-fourths of a mile. Who ran farther? Jake or Shayne? Write a number sentence to show the difference between the two distances. Michaela spent two-thirds of her allowance on a magazine. She spent one-fourth of her allowance on candy. Write a number sentence to show the fraction of her allowance that she spent on both items. Two-sevenths of the students in Sammy s class were at band practice. One-fourth of the students were at chorus practice. Are there more students at band practice or at chorus practice? Write a number sentence to show the fraction of her allowance she has left. What fraction of the class is out of the room? Write a number sentence to show the fraction of the class that is still in the room CCXIX two hundred nineteen 219

223 Joseph and Derek had a goal to collect twenty-four used books for the school book sale. In the first week Joseph collected 9 books and Derek collected 8 books. What fraction of the goal has Joseph collected so far? What fraction of the goal has Derek collected so far? One day, Ahmad spent five-sixths of an hour on his homework and practiced piano for three-fifths of an hour. How many minutes did he spend on homework? How many minutes did he spend on piano? Write a number sentence to show the fraction of the goal that remains. Write a number sentence to show how many minutes he worked in all. Write a number sentence to show how many hours he worked. Tifani braided yarn until she had a rope that was five-sixths of a yard long. Then Danisha braided another three-fourths of a yard onto the end of Tifani s rope. How many yards long is the rope now? Challenge Ani had fewer than 25 marbles. She dropped one-fifth of them behind the sofa and hid threefourths of them in her brother s room. She put the rest in her room. Could Ani have started with 12 marbles? How many inches did Tifani braid? How many inches did Danisha braid? Write a number sentence to show how many more inches they have to braid to have a rope 5 feet long. How many marbles did Ani have to start with? How many are in her room? 220 two hundred twenty CCXX

224 Chapter 11 Using Area to Multiply Fractions Fill in the blanks and find the shaded areas to multiply the fractions. Name NCTM Standards 1, 4, 7, 9, 10 TEKS 5.10B Date prime CCXXI two hundred twenty-one 221

225 Complete each sentence and find the shaded areas to multiply the fractions. Shade the indicated areas and complete the sentences to multiply the factors. Challenge 222 two hundred twenty-two CCXXII

226 Chapter 11 Name Using Other Models to Multiply Fractions NCTM Standards 1, 7, 10 Date Use the sketches to help you complete the number sentences. prime CCXXIII two hundred twenty-three 223

227 Draw dot sketches to show multiplication of fractions. Complete the number sentences. Challenge Find different solutions. 224 two hundred twenty-four CCXXIV

228 Chapter 11 Name Fractions of Quantities NCTM Standards 1, 6, 7, 8, 9 TEKS 5.16B The input is 12 eggs. Write the outputs (the number of eggs) in the white boxes. Date Complete each sentence. 1 4 of 12 eggs eggs 5 of 12 eggs 5 eggs 6 4 of 12 of of _ of CCXXV two hundred twenty-five 225

229 Complete each number sentence. 2_ _ _ _ 96 8 Complete each number sentence. 1_ _ _ _ 9 3 Blake bought a dozen eggs. He used 1_ of the eggs to 3 make muffins and 1_ of eggs to make custard. How 2 many eggs does he have left? Explain. Challenge Complete the number sentence. Tell why your answer makes sense and explain what you did. 3_ _ two hundred twenty-six CCXXVI

230 Chapter 11 Name Stories About Multiplying Fractions NCTM Standards 1, 2, 6, 7, 10 TEKS 5.14A, 5.14B, 5.14C Date Solve the story problems. Show how you got your answers by drawing pictures or writing number sentences. Matt s dad agreed to make him a new shelf for his room if he could figure out what fraction of a sheet of plywood he needed. Matt decided that the shelf needed to be three-quarters of its length and one-fifth of its width. What fraction of the sheet of plywood is the shelf? Batoul wanted to fence in an area of her backyard for her new rabbit. She promised her mother that she would only use one-third of the length and one-fourth of the width of the backyard. What fraction of the whole backyard would be fenced for the rabbit? Parisa s brownie recipe makes 4 dozen brownies. She wants to make 2 dozen brownies, and the recipe calls for three-quarters of a cup of oil. How much oil will she need? John had already walked one-third of the half-mile walk to school when he stopped to pat a horse. How far had he already walked? (Give your answer as a fraction of a mile.) What fraction of a mile does he have left to walk? CCXXVII two hundred twenty-seven 227

231 It s three-quarters of a mile from Caitie s home to the school. She was one-third of the way home from school when it started to rain. How far had she walked when it started to rain? (Give your answer as a fraction of a mile.) A sheet of glass is cut into rectangular panes. Each pane is one-quarter of the length and one-quarter of the width of the original sheet. What fraction of the sheet of glass is left after cutting out one pane? What fraction of the sheet is left after cutting out four panes? The picture shows a 1-mile by 1-mile field divided into four sections for four different crops. Write in the missing dimensions and figure out the area of each section. Challenge A field has an area of 1 square mile. A rectangular section is planted with corn. That section measures two-thirds of a mile along one side. If the area of the section is one-half a square mile, what is the length of the other side of the section? (HINT: You may want to use different equivalent fractions for one-half.) A B C D 228 two hundred twenty-eight CCXXVIII

232 Chapter 11 Name Solve each problem. Problem Solving Strategy Solve a Simpler Problem NCTM Standards 1, 2, 6 TEKS 5.2C, 5.3E, 5.14A, 5.14B, 5.14C Date Joshua had spent two-tenths of his allowance by Monday. By Wednesday, he had spent a total of three-fifths of it. What fraction of his allowance did he spend between Monday and Wednesday? Jayne walked a third of the way home from school, which brought her to the library. Then she walked a little farther to her friend s house. If Jane s friend lives four-sevenths of the way home from school, what fraction of Jane s walk is between the library and her friend s house? Ariel spent 3_ of an hour doing 4 homework, Brad spent 5_ of an 6 hour doing homework and Carla spent 2_ of an hour doing homework. 3 List the children in order from the one who spent the most time to the one who spent the least time doing homework. Marti bought 3_ of a pound of 4 green grapes and 7_ of a pound 8 of red grapes. How many pounds of grapes did she buy? CCXXIX two hundred twenty-nine 229

233 Problem Solving Test Prep Choose the correct answer. Colleen s plant is 3 1_ inches tall. It 2 grows an average of 2 1_ inches per 2 week. How tall is it after 5 weeks? A. 17 inches C. 15 1_ 2 inches B. 16 inches D. 14 1_ 2 inches Diagonals from the same vertex cut a polygon into triangles. How many triangles can be made from the diagonals of a 20-sided polygon? A. 15 C. 17 B. 16 D. 18 A photograph is 5_ foot wide and 6 1_ foot high. How much greater is the 2 photograph s width than its height? A. 3 inches C. 5 inches B. 4 inches D. 6 inches Which relationship is shown by the data in the table? x y A. y x 3 B. y x 4 C. y 2x 1 D. y 2x 1 Solve each problem. Explain your answer. Use the grid. Draw the result of rotating triangle A 90 counterclockwise around the dot. Then explain how you could show that the image of triangle A is congruent to triangle B. Pedro is making packages of pens and pencils for the school store. He has 48 pens and 60 pencils. Each package will have the same number of items. Each package will have only pens or only pencils. In how many different ways can he make the packages? If Pedro puts the greatest number of pens and pencils in each package, how many packages can he make in all? 230 two hundred thirty CCXXX

234 Name Review/Assessment NCTM Standards 1, 2, 4, 6, 7, 9, 10 Date Complete the number sentences. Lessons 1 and 2 17 _ 18 _ _ 25 _ _ _ _ _ 16 Solve the problem. Lesson 3 Fran folded a piece of paper into 12 sections. She colored 5_ of the paper red and 1_ of paper green What fraction of the paper is NOT colored? Complete the number sentences. Lesson 4 3 m 4,000 cm m 192 in. 68 ft ft lb 16 oz 7 lb Complete the number sentences by choosing a common denominator. Lesson 5 min 3 _ hr 1 hr 4 CCXXXI two hundred thirty-one 231

235 Write a multiplication number sentence for each sketch. Lessons 7 and 8 Complete each sentence. Lesson 9 2_ 3 of 12 5_ of _ 3 of 12 3_ of 24 8 Solve. Lesson 10 Sara bought 2_ of a pound of walnuts 3 and used 3_ of what she bought to 4 make granola bars. What fraction of a pound of the walnuts did she use to make the granola bars? A rectangular field has been prepared for planting. A portion of the field measuring one-fourth the length and two-fifths the width of the whole field will be planted with soybeans. What fraction of the whole field will that soybean patch be? Solve. Lesson 11 Andee spent 2_ of her allowance 3 on a movie and 1_ on a book. Has 4 she spent all of her allowance? Tell or show how you know. 232 two hundred thirty-two CCXXXII

236 Chapter 12 Name Transforming Two-Dimensional Nets into Three-Dimensional Figures NCTM Standards 3, 7, 8, 9, 10 TEKS 5.7, 5.10C, 5.15A, 5.16B Look at each three-dimensional figure and answer the questions by writing yes or no. Does this three-dimensional figure appear to have any faces that are Date parallelograms? triangles? trapezoids? perpendicular? congruent? parallel? Does this three-dimensional figure appear to have any faces that are parallelograms? triangles? trapezoids? perpendicular? congruent? parallel? Does this three-dimensional figure appear to have any faces that are parallelograms? triangles? perpendicular? congruent? trapezoids? parallel? CCXXXIII two hundred thirty-three 233

237 Use the small copy of your net. Tape or glue the net here. Describe your net. Challenge Tell how you could find the total area of the net. 234 two hundred thirty-four CCXXXIV

238 Chapter 12 Name Describing Three-Dimensional Figures NCTM Standards 2, 3, 7, 8, 9, 10 TEKS 5.7, 5.15A, 5.16A, 5.16B Choose a three-dimensional figure and record its letter here: Describe the faces of your three-dimensional figure and tell if any faces appear to be congruent, parallel, or perpendicular. Date Complete the chart to show how many faces, vertices, and edges your three-dimensional figure has. Faces Vertices Edges Add the number of faces and vertices: F V From that sum, subtract the number of edges: F V E CCXXXV two hundred thirty-five 235

239 Find out what other students got as their answer for Problem 2. Are you surprised? Based on what you find out, write a sentence or two stating a possible conclusion about polyhedra. Pick any prism. Choose one vertex of that prism. Count how many faces meet at that vertex. A Is there any vertex of that prism at which a different number of faces meet? B Would your answer be different if you chose a prism with a different base? Explain why. Pick any pyramid that has one non-triangular face. Choose one vertex of that pyramid. Count how many faces meet at that vertex. A Is there any vertex of that pyramid at which a different number of faces meet? B Would your answer be different if you chose a pyramid with a different non-triangular base? Explain why. Challenge Sketch one of the three-dimensional figures you used on this page. 236 two hundred thirty-six CCXXXVI

240 Chapter 12 Name Sorting Three-Dimensional Figures NCTM Standards 3, 7, 8, 9, 10 TEKS 5.7, 5.15A, 5.16A For each three-dimensional figure, write the letters of all attributes that apply. Some attributes apply to more than one figure. Date Pyramid Attributes A All its faces are polygons. B It has at least one circular base and one other surface. Cone C It has more vertices than faces. D The number of vertices equals the number of faces. E It is a polyhedron. Prism F All its faces are polygons, and all but one of the faces share a vertex. Sphere Cylinder G It has two parallel, congruent bases. H It has no vertices or faces. I One of its faces can be any polygon. The rest are triangles. J All points on this figure are the same distance from a single point. K It is two-dimensional. L It is three-dimensional. M All its faces must be rectangles. N All its faces must be triangles CCXXXVII two hundred thirty-seven 237

241 Describe the differences between pyramids and prisms. Be sure to use attributes such as congruent, parallel, and perpendicular. Challenge Look at the polyhedra your class sorted that are neither prisms nor pyramids. Describe some of the attributes of these three-dimensional figures (G, H, I, J, M, Y) that make them neither prisms nor pyramids. 238 two hundred thirty-eight CCXXXVIII

242 Chapter 12 Name Volume of Rectangular Prisms NCTM Standards 1, 3, 4, 7, 8, 9 10 TEKS 5.10C, 5.16B Find the area of the base and the volume of each rectangular prism built out of inch cubes. Date 1 cu in. Area of base: sq in. Area of base: Area of base: Volume: cu in. Volume: Volume: Area of base: Area of base: Area of base: Volume: Volume: Volume: Area of base: Area of base: Area of base: Volume: Volume: Volume: CCXXXIX two hundred thirty-nine 239

243 Find the area of the base and the volume of each rectangular prism built out of inch cubes. 1 cu in. Area of base: Volume: Area of base: Volume: Area of base: Area of base: Volume: Volume: Challenge This shape is different. It is related to the rectangular prism shown in Problem 13. Figure out its volume and explain your thinking. Volume: 240 two hundred forty CCXL 20 dozen

244 Chapter 12 Name Volume of Prisms NCTM Standards 1, 3, 4, 7, 9, 10 TEKS 5.10B, 5.10C, 5.15A Each right triangular prism is sitting on its base. Use the dimensions to compute the volume. Date Show your work. Volume: Show your work. Volume: Show your work. Volume: CCXLI two hundred forty-one 241

245 Each right triangular prism is sitting on a face that is not its base. Use the dimensions to compute the volume. Show your work. Volume: Show your work. Volume: Challenge Show two ways to calculate the volume of this right triangular prism. Volume: 242 two hundred forty-two CCXLII

246 Chapter 12 Name Area of Nets NCTM Standards 1, 3, 4, 6, 7, 8, 9, 10 TEKS 5.10C, 5.14C, 5.16B Use a net for Figures AA, BB, or CC. Date Tape or paste the small copy of the net here. Label your small net to show the true dimensions (full-size) of each face of your three-dimensional figure. Measure to the nearest half-inch. Label your small net to show the area of each face of your three-dimensional figure. What is the total area of your large net? Example: CCXLIII two hundred forty-three 243

247 Solve the problems. Jonah was not sure he had enough wrapping paper to wrap a gift box. He measured the box and wrote the measurements on a net sketch. How much wrapping paper does he need to cover the box? Courtney made only a few measurements to figure out how much wrapping paper she needed to wrap a tall, rectangular prism-shaped box. The small rectangular base measured 5 in. by 10 in. The height of the box is 12 in. How much wrapping paper does she need? Use this net if you wish. Challenge Tell how you would find the total area of a net of a triangular prism. Tell all the measurements you would make and how you would compute the area with those measurements. 244 two hundred forty-four CCXLIV

248 Chapter 12 Name Surface Area Polyhedra NCTM Standards 1, 3, 4, 6, 7, 8, 9, 10 TEKS 5.10C, 5.15A, 5.16B Find the surface area of each polyhedron using the measurements (in inches) shown on the nets. Date Show your work. Surface area: sq in. Show your work. Surface area: CCXLV two hundred forty-five 245

249 Double the length of each dimension of each polygon. Record the area inside each polygon. You know what happened to the dimensions in each case: they doubled. What happened to the area in each case? Challenge What happens to the surface area of a polyhedron when you double each dimension of each face? Record the doubled dimensions and find both surface areas. Surface area: Surface area: How do the two surface areas compare? 246 two hundred forty-six CCXLVI

250 Chapter 12 Name Comparing Volume and Surface Area NCTM Standards 1, 3, 4, 6, 7, 9, 10 TEKS 5.10C, 5.14C, 5.16B The floor of Taylor s room measures 12 ft by 12 ft. The height from floor to ceiling is 10 ft. Date Taylor wants to paint the four walls of his room with some paint he already owns. It says on the can that a gallon of paint will cover 450 sq ft. If the can is full, does he have enough paint to paint the four walls? Show how you know. If he buys another gallon of the same paint, will he have enough to paint the walls and ceiling? Show how you know. Opening a window will give Taylor enough ventilation so that he is not bothered by the paint fumes, but he wants to know how much air is in the room itself. How many cubic feet of air does the room contain? Show your computations CCXLVII two hundred forty-seven 247

251 Solve the problems. Draw a diagram if you wish. The volume of a room is 1,200 cu ft, and the height from floor to ceiling is 10 ft. What is the area of the floor? Show your computations. What is the area of the flat ceiling? How do you know? What might be the measurements of the floor? by Using those measurements, what is the area of each wall? Wall: Wall: Wall: Wall: Challenge If all the dimensions of the room were doubled, how would the volume change? Explain. 248 two hundred forty-eight CCXLVIII

252 Chapter 12 Name Problem Solving Strategy Guess and Check NCTM Standards 1, 2, 3, 4, 6, 7, 8, 9, 10 TEKS 5.10C, 5.14A, 5.14B, 5.14C, 5.16B You may use a calculator and the tables to help you solve the problems. Date Hope has a cube-shaped box. Its volume is 500 cubic units. About how many units long is each edge? The volume of a large ice cube is 100 cubic centimeters. What is the approximate length of one edge? Edge n Volume n 3 or Target Volume Edge n Volume n 3 or Target Volume CCXLIX two hundred forty-nine 249

253 Problem Solving Test Prep Henry, Jamie, and Sam are three friends. Their ages are consecutive numbers. The product of their ages is 2,145 more than the sum of their ages. Sam is the oldest. How old is Sam? A. 12 B. 13 C. 14 D. 15 The surface area of a cube is 150 square inches. What is the volume of the cube? A. 150 cubic inches B. 125 cubic inches C. 100 cubic inches D. 75 cubic inches Solve each problem. Explain your answer. Darla has a square beach towel that measures 96 inches on each side. She folds it in half, then folds it in half again, and finally folds it in half again. What is the area that the folded towel would cover? Explain how you solved the problem. Students in the architecture club are using cubes to build a model of an apartment house. Each cube represents one room. Every outside wall of a cube will have one window. If the students use 27 cubes, what is the least number of windows that is possible? What is the greatest? Explain how you solved the problem. 250 two hundred fifty CCL

254 Name Review/Assessment NCTM Standards 1, 2, 3, 4, 6, 7, 9, 10 Date Look at each three-dimensional figure and answer the question by writing yes or no. Lesson 1 Does this figure appear to have any faces that are parallelograms? triangles? trapezoids? perpendicular? congruent? parallel? Does this figure appear to have any faces that are parallelograms? triangles? trapezoids? perpendicular? congruent? parallel? How may faces, vertices, and edges does a triangular prism have? Lesson 2 faces vertices edges For each three-dimensional figure, write the letters of all attributes that apply. Some attributes apply to more than one three-dimensional figure. Lesson 3 Pyramid Cone Cylinder Prism Attributes A All its faces are polygons. B It has at least one circular base. C It has two parallel, congruent bases. D All of its faces but two must be parallelograms. The remaining two faces can be any polygon. E All of its faces but one must be triangles. The remaining face can be any polygon. prime CCLI two hundred fifty-one 251

255 Find the area of the base and the volume of each rectangular prism built out of cubes. Lesson 4 Area of base: Area of base: Volume: Volume: This right triangular prism is sitting on its base. Use the dimensions to compute the volume. Lesson 5 Show your work. Volume: Use the dimensions shown on the net to find the surface area of each three-dimensional figure. Lessons 6 and 7 Solve the problem. Lesson 9 Brad has a cube-shaped box. Its volume is 400 cubic centimeters. To the nearest whole centimeter, how long is each edge of the box? Keaton wants to plant a square garden with an area of 50 square feet. To the nearest foot, how long should she make each side of the garden? 252 two hundred fifty-two CCLII

256 Chapter 13 Name Introducing Mobiles NCTM Standards 1, 2, 7, 9, 10 TEKS 5.6 Rubin balanced some, but not all of the arms of a mobile. Write the letter of the diagram for Rubin s unbalanced mobile. Mobile A Date Mobile B Total Weight: 12 Total Weight: 12 Write yes or no at each arm to show if it is balanced. Write the total weights. Total Weight: Total Weight: Total Weight: Total Weight: CCLIII two hundred fifty-three 253

257 Complete the mobiles so that they are balanced. Total Weight: 28 Total Weight: 48 Total Weight: 32 Total Weight: 72 Challenge Make up your own balanced mobile for any number that is a multiple of 4. Total Weight: 254 two hundred fifty-four CCLIV 2 127

258 Chapter 13 Name Solve these mobile puzzles. Balancing Mobiles NCTM Standards 1, 2, 7, 8, 9 TEKS 5.6, 5.15B, 5.16B Date Total Weight: 48 Total Weight: 60 Solve this mobile puzzle and explain how you solved it. Total Weight: 16 Explanation: CCLV two hundred fifty-five 255

259 Martina made a balanced mobile with a total weight of 40. Each 4, each 2, and each 5. Write the letter of the correct diagram of Martina s mobile. Mobile A Mobile B Challenge Complete this mobile so that it balances and its total weight is two hundred fifty-six CCLVI

260 Chapter 13 Name Write an equation to describe each mobile. Equations for Mobiles NCTM Standards 1, 2, 7, 8, 9 TEKS 5.6 weight t weight c weight r Date weight p weight s Total Weight: 48 Total Weight: 24 Equation: Equation: Write three equations that describe the mobile and find the weight of each shape. Total Weight: 48 Equations: prime CCLVII two hundred fifty-seven 257

261 Find the weight of each shape. Total Weight: 48 Total Weight: 40 Challenge Find the weight of each shape, and then complete this mobile so it balances and its total weight is two hundred fifty-eight CCLVIII

262 Chapter 13 Name Solve these balance puzzles. Balance Puzzles NCTM Standards 1, 2, 7, 9, 10 TEKS 5.6, 5.15A Date _ 2 Laurel wrote the following equation: She sketched two diagrams of balance puzzles. Select and circle the diagram that matches the equation CCLIX two hundred fifty-nine 259

263 Draw shapes in the balances to represent these equations. 2s c c 8 c s 2t t 2s 3 Write equations for these balance puzzles. Can you find the weights of any of the shapes (triangle or square)? Equation: Shape weights: Equation: Shape weights: Challenge Each pair of puzzles has enough information for you to find the weights of both kinds of blocks. Find the weights! 260 two hundred sixty CCLX

264 Chapter 13 Name Number Tricks NCTM Standards 1, 2, 6, 7, 9 TEKS 5.6, 5.16B Seon Hwa and Se Ri drew diagrams for some steps of different number tricks. As you can see, they did not agree. Select and circle the correct diagram for each step. Date Words Seon Hwa s Diagram Se Ri s Diagram Multiply a number by 3 Multiply a number by 2 and add 6 Add 2 to a number and multiply the sum by 3 Here s another number trick. Complete the table, first by choosing any number. Then, figure out the starting number if the result is 59. Words Diagram Shorthand Number 1. Pick a whole number. N 2. Multiply the number by Add Multiply by Subtract When using this trick, what can you do to the final result to find the original number? CCLXI two hundred sixty-one 261

265 For a fundraiser, Grades 3, 4, and 5 at Michael s school sold pool and beach toys. Together they raised $934! The fifth graders raised $52 more than the third graders, and the fourth graders raised $30 more than the third graders. Fill in this table to find how much each grade raised. Grade Picture Shorthand Amount Raised 3 x $ 4 $ 5 $ All three grades $934 Challenge For another fundraiser, the third graders raised $23 more than the fifth graders, and the fourth graders raised $71 more than the fifth graders. Together, they raised $1,054. How much did each grade raise? Explain. Grade 3: Grade 4: Grade 5: 262 two hundred sixty-two CCLXII 2 131

266 Chapter 13 Name Making Diagrams NCTM Standards 2, 8, 10 TEKS 5.6 Draw a diagram to illustrate each situation. Date There were P people standing in line to buy movie tickets. There were P people standing in line and then my friend and I got in line, too. John put on a puppet show for his family. He set out a row of 5 chairs for them to sit in. John decided to invite some friends, too, so he added some rows. Every row had 5 chairs. John s mother invited a few of her friends. She added 2 chairs to each row. prime CCLXIII two hundred sixty-three 263

267 Fill in the table below to match the diagrams with the shorthand. A x B x 4 M x y N 4x C x D x y O x p y 4 x E y x 4 F y 4 Q 4x 3 G y R xy x S 4y Diagram A B C D E F G Shorthand Pick a diagram from above that represents the situation. Jennifer arranged some chairs into 4 rows. Each row had the same number of chairs. Diagram Misao laid two boards together, endto-end. One of the boards was 4 feet long. How long were they together? Diagram Challenge Write a situation that fits Diagram C. 264 two hundred sixty-four CCLXIV

268 Chapter 13 Name Equations for Stories NCTM Standards 1, 2, 6, 7, 8, 9 TEKS 5.6, 5.16B An ant crawled from one corner of a rectangular room, along all four walls, and ended back where it started. One dimension was l feet, one dimension was w feet, and it took lw square-foot tiles to cover the floor. Date Complete the table. l w Area (lw) Perimeter (2l 2w) The ant crawled along 3 walls and had 11 feet to go before reaching its starting place. The trip around the three walls had been 25 feet. What are the room s dimensions? Explain your answer. Select and circle a diagram that correctly represents Problem CCLXV two hundred sixty-five 265

269 At the science museum, adult tickets cost $10, and child tickets cost $7. Mrs. Nikula took some fourth graders to the museum. Circle the number sentence that best describes the total cost of the tickets. T stands for the total cost; C stands for the number of children in the group. Remember, Mrs. Nikula bought herself a ticket, too! T 10C 7 T 7C 10K K 7C T 7C 10 Several families visited the museum together. Write an equation to describe the total cost of tickets. Use T to stand for the total cost, A to stand for the number of adults in the group, and C to stand for the number of children. Two different groups visited the museum. Each group paid $121 for their tickets. The two groups did not have the same number of children. How many adults and children were in each group? Adults Children Group 1 Group 2 Challenge The museum changed its ticket prices. Now, three child tickets cost the same as two adult tickets. A group of 5 adults and 6 children paid $108. One adult ticket costs $, one child ticket costs $. Explain how you found your answer. 266 two hundred sixty-six CCLXVI

270 Chapter 13 Name Problem Solving Strategy and Test Prep Work Backward NCTM Standards 1, 2, 5, 6, 7, 8, 9, 10 TEKS 5.3A, 5.13B, 5.14B, 5.14C Vlad enjoyed inventing number tricks for his friends. He gave this one to Lecia. Date Pick a whole number. Add 10. Multiply by 3. Subtract 12. Divide by 3. Tell me your result, and I ll tell you your starting number Lecia s result was 14. What was her starting number? Vlad has a younger brother, Sergi. Sergi is half the age of their sister, Katya. Katya is two years older than their sister, Sonya. Sonya is half Vlad s age. Vlad is 16. How old is Sergi? Abby, Belinda, Charles, and Ernie each brought some cars to Dante s house. They decided to make teams of their cars and have races. When they put the cars together, they noticed that Abby had one more car than Charles, Belinda had one more than Abby, Dante had one more than Belinda, and Ernie had one more than Dante! When they shared their cars, each friend had 5 cars for their team. How many cars did each of the friends have at first? Abby: cars Belinda: cars Charles: cars Dante: cars Ernie: cars 3 89 CCLXVII two hundred sixty-seven 267

271 Problem Solving Test Prep Choose the correct answer. Kara had 1_ pound of sugar left after 8 making a cake. She used 1_ 4 pound of sugar for the batter and 1_ 8 pound of sugar for the icing. How much sugar did Kara start with? A. 1 pound C. 1 2 pound B. 3 4 pound D. 3 8 pound Which is the only measure that is not one of the numbers in the set? 2, 2, 4, 4, 4, 5, 6, 7, 8 A. mean C. mode B. range D. median Which product is shown by the model? A B C. 1 3 D. 3 4 Marco s dog weighs 34 pounds. Since its birth, it has gained 33 pounds and lost 1 pound. How much did Marco s dog weigh when it was born? A. 1 pound C. 3 pounds B. 2 pounds D. 4 pounds Solve each problem. Explain your answer. The total weight of the mobile is 48 pounds. Write the shapes in order from lightest to heaviest. An amusement park charges $16 admission. Special rides are S dollars each. Write an equation to find the total cost, T, including W special rides. If you spent $30 in all and special rides cost $2 each, how could you use your equation to find the number of special rides you went on? 268 two hundred sixty-eight CCLXVIII

272 Name Review/Assessment NCTM Standards 1, 2, 6, 7, 9, 10 Date Circle the equations that agree with the mobile. 2C S 3T 2S 7C Lessons 1 3 Total Weight: 40 3C T 2S Find the weight of each shape. Lessons 1 3 Write two equations that describe the mobile. Lessons 1 3 Total Weight: 24 Find the weight of each shape. Lessons 1 3 Solve these balance puzzles. Lesson 4 prime CCLXIX two hundred sixty-nine 269

273 Nimit wrote this number trick for his friend Catherine. Catherine s resulting number was 3. What was Catherine s starting number? Lesson 5 Number Trick 1. Pick a number. 2. Add 5 to it. 3. Multiply the result by Subtract 10 from that. 5. Divide by 2 Draw a diagram to describe this situation. Lesson 6 The theater had four rows of chairs and two extra chairs set up for the play. Randy has to pay the same for each of his four overdue library books. He also has to pay five dollars for a book he lost. Circle the equation that best describes the total amount he owes. T stands for the total amount; F stands for the overdue fine for each book. Lesson 7 Grayson is 5 years older than his sister, Greta. Greta is half as old as Greg. If Greg is 16, how old is Grayson? Lesson 8 T F 5 T F 5 T 5 2F T 4F 5 Show how you solved the problem. 270 two hundred seventy CCLXX

274 Chapter 14 Name Conducting a Probability Experiment NCTM Standards 5, 7, 8, 9 TEKS 5.12A, 5.12C A probability experiment: How many heads? If you flip one penny and one nickel at the same time, what are the possible outcomes? Date Penny H T Nickel h t hh Perform the experiment. Flip the two coins 20 times. Record the number of heads for each flip in the table below. Trial Number of Heads Trial Number of Heads Use fractions to describe your results. 0 heads: _ 20 1 head: _ 2 heads: _ prime CCLXXI two hundred seventy-one 271