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4 Contents Chapter 1 Algebra: Machines and Puzzles 1.1 Introducing This Year s Mathematics...P1 1.2 Investigating Cross Number Puzzles...P2 1.3 Investigating Input-Output Tables...P3 1.4 Connecting Input-Output Machines and Puzzles... P4 1.5 Introducing Negative Outputs...P5 1.6 Determining Rules Using Two Operations...P6 1.7 Multiplying Cross Number Puzzles...P7 Chapter 2 Multiplication and Large Numbers 2.1 Finding Patterns in the Multiplication Table...P8 2.2 Splitting Area Models...P9 2.3 Doubling and Adding... P Multiplying by Multiples of P Working with Large Numbers... P Estimating Products... P Estimating in Various Ways...P Discovering a Useful Multiplication Pattern... P Extending the Multiplication Pattern... P Investigating Why the Pattern Works... P Finding Products of Large Factors... P18 Chapter 3 Factoring and Prime Numbers 3.1 Investigating Mystery Number Puzzles... P Factoring...P Finding Common Factors...P Investigating Prime and Composite Numbers...P Writing a Number as the Product of Prime Factors...P Investigating Divisibility by 2, 5, and 10...P Investigating Divisibility by 3, 6, and 9...P25 Chapter 4 Equivalence and Comparison of Fractions 4.1 Investigating the Result of Two Operations...P Investigating the Order of Two Operations... P Finding Equivalent Fractions...P Equivalent Fractions Using Dot Sketches...P Strategies for Comparing Fractions...P Comparing Fractions Using Common Denominators... P Area Models and Number Lines...P Numbers Greater Than 1...P Equivalent Fractions Greater Than 1...P34 iii

5 Contents Chapter 5 Recording Multi-Digit Multiplication 5.1 Multiplying Multi-Digit Numbers...P Writing Vertical Records...P Writing Shorter Records... P Using Square Number Differences...P Multiplying Large Numbers...P39 Chapter 6 Grids and Graphs 6.1 Making Figures on a Coordinate Grid...P Translating Figures on a Grid... P Reflecting Figures on a Grid...P Rotating Figures on a Grid...P More About Transformations...P Graphing with Negative Numbers...P Moving on a Coordinate Grid...P Graphing Data... P What is Typical?...P Another Way of Describing What s Typical...P Reading Graphs and Tables...P50 Chapter 7 Decimals 7.1 Investigating Decimals... P Comparing and Ordering Decimals...P Large and Small Numbers... P Connecting Decimals to Fractions...P Connecting Decimals to Other Fractions...P Estimating Decimals Using Familiar Fractions...P Estimating Decimals Using Rounding... P Adding with Decimals...P Subtracting with Decimals...P Adding and Subtracting Decimals...P Multiplying with Decimals... P61 Chapter 8 Developing a Division Algorithm 8.1 Exploring Missing Factors...P Connecting Multiplication and Division...P Dividing Using Multiplication and the Area Model...P Recording the Steps in Division...P Dividing and Recording Division Efficiently...P Using Multiplication to Check Division...P Investigating Remainders...P Interpreting Remainders in Word Problems...P Another Option for Interpreting Remainders...P70 iv

6 Chapter 9 Attributes of Two-Dimensional Figures 9.1 Investigating Angles...P Classifying Angles and Triangles...P Constructing Triangles...P Constructing Similar Triangles... P Angles Formed by Intersecting Lines... P Angles Formed by a Line Intersecting Parallel Lines... P Comparing and Classifying Quadrilaterals...P Investigating Quadrilaterals...P78 Chapter 10 Area and Perimeter 10.1 Length and Perimeter...P Perimeter Formulas...P Area of Parallelograms...P Measuring to Find Areas of Parallelograms...P Area of Triangles and Trapezoids...P Area and Perimeter of Other Polygons...P84 Chapter 11 Fraction Computation 11.1 Adding and Subtracting Fractions with Like Denominators...P More Adding and Subtracting Fractions with Like Denominators...P Stories About Adding and Subtracting Fractions...P Adding and Subtracting Unlike Things...P Adding and Subtracting Fractions with Unlike Denominators...P Stories with Fractions...P Using Area to Multiply Fractions...P Using Other Models to Multiply Fractions...P Fractions of Quantities...P Stories About Multiplying Fractions...P94 Chapter 12 Three- Dimensional Geometry 12.1 Transforming Two-Dimensional Nets into Three-Dimensional Figures...P Describing Three-Dimensional Figures...P Sorting Three-Dimensional Figures...P Volume of Rectangular Prisms...P Volume of Prisms...P Area of Nets...P Surface Area of Polyhedra...P Comparing Volume and Surface Area... P102 v

7 Contents Chapter 13 Fun with Algebra 13.1 Introducing Mobiles...P Balancing Mobiles...P Equations for Mobiles...P Balance Puzzles...P Number Tricks... P Making Diagrams...P Equations for Stories...P109 Chapter 14 Data and Probability 14.1 Conducting a Probability Experiment... P Finding Probabilities... P Sampling Experiments... P Another Sampling Experiment... P Introducing Percents... P Circle Graphs... P115 Chapter 15 Graphing 15.1 Graphing... P Graphing Capacity Conversions... P Changing the Scale of Graphs... P Graphing Change Over Time... P Graphing the Story of a Trip...P Graphing Temperature Conversions... P121 vi

8 These pages provide additional practice for each lesson in the chapter. The exercises are used to reinforce the skills being taught in each lesson. Book

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10 Lesson 1 Introducing This Year s Mathematics Use the table to make an organized list of all possible combinations of dimes, nickels, and pennies that make 28. Order may vary. DIMES NICKELS PENNIES Which combination of coins is NOT worth 49? A. 4 dimes, 1 nickel, 4 pennies B. 3 dimes, 3 nickels, 4 pennies C. 2 dimes, 5 nickels, 4 pennies D. 1 dime, 4 nickels, 4 pennies Sandy has 2 quarters, 1 dime, and 4 pennies. How much money does she have? A. 39 C. 60 B. 59 D. 64 Chapter 1 Book P1

11 Lesson 2 Investigating Cross Number Puzzles Complete each Cross Number Puzzle by filling in numbers that make amounts on both sides of the thick line the same. John leaves his house at 7:30 A.M. He arrives at school at 8:25 A.M. How long does it take John to get to school? Explain how you found your answer. 55 minutes; Possible explanation: I thought about a clock. It is 30 minutes from 7:30 A.M. to 8:00 A.M. and 25 minutes from 8:00 A.M. to 8:25 A.M. 30 minutes 25 minutes 55 minutes P2 Book Chapter 1

12 Investigating Input-Output Tables Complete the tables. Lesson 3 INPUT Add Multiply by Subtract MACHINE OUTPUT INPUT Divide by Multiply by MACHINE OUTPUT MAKE YOUR OWN. Many correct answers are possible for last column. INPUT Add Double Subtract MACHINE OUTPUT Which expression does NOT equal 16? A. 4 4 B C. 9 7 D Chapter 1 Book P3

13 Connecting Input-Output Machines and Puzzles Lesson 4 The numbers in the puzzle on the right are all double the numbers on the left. Complete the pairs of Cross Number Puzzles. Write the numbers in order from greatest to least. Explain how you decided how to order the numbers. 648, , , ,301; 684,299; 648,831. Possible explanation: I compared the digits of the same place value beginning with the hundred thousands. All three numbers have 6 in the hundred thousands place, so I looked at the ten thousands place. 648,831 is the least number. The other two numbers have the same digit in the ten thousands and thousands places. In the hundreds place, 2 is less than 3, so 684,299 is less than 684,301. P4 Book Chapter 1

14 Introducing Negative Outputs Each of the tables was made using one of the rules below. For each table, write the letter of the rule that was used to create it. Then complete the table. Lesson 5 Rule A: Multiply the input by 3. Rule B: Subtract 6 from the input. Rule B Rule C: Multiply the input by itself. INPUT OUTPUT Rule C INPUT OUTPUT Rule A INPUT OUTPUT The temperature was 97F at 2:00 P.M. Then a thunderstorm rolled in and the temperature dropped 16F. After the storm, the temperature rose 8F. What was the temperature then? Explain your answer. 89F; Possible explanation: I drew a thermometer. I started at 97F, went down 16F, and then up 8F to 89F. Chapter 1 Book P5

15 Lesson 6 Determining Rules Using Two Operations Complete the tables. Some of the rules use two operations. INPUT OUTPUT INPUT OUTPUT INPUT OUTPUT INPUT OUTPUT Marti used a rule to make this list of numbers. 1, 3, 7, 13, 21, If she uses the same rule to continue the list, which number would come next? A. 23 C. 33 B. 31 D. 37 What is the value of c in the equation 63 c 29? A. 34 B. 44 C. 46 D. 92 P6 Book Chapter 1

16 Multiplying Cross Number Puzzles Complete all the puzzles. Lesson 7 Which number sentence is correct? A B C D Jacob left for school with 4 boxes of pencils. Each box had 12 pencils. At school, he gave 6 pencils to each of his 4 friends. Which number sentence below can be used to find the remaining number of pencils? A. (4 12) (6 4) B. (4 12) (6 4) C. (12 6) (6 4) D. (4 12) (6 4) Chapter 1 Book P7

17 Finding Patterns in the Multiplication Table Complete the table. Lesson 1 Notice the pattern of the squares that are shaded in the designs below. How many squares would be shaded in Design 4? Explain how you know. 20 squares; there would be a 4-by-4 array of 16 shaded squares in the center and a shaded square in each corner P8 Book Chapter 2

18 Lesson 2 Splitting Area Models Complete the area models and puzzles Which is NOT a way to describe a area model? A. (10 3) (10 4) D. (12 1) (13 1) B. (5 8) (6 8) E. (13 9) (13 5) C. (10 3) (10 4) Chapter 2 Book P9

19 Doubling and Adding Fill in the columns by adding or doubling. Lesson Complete , so , so An adult takes 180 breaths in 15 minutes and a baby takes 300. How many more breaths than an adult will a baby take in one hour? Explain how you know. 480 more breaths; Possible explanation: One hour is 4 times longer than 15 minutes; in one hour an adult takes 4 180, or 720 breaths and a baby takes 4 300, or 1,200, breaths. 1, P10 Book Chapter 2

20 Multiplying by Multiples of 10 Lesson 4 Complete the puzzles , , , , , , ,250 Complete the number sentences , ,000 Marco had 1,400 baseball cards and 50 football cards in his collection. After selling some cards to his brother, he had 1,274 cards left. How many cards did he sell to his brother? Explain how you solved the problem. 176 cards; Possible explanation: I added the number of baseball cards and football cards, and then subtracted the number of cards he had left from the sum. 1, ,450; 1,450 1, Chapter 2 Book P11

21 Working with Large Numbers Write numbers to match the words. Lesson 5 Twelve million, forty-nine thousand, nine hundred two 12,049,902 Two hundred fourteen billion, five hundred million, seven hundred seventeen thousand, twelve 214,500,717,012 Six hundred eight million, eight 608,000,008 Compare the numbers and order them from least to greatest by writing 1, 2, or 3 in the boxes. 3 29,642,831, ,642,813, ,624,831,760 Which expression does NOT have a value equal to 2,000? A B C D Which shows another way to write 10,000? A B C D P12 Book Chapter 2

22 Estimating Products Complete the number sentences , , , , , ,000 Lesson , , , , ,200 Solve the problem. Fifty students each spend about 300 hours a year studying and doing homework. About how many hours per year do they spend altogether? 15,000 hours A large bag of potato chips costs $0.75 more than a small bag. If represents the price of the large bag, which expression shows the price of a small bag? A. $0.75 C. $0.75 B. $0.75 D. $0.75 Chapter 2 Book P13

23 Estimating in Various Ways Estimate the products. Estimates may vary Lesson 7 Estimate: Estimate: , Estimate: Estimate: ,800 Natalee wants to buy 24 cupcakes at tomorrow s bake sale. She knows that each cupcake will cost 32. How much money should she bring to be sure she has enough money? Show your work and explain your answer. Estimate: Estimates and explanations will vary. She should bring 960 cents, or $9.60. For the estimate I rounded 32 up to 40 to make sure she had enough money. Which list shows the common factors of 12 and 30? A. 1, 2, 3, 4, 5, 6, 10, 12, 15, 30 B. 2, 4, 6, 10, 12 C. 1, 3, 5, 15 D. 1, 2, 3, 6 Which pair of signs would make this sentence true? A., B., C., D., P14 Book Chapter 2

24 Discovering a Useful Multiplication Pattern Complete the diagrams and number sentences. Lesson Jake makes $21 each day he works. He plans to work 112 days this year. At the end of the year, will he have earned the $2,000 he wants to save for a trip to visit his grandmother? Estimate to solve and explain your answer ,240; yes; Possible explanation: I adjusted the factors, so that the estimated product is less than the actual product. The actual product will be more than 2,240. Chapter 2 Book P15

25 Lesson 9 Extending the Multiplication Pattern Complete the diagram and tables. Steps Away Steps Away Steps Away A certain number is multiplied by 3. The product is 8 less than 35. What is the number? A. 8 C. 7 B. 5 D. 9 A certain odd number is less than 10. If it is multiplied by 6, and 6 is added to the product, the result is 60. What is the number? A. 9 C. 7 B. 5 D. 3 P16 Book Chapter 2

26 Lesson 10 Investigating Why the Pattern Works Fill in the missing numbers. An eagle beats its wings 150 times in a minute. A hummingbird beats its wings 30 times as fast as an eagle. How many times does a hummingbird beat its wings in one minute? Explain how you know? 4,500 times; I need to multiply 150 x 30. First I multiply (1,500) and then I multiply that product by 3: 3 1,500 4,500. Chapter 2 Book P17

27 Finding Products of Large Factors Fill in the missing numbers. Lesson 11 (20 30) (30 40) 25 1,225 ( ) 25 3,025 ( ) 25 2,025 Which group contains a number that is NOT a square number? A. 121, 11, 25, 4 B. 16, 49, 1, 144 C. 36, 16, 0, 4 D. 100, 49, 9, 25 Which group of words correctly describes the number 25? A. multiple of 5, multiple of 20 B. odd, multiple of 10 C. prime, square, odd D. odd, square, composite P18 Book Chapter 2

28 Investigating Mystery Number Puzzles Solve the puzzles. The boxes below the clues show you the number of digits in the solution. Clues Puzzle A Multiple of 9 less than 81 Even Difference between the digits 5 Workspace Lesson Puzzle B Multiple of 20 greater than 80, but less than 300 Sum of the digits is even Sum of the digits is a 2-digit number Ms. Nichols wanted to put the same number of computers into 3 classrooms. She had a total of 84 computers. Which statement is true? A. She cannot put the same number of computers into each classroom. B. She can put 29 computers into each classroom. C. She can put 43 computers into each classroom. D. She can put the same number of computers into each classroom. Chapter 3 Book P19

29 Factoring Lesson 2 Write all the factors of each product in the diagram. Connect pairs of factors. Gayle is shading squares with multiples on the grid. If she shades all the squares with multiples of 2, how many squares will she shade? 50 If she shades all the squares with multiples of 4, how many squares will she shade? 25 If she shades all the squares with multiples of 5, how many squares will she shade? 20 P20 Book Chapter 3

30 Finding Common Factors To solve these puzzles, you may need to make more than one list of numbers. Lesson 3 Read all the clues for each puzzle before you begin. The boxes below the clues show you the number of digits in the solution. Some puzzles have more than one solution. Clues Workspace Puzzle A Odd Common factor of 12 and 18 1 or 3 Puzzle B Less than 200 Sum of the digits 6 Product of the digits 0 Each factor of 75 is its factor too Which number is NOT a common multiple of 8 and 5? A. 80 B. 0 C. 140 D. 200 Lois arrived at the library at 9:30 A.M. She spent 35 minutes in the magazine section, 48 minutes in the fiction section, and 1 hour and 15 minutes in the biography section. What time did Lois leave the library? 12:08 P.M. Chapter 3 Book P21

31 Investigating Prime and Composite Numbers List the factors. Write P for Prime, C for Composite, or N for Neither. Lesson 4 Number Factors P, C, or N 40 C 23 P 49 C 1 N 100 Which group contains all of the factors of 18? A. 1, 18 B. 1, 2, 6, 9, 18 C. 1, 2, 3, 6, 9, 18 D. 1, 3, 6, 9, 18 Kenji and John drive 270 miles using 9 gallons of gas. How many miles do they drive on one gallon of gas? 30 miles C P22 Book Chapter 3

32 Writing a Number as the Product of Prime Factors Draw factor trees and circle the prime factors. Write number sentences with the prime factors. Lesson 5 The factor trees and the order of the factors in the sentences may vary Which number is divisible by 2, 3, 5, 6, and 10? A. 48,405 B. 45,840 C. 36,315 D. 63, A bead factory divides 54,000 beads evenly into 6 containers. How many beads are in each container? Are there any beads left over? 9,000 beads; no Chapter 3 Book P23

33 Investigating Divisibility by 2, 5, and 10 Write yes or no. Lesson 6 Is it divisible by 2? How do you know? 128 yes 1,046 yes 2,468 yes 465 no 1,298 yes 788 yes ones digits of 0, 2, 4, 6, or 8. Possible answer: Numbers divisible by 2 have Is it divisible by 5? How do you know? 110 yes 65 yes 105 yes 42 no 1,040 yes 6,630 yes ones digits of 0 or 5. Possible answer: Numbers divisible by 5 have Is it divisible by 10? How do you know? 425 no 1,250 yes 16,802 no 760 yes 405 no 21,970 yes a ones digit of 0. Possible answer: Numbers divisible by 10 have Mr. Ruiz used a copy machine to print 395 pages. The machine stapled them into packets of 5 pages each. How many pages were left over? A. 0 B. 2 C. 3 D. 4 P24 Book Chapter 3

34 Lesson 7 Investigating Divisibility by 3, 6, and 9 Write yes or no. Is the number divisible by 3? 102 yes 473 no 780 yes 312 yes 561 yes 803 no How can you tell if a number is divisible by 3? by 3 if the sum of the digits is divisible by 3. Numbers are divisible Is the number divisible by 9? 333 yes 612 yes 3,210 no 945 yes 514 no 4,959 yes How can you tell if a number is divisible by 9? by 9 if the sum of the digits is divisible by 9. Numbers are divisible Is the number divisible by 6? 501 no 840 yes 4,545 no 102 yes 134 no 5,454 yes How can you tell if a number is divisible by 6? by 6 if the number is even and divisible by 3. The number 8,955 is NOT divisible by A. 3 C. 9 B. 5 D. 10 Numbers are divisible On Friday, Saturday, and Sunday, a total of 630 newspapers were delivered. If the same number of newspapers were delivered each day, how many newspapers were delivered on Sunday? 210 newspapers Chapter 3 Book P25

35 Investigating the Result of Two Operations Write the outputs. Lesson 1 Example: What are all the common factors of 24 and 36? A. 1, 2, 4, 24, 36 B. 1, 2, 3, 6, 12 C. 1, 2, 3, 4, 12 D. 1, 2, 3, 4, 6, 12 Which group shows common multiples of 6 and 4? A. 1, 6, 4, 12 B. 36, 12, 24 C. 1, 12, 18 D. 12, 18, 24, 36 P26 Book Chapter 4

36 Investigating the Order of Two Operations Record the outputs. Lesson 2 Record the missing numbers. If you multiply 12 by 3 and divide the result by 4, which statement is NOT true? A. You can either multiply 12 by 3 first or divide 12 by 4 first and still get the correct answer. B. The correct answer is 9. C. You can divide 12 by 4 and then multiply the result by 3 to get the correct answer. D. The correct answer is 4. Chapter 4 Book P27

37 Finding Equivalent Fractions 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. Lesson 3 Mackenzie used 12 feet of ribbon to wrap a gift. Tyler used twice as much ribbon to wrap 4 small gifts. He used the same amount of ribbon for each gift. How much ribbon did Tyler use for each gift? A. 24 feet C. 6 feet B. 8 feet D. 4 feet P28 Book Chapter 4

38 Lesson 4 Equivalent Fractions Using Dot Sketches Use dot sketches to find equivalent fractions. 5_ 6 15 _ 18 3_ 5 15 _ 25 Find any equivalent fraction with a dot sketch. Answers will vary. 6 2_ 7 _ 21 7_ 8 14 _ _ 5 _ 20 Which fraction is equivalent to 2 _ 9? A. _ 1 18 B. 1 _ 3 C. _ 6 27 D. 9 _ 2 4_ 7 12 _ 21 What fraction is the simplest form of 15 _ 25? A. _ 6 10 B. 3 _ 5 C. _ D. _ 9 15 Chapter 4 Book P29

39 Strategies for Comparing Fractions Compare the fractions. Write,, or. How did you figure it out? Choose one or more. Compared each fraction to 1. Choices will vary _ 12 3 _ 8 Figured out which fraction is closer to 1. Recognized equivalent fractions. Something else: Lesson 5 How did you figure it out? Choose one or more. Compared each fraction to 1. Choices will vary. 2 5_ 6 4 _ 10 Figured out which fraction is closer to 1. Recognized equivalent fractions. Something else: How did you figure it out? Choose one or more. Compared each fraction to 1. Choices will vary. 2 3_ 4 6 _ 8 Figured out which fraction is closer to 1. Recognized equivalent fractions. Something else: Damon wrote this riddle. Find the answer to the riddle. Explain the strategy you used. 7 ; Possible explanation: 14 The denominator has to be twice the numerator, so I guessed a number for the numerator, doubled the number for the denominator and then checked to see if the sum was 21. I kept guessing and checking until I found numbers with a sum of 21. I am a fraction equivalent to 2_ 4. The sum of my numerator and my denominator is 21. What fraction am I? P30 Book Chapter 4

40 Comparing Fractions Using Common Denominators 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. Lesson 6 If used, dot sketches may be drawn and shaded in various ways. Example: 5_ 8 3_ 4 1_ 4 2_ 6 5_ 6 _ _ 12 4 _ 12 2_ 3 3_ 5 5_ 6 6_ 8 7_ 8 10 _ 15 9 _ 15 2_ 3 3_ 4 20 _ 24 Common denominators and fractions may vary. 18 _ 24 4_ 5 21 _ _ _ _ 20 Chapter 4 Book P31

41 Area Models and Number Lines Shade the sketches for the fractions. Lesson 7 The sections shaded may vary. 1_ 4 4_ 6 2_ 6 2_ 12 1_ 3 3_ 12 1_ 6 2_ 3 Write the fractions from Problems 1 8 as pairs of equivalent fractions. 1 3 _ 4 _ 12 Order may vary. 4 2 _ 6 _ _ 6 _ _ 12 _ 6 Jake hiked 3_ mile around the pond. Marcia hiked 3_ mile to the cabin. 4 5 Who hiked farther? Explain how you know. Jake; Possible explanation; 3_ 4 is greater than 3_ 5. Both fractions have the same numerator, so the fraction with the smaller denominator is larger. P32 Book Chapter 4

42 Numbers Greater Than 1 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. Lesson 8 7_ 3 13 _ _ 3 8_ 3 5_ 4 1_ _ Solve the problem. Small paper cups at the water machine hold 1_ cup of 4 water. Erika was very thirsty and filled her cup eleven times. How much water did she drink? Explain how you know _ 4 4 4_ 4 1 and 8_ 4 cups of water; Possible explanation: I know that 2, so _ 4 Katie has $8 in her wallet. She has 1_ of that amount in 2 her pocket and 1_ of that amount in her hand. How much 4 money does she have in all? Explain how you know. $14; Possible explanation: 1_ 2 $8 is $2. $8 $4 $2 $14 of $8 is $4 and 1_ 4 of Chapter 4 Book P33

43 Lesson 9 Equivalent Fractions Greater Than 1 Draw lines to match the equivalent numbers. 9_ _ _ _ _ _ 16 18_ _ 15 Write equivalent fractions or mixed numbers. 25_ 8 1 _ 3 8 2_ _ 3 4 Answers will vary. 27 _ 4 6 6_ 8 38 _ 6 6 2_ 6 6 1_ 3 43 _ 8 5 3_ 8 5 9_ 24 Look at the hexagon covered with 3 different shapes. Which statement is NOT true? A. The triangle is 1_ of the hexagon. B. The trapezoid is 1_ 2 C. The rhombus is 1_ 3 D. The triangle is 1_ 6 3 of the hexagon. of the hexagon. of the hexagon. P34 Book Chapter 4

44 Multiplying Multi-Digit Numbers Complete the multiplication sentences after splitting and completing an area model or completing a puzzle. Lesson , , , ,608 Which fraction represents the shaded part? Which fraction represents the shaded part? A. 1_ 3 B. 1_ 4 C. 2_ 6 D. 1_ 6 A. 2_ 3 C. 2_ 8 B. 2_ D. 1_ 5 3 Chapter 5 Book P35

45 Writing Vertical Records Fill in the puzzle. Then complete the multiplication records. Lesson 2 Order of partial products may vary. Write the partial products on the area models. Then complete the multiplication records. Write a word problem that can be represented by the number sentence 19 36?. Then solve your problem. Problems will vary. Possible problem: Each of the 19 students in the fifth-grade class baked three dozen cookies. How many cookies were baked? 684 cookies P36 Book Chapter 5

46 Writing Shorter Records Complete the puzzle and record. Lesson 3 Complete the area model. Then complete the puzzle and record. Which of the following is NOT equal to 86 24? A. (80 24) (6 24) B. (80 6) (20 4) C. (20 86) (4 86) D. (24 6) (24 80) Which will NOT produce the same result as 81 69? A B. (80 1) (9 60) C. (60 9) (80 1) D. (81 60) (81 9) Chapter 5 Book P37

47 Using Square Number Differences Complete the tables. Lesson 4 a a ,600 2,500 b b c (c 2) (c 2) c A certain pair of numbers have a sum of 25 and a difference of 9. The numbers must be: A. 5, 5 C. 25, 9 B. 17, 8 D. 9, 16 The square of one number is added to the square of another number. The sum is 41. The numbers could be: A. 6, 2 C. 5, 4 B. 40, 1 D. 3, 5 P38 Book Chapter 5

48 Multiplying Large Numbers Complete the area model, puzzle, and record. Lesson ,816 Partial products and their order may vary. The Gomez family is planning a party at a restaurant. They are inviting 51 adults and 26 children. If the cost is $49 per adult and $24 per child, how much should they expect to spend on the party? Explain how you found your answer. $3,123; Possible explanation: I need to find the sum of what it costs for the adults (51 $49) and what it costs for children (26 $24). I can use the pattern of squares to find the two products: 51 $49 $2,499; 26 $24 $624; $2,499 $624 $3,123. Chapter 5 Book P39

49 Making Figures on a Coordinate Grid Plot each point, label it, and then connect A B C D E A. Name A B C D E Coordinates (1,2) (3,4) (4,3) (5,1) (3,1) Lesson 1 Complete the table for the rule given. Name A B C D E Coordinates (x,y) (1,2) (3,4) (4,3) (5,1) (3,1) New Ordered Pair: Add 7 to the First Coordinate (x 7, y) (8,2) (10,4) (11,3) (12,1) (10,1) Plot the points whose coordinates are given in the new ordered pairs. Connect the new points: A B C D E A. Jessica added 3_ cup of pineapple, 2_ cup of chopped almonds, 4 3 and 3_ cup of dried cranberries to a salad. Did she add more 5 pineapple or dried cranberries? Explain how you know. more pineapple; 3_ 3_ ; Possible explanation: 3_ the same numerators, so the fraction with the smaller denominator is the greater fraction. and 3_ 5 have P40 Book Chapter 6

50 Translating Figures on a Grid In the first row of the table below, record the coordinates of each vertex of Figure F. Lesson 2 Slide Figure F five spaces down. Draw it, and record the new coordinates and the rule in the table. Label the new image Figure G. Slide Figure G three spaces to the right. Draw it and record the new coordinates and the rule in the table. Label the new image Figure H. Order of columns may vary. Rule F (1,7) (2,7) (2,5) (1,5) (0,6) (x,y) G (1,2) (2,2) (2,0) (1,0) (0,1) (x, y 5) H (4,2) (5,2) (5,0) (4,0) (3,1) (x 3, y 5) Which 2 figures look congruent? Explain how you could check to make sure they are congruent. Figures Q and R. Possible answer: I could trace Figure R and then put the tracing on top of Figure Q to see if they match. If they are the same size and shape, they are congruent. Chapter 6 Book P41

51 Reflecting Figures on a Grid The vertices of a figure are given in the table below. Plot and label each vertex. Lesson 3 Use a straightedge to connect A B C D E F G A. Reflect the figure over the dotted, horizontal line. Plot each new vertex, draw the figure, and write its coordinates in the table. Vertices Original Figure New Figure A (1,3) (1,5) B (2,4) (2,4) C (4,4) (4,4) D (5,3) (5,5) E (5,1) (5,7) F (3,2) (3,6) G (1,1) (1,7) Aaron made this map showing some locations in his neighborhood. Which ordered pair represents the location of the school? A. (2,3) C. (4,5) B. (5,2) D. (5,4) What is located at (2,3)? A. Library C. School B. Park D. Home P42 Book Chapter 6

52 Rotating Figures on a Grid Figures B, C, and D are rotations of Figure A around (4,4). Complete the table of coordinates for Figures C and D. Lesson 4 A B C D (4,6) (2,4) (4,2) (6,4) (3,6) (2,3) (5,2) (6,5) (3,5) (3,3) (5,3) (5,5) (1,5) (3,1) (7,3) (5,7) (1,4) (4,1) (7,4) (4,7) (4,4) (4,4) (4,4) (4,4) Draw and label Figures B and D on the grid. Does the diagram show a translation, a reflection, or a rotation? If it is a rotation, show the point around which the figure is rotated. If it is a reflection, show the line over which it is reflected. If it is a translation, give directions to tell how much to add to or subtract from each coordinate. a reflection Chapter 6 Book P43

53 More About Transformations List the coordinates of Figure A s vertices in the table. Draw any reflection of Figure A and label it B. List the coordinates of its vertices. Draw a translation of Figure A and label it C. Record its vertices. Rotate Figure A and label the result D. Record D s vertices. Lesson 5 Figures B, C, and D will vary. A B C D (5,5) (5,8) (8,9) (7,7) (7,5) Which group shows all the numbers that are common factors of 24 and 30? A. 1, 2, 3, 6 B. 1, 2, 3, 5, 6 C. 1, 2, 3, 4, 6, 8, 12, 24 D. 1, 2, 3, 5, 6, 10, 15, 30 Which is the greatest common factor of 24 and 30? A. 3 B. 6 C. 24 D. 30 P44 Book Chapter 6

54 Graphing with Negative Numbers For each coordinate pair, write the letter that labels the point. Lesson 6 (4,3) C (3, 4) F ( 4, 3) I ( 3,4) L (5,0) D (0, 5) G ( 5,0) J (0,5) A (3,4) B (4, 3) E ( 3, 4) H ( 4,3) K Rebecca had only a 1_ 4 -measuring cup to measure flour for a muffin recipe. She filled the measuring cup six times. How much flour did she measure? A. 1 1_ cups 4 C. 13_ 4 cups B. 1 1_ cups 2 D. 21_ 2 cups Jake ordered a pizza for lunch and ate 3_ of the pizza. He took the 8 rest of the pizza home. What part of the pizza did he take home? A. 3 _ 8 B. 1 _ 2 C. 5 _ 8 D. 3 _ 4 Chapter 6 Book P45

55 Moving on a Coordinate Grid Draw the following segments. ( 4,6) to ( 3,5) ( 4,2) to ( 2,1) ( 4, 2) to ( 2, 2) ( 4, 5) to ( 2, 5) (4,6) to (4,3) (4,1) to (4,0) (3, 2) to (3, 4) (2,6) to (2,3) (2,2) to (2, 1) ( 1,6) to (1,6) Lesson 7 ( 1,2) to (1,2) ( 1, 2) to (1, 2) ( 2,0) to ( 4, 1) (0, 1) to (0,2) ( 1,6) to ( 1,3) ( 4,2) to ( 4, 1) ( 3,5) to ( 2,6) ( 1, 1) to (1, 1) (2,2) to (4,1) ( 1,3) to (1,3) (0, 2) to (0, 5) ( 3,3) to ( 3,5) (4,0) to (2, 1) ( 3, 2) to ( 3, 5) (2,3) to (4,3) ( 2,0) to ( 2,1) (1,6) to (1,3) Draw a big dot at (3, 5) Which fraction is closest to 1? Explain how you decided. 2 5_ ; possible answer: I can think about 9 decimals for the fractions; 5_ 9 than the decimals for the other three fractions which is closer to 0.5 P46 Book Chapter 6

56 Graphing Data A group of students wondered ABOUT how many raisins are in a small box. They counted the number of raisins in each of 17 boxes. Here are the numbers they found: Lesson 8 37, 33, 35, 36, 38, 34, 35, 38, 35, 37, 35, 33, 35, 35, 36, 37, 40. Make a line plot for the data What is the greatest (maximum) number of raisins found? 40 What is the least (minimum) number of raisins found? 33 What is the difference (range) between the greatest number of raisins and the least number of raisins in a box? 7 What is the number of raisins that was found the most often (the mode)? 35 Summer camp runs for ten weeks. The campers are served 3 meals a day. How many meals are served in the ten weeks? Each week at summer camp costs $79 per person. If 27 girls and 23 boys attend the camp, what is the total cost? A. 30 meals C. 210 meals B. 150 meals D. 250 meals A. $1,817 C. $3,590 B. $2,133 D. $3,950 Chapter 6 Book P47

57 What Is Typical? Lesson Use the line plot to decide if the statements are true or false. The title might be Ages of Fifth Grade Boys Mothers. false The range is 6. true Both the mode and median are 2. true The title could be Number of Servings of Fruit and Vegetables in a Day. true Derek drew a triangle on a grid. The vertices of the triangle are (1,2), (3,2), and (2, 1). If he translates the triangle 2 spaces to the left and 3 spaces down, what will the coordinates of the new triangle be? Explain how you know. ( 1, 1), (1, 1), (0, 4); Possible explanation: If the triangle moves 2 spaces to the left and 3 spaces down, each vertex will move the same. P48 Book Chapter 6

58 Another Way of Describing What s Typical Answer as many questions as you can. If the graph or table does not provide a way to figure out the answer, write Cannot tell. Lesson 10 Morgan made a graph to show the ages of children in her neighborhood that were in kindergarten through fifth grade CHILDREN S AGES 11 How many children does the graph represent? 10 What is the median age? 7 How many people live in the U.S.? cannot tell What is the median population of the 9 most populous U.S. cities? 1,479,339 Which statement is NOT true for this data set? 10, 12, 14, 8, 14 A. The mode is greater than the minimum. B. The median is greater than the mode. C. The mode is the same as the maximum. D. The range is 6. Chapter 6 Book P49

59 Lesson 11 Reading Graphs and Tables Bob took a survey to find out which pets some first graders preferred. Dog Cat Bird Fish Other Which choice is the mode? dog How many 1st graders were surveyed? 50 How many more people chose cats than birds? 10 The line plot shows some students spelling scores. How many students had a score of 80 or better? A. 3 students B. 4 students C. 12 students D. 13 students Which score did 4 students receive? A. 85 B. 90 C. 95 D. 100 P50 Book Chapter 6

60 Investigating Decimals Write any number that comes between the two given numbers. Lesson 1 Answers will vary. Possible answers are given Write the number that comes halfway between the two given numbers. Which number could not be a common denominator for fractions with denominators of 6 and 8? A. 24 C. 96 B. 12 D. 48 The table shows the prices for tickets to a museum. How much will it cost for a class of 23 students? Tickets Prices $8.25 $19.25 $30.25 $41.25 A. $57.25 C. $63.25 B. $62.25 D. $68.50 Chapter 7 Book P51

61 Comparing and Ordering Decimals Write,, or to complete the number sentences. Lesson Write the numbers in order from least to greatest Which is not a fraction for the shaded part? A. 1 3 B. 2 6 C. 3 9 D. 3 6 On Sunday, Ben started an exercise program by lifting weights. On Monday, he went for a run. He will run every third day and lift weights every fifth day. On which day of the week will he do both activities together for the first time? A. Tuesday C. Thursday B. Wednesday D. Friday P52 Book Chapter 7

62 Large and Small Numbers Write the numbers in order from greatest to least. Lesson 3 23,540,610 23,450,601 23,450,061 23,456,100 23,540,610 23,456,100 23,450,601 23,450, Which fraction matches the shaded part of the sketch? A B C. 2 8 D. 2 6 A room has 31 rows of 31 chairs. One row is added, and one chair is removed from each row. Which is the only expression that does not show how many chairs there will be? A. (31 1) (31 1) B C. (31 1) 31 D Chapter 7 Book P53

63 Connecting Decimals to Fractions Fill in the fraction notation (above the picture) and decimal notation (below the picture) to match the blocks. Lesson 4 Example Lucie swam 50 meters in more than 31.5 seconds, but less than 31.6 seconds. Name three different answers for how long she could have taken. Explain your answer. Answers will vary. Possible answers: seconds, seconds, seconds; 31.52, 31.55, and are all greater than 31.5 and less than P54 Book Chapter 7

64 Connecting Decimals to Other Fractions Write equivalent fractions and decimals. Lesson Write the mixed numbers above the number line and the matching decimals below. Erika has $ Which could NOT be true? A. She has 12 whole dollars, 26 tenths of a dollar, and 49 hundredths of a dollar. B. She has 12 dollars, 26 dimes, and 49 pennies. C. She has 12 dollars, 10 quarters, 5 dimes, and 9 pennies. D. She has 15 dollars, and 9 tenths of a dollar. Jackie has 24 markers and 40 pencils to put into bags. Each bag must have the same number of markers and the same number of pencils. What is the greatest number of bags she can fill if she uses all the markers and pencils? A. 2 C. 8 B. 3 D. 12 Chapter 7 Book P55

65 Lesson 6 Estimating Decimals Using Familiar Fractions Make designs by shading in some of the hundredths. Record the fractions and decimals. Answers will vary Answers will vary Which point is incorrectly labeled on the number line? A. 1 8 B. 1 2 C D A bug is sitting at the point above 1 3_ on the number line. It starts 4 crawling toward 0 at the rate of 1_ unit every 10 seconds. How long 4 will it take it to reach 0? A. 50 seconds B. 1 minute C. 1 minute 10 seconds D. 1 minute 20 seconds P56 Book Chapter 7

66 Estimating Decimals Using Rounding Round each number to the nearest whole number. Lesson Round each number to the nearest tenth Round each number to the nearest hundredth Ryan bought four items that cost $12.29, $16.45, $1.99, and $9.49. Which is the best estimate of the amount he paid? A. between $33 and $35 B. between $35 and $37 C. between $37 and $39 D. between $39 and $41 A factory produced 5,712 snacks. Which is the only way the snacks cannot be packaged if they are all used? A. packages of 9 B. packages of 6 C. packages of 3 D. packages of 2 Chapter 7 Book P57

67 Adding with Decimals Complete the number sentences. Lesson _ _ _ _ _ _ Renee s kitchen floor is a rectangle greater than 60 square feet, but less than 70 square feet in area. Each dimension of the floor is greater than 6 feet and the floor is perfectly tiled with 1-foot square tiles, none of which have been cut. What could the area be? Explain. Possible answers: 63 sq ft or 64 sq ft; since each dimension is a whole number greater than 6 feet, and 9 9 is already more than 70, at least one of the dimensions must be 7 or 8. 7 by 9 and 8 by 8 are the ones that work. P58 Book Chapter 7

68 Subtracting with Decimals Complete the number sentences. Lesson _ _ _ _ _ _ 0.14 Seven of the 56 musicians in the Somer School band are drummers. The same fraction of the Euclid School band are drummers. Euclid has 10 drummers. How many musicians are in the Euclid School band? Explain how you found your answer. 80 musicians; Possible answer: 7 56, or 1_, of the musicians in the 8 Somer School band are drummers. If Euclid School has 10 drummers, then they must have 80 musicians because is equivalent to 1_ 8. Chapter 7 Book P59

69 Lesson 10 Adding and Subtracting Decimals Add or subtract _ _ Estimate. Estimates will vary or Explain how to determine if is equivalent to Possible answer: by comparing the digits in the same place-value positions beginning at the left. The digits in the ones, tenths, and hundreds places are the same. In the thousandths place, 7 > 0, so > P60 Book Chapter 7

70 Multiplying with Decimals First, circle the best estimate. Then, calculate an exact answer _ 49.6 closer to _ 3.22 closer to Lesson _ 3.18 closer to _ closer to _ 3.24 closer to _ 5.19 closer to _ closer to _ closer to Which of these sentences is true? A B C D Oranges are packed 144 to a crate and apples 96 to a crate. A truck can carry 90 crates of oranges and 60 crates of apples. What is the maximum number of pieces of fruit the truck can carry? A. 16,820 C. 17,780 B. 17,620 D. 18,720 Chapter 7 Book P61

71 Exploring Missing Factors Lesson 1 Complete the puzzles and number sentences. Use one stamp from Group A and one from Group B. A B A B A B A B The Haskell family has been driving at 60 miles per hour for three hours. They still have 45 miles to go before arriving at the beach. How many miles is the whole trip to the beach? Explain how you found the answer. 225 miles; to find the number of miles they drove in the first 3 hours, I multiplied 60 miles by 3: Then I added the miles to go: P62 Book Chapter 8

72 Lesson 2 Connecting Multiplication and Division Each of these rectangles should be labeled with its area (inside) and the lengths of its sides. Fill in the missing values. Fill in the missing numbers Use each problem to help you with related problems Fifteen minutes after the time shown on the clock, Marcie began dinner. She finished dinner at 6:10 P.M. How long did she spend eating dinner? A. 25 minutes C. 35 minutes B. 30 minutes D. 40 minutes Chapter 8 Book P63

73 Dividing Using Multiplication and the Area Model This time there are nineteen rows. How many squares are there per row? To make your work easier, list some useful multiples of 19 or use multiples of 20 to estimate. Lesson 3 Shira has less than 500 pennies. She can divide them evenly into 2 piles, 3 piles, 4 piles, 5 piles, 6 piles, or 7 piles. How many pennies does she have? A. 240 C. 350 B. 300 D. 420 P64 Book Chapter 8

74 Recording the Steps in Division Complete the table of multiples of 27. Lesson ,080 1,350 2,160 Complete the area model and division record. Solve these problems on a separate sheet of paper , , Hamburgers come in packages of 6, and hamburger buns come in packages of 8. If Shane buys 5 packages of hamburgers and enough buns, what is the least number of buns he will have left? Explain how you know. 2 buns; Shane buys 5 6, or 30, hamburgers. Buns come in packages of 8; so the number of buns he buys is a multiple of is the smallest multiple of 8 that is greater than 30. Chapter 8 Book P65

75 Dividing and Recording Division Efficiently Complete the table of multiples of 31. Lesson Complete the area model and division record. Solve these problems on a separate sheet of paper Which of these problems has the greatest quotient? Try to figure this out without actually calculating the quotients. A C B D , Which of these problems has the greatest divisor? A B C D , P66 Book Chapter 8

76 Lesson 6 Using Multiplication to Check Division Complete the table of multiples of 47, or $0.47. Save work by doubling and adding $0.47 $0.94 $1.41 $1.88 $2.35 $2.82 $3.29 $3.76 $4.23 Use the multiples to compute the cost of different numbers of items that cost 47 each. 40 at 47 each $ at 47 each $ at 47 each $ at 47 each $ at 47 each $ at 47 each $ at 47 each $ at 47 each $ at 47 each $ at 47 each $ at 47 each $ at 47 each $46.53 How many 47 items can be bought for the three amounts shown below? Divide to find out. If you need more room, do the work on a separate sheet of paper, and write the summaries here. 1 7 $0.47 $ $0.47 $ A large cardboard box is sitting on a table. The area of one side of the box is 3 square feet. The height of the box is 3 feet. Mark all statements that could be true. A. The volume is 9 square feet. C. The volume is 4 1_ cubic feet. 2 B. The box is a cube. D. The dimensions of the base are 3 feet by 1 foot. 4 5 $0.47 $ Chapter 8 Book P67

77 Investigating Remainders Look at the example to see how it is labeled. Fill in the missing numbers and number sentences for the other area models. Lesson 7 EXAMPLE _ _ _ _ _ _ _ _ _ _ 11 4 Ben bought 4 packets of stamps. Each packet had 100 stamps in it. He mounted the same number of stamps on each of 5 pages. How many stamps did he mount on each page? Explain how you know. 80 stamps; Ben bought 4 100, or 400, stamps in all. To find the number on each page, I divided 400 by P68 Book Chapter 8

78 Interpreting Remainders in Word Problems Read the stories and solve the problems by drawing a diagram or writing a record. What do you do about the remainder ignore it or include it as a fraction or decimal? You would not believe how hungry Lydia, Arthur, Ray, and Katy are today! If they share their 5 small pizzas equally, how much pizza will each get? Many methods are possible. One such method is shown. Lesson pizzas What should you do with the remainder? show it as a fraction Graham is unloading a box of twelve dozen paperback books onto a bookshelf. Each shelf can hold 25 books. How many shelves will these books completely fill? Many methods are possible. One such method is shown. 5 shelves What should you do with the remainder? If there are 7 yards of ribbon in a full roll, how many feet of ribbon are on 5 full rolls? A. 35 C. 105 B. 12 D. 21 ignore it Which would give the best estimate for 77 93? A C B D Chapter 8 Book P69

79 Another Option for Interpreting Remainders Solve. Decide what to do when there is a remainder ignore it (round down), include it as a fraction or a decimal, or round up. Show your work. Some mini-vans can carry 7 people. How many 7-person mini-vans will be needed to take 18 people to a museum? Solution: 3 mini-vans What should you do about the remainder? round up There are 350 seats in the auditorium where the fifth-grade graduation will be held. If each of the 58 fifth graders gets an equal number of tickets, how many will each fifth grader get? Solution: 6 tickets What should you do about the remainder? ignore it Lesson A class of fifth graders sold homemade cheese pizzas as a fundraiser. They sold 20 pizzas and made $165. If the price of each pizza was the same, how much did each pizza cost? Solution: $8.25 What should you do about the remainder? include it as a decimal Alvin had fewer than 100 pennies. He found he could divide them evenly into 2 piles, 3 piles, 4 piles, 5 piles, or 6 piles. How many pennies did he have? Explain how you know. 60 pennies; Possible explanation: 60 is the only number less than 100 that is divisible by 2, 3, 4, 5, and _ 4 P70 Book Chapter 8