written by Raven Deerwater Anne E. Fischer Allyn Fisher

written by Raven DeerwaterAnne E. Fischer

Allyn Fisher

illustrated by Tyson Smith

B5HC-BISBN 9781602621008

Home Connections Blackline Masters

Bridges in Mathematics, Grade 5

Bridges in Mathematics, Grade 5, package consists of—

Getting Started

Bridges Teachers Guide, Volume One

Bridges Teachers Guide, Volume Two

Bridges Teachers Guide, Volume Three

Bridges Teachers Guide, Volume Four

Bridges Blackline Masters

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Bridges Student Book Blacklines

Home Connections Blacklines

Work Place Student Book Blacklines

Student Math Journal Blacklines

Word Resource Cards

Manipulatives

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Bridges in Mathematics is a standards-based K–5 curriculum that provides a unique blend

of concept development and skills practice in the context of problem solving. It incorpo-

rates the Number Corner, a collection of daily skill-building activities for students.

The Math Learning Center is a nonprofit organization serving the education community.

Our mission is to inspire and enable individuals to discover and develop their mathematical

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ISBN 9781602621008

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Unit One: Connecting Mathematical TopicsHome Connection 1: Worksheet, Math Interviews 1

Home Connection 2: Worksheet, More about Today’s Cube Sequence 3

Home Connection 3: Worksheet, Exploring a New Sequence 5

Home Connection 4: Worksheet, Story Problems 7

Home Connection 5: Worksheet, Primes & Composites 11

Home Connection 6: Worksheet, Using Arithmetic Properties 13

Home Connection 7: Worksheet, Taking Orders 15

Home Connection 8: Worksheet, Tile Sequences 19

Home Connection 9: Worksheet, Range, Mode, Median & Mean (Average) 23

Home Connection 10: Worksheet, Home Averaging 27

Unit Two: Seeing & Understanding Multi-Digit Multiplication & DivisionHome Connection 11: Worksheet, Estimating Length in Metric Units 29

Home Connection 12: Activity, Instructions for Multiplication Four in a Row 35

Multiplication Four in a Row Record Sheet 37

Home Connection 12: Worksheet, Multiplication Four in a Row 38

Home Connection 13: Worksheet, Multiplication Sketches 41

Home Connection 14: Worksheet, Coins & Quick Sketches 45

Home Connection 15: Worksheet, Looking for Metric Measures at Home 49

Home Connection 16: Worksheet, Multiplication Interview 53

Home Connection 17: Activity, Multiplication Strategies 55

Home Connection 18: Worksheet, Agree or Disagree? 59

Home Connection 19: Activity, Instructions for Quotients Win 63

Game Spinners 65

Quotients Win Game Sheet 1 67

Quotients Win Game Sheet 2 68

Go for Zero Record Sheet 69

Home Connection 20: Worksheet, Area & Perimeter 71

Home Connection 21: Worksheet, Unit Review 77

Unit Three: Geometry & MeasurementHome Connection 22: Worksheet, Shape Puzzles 81

Home Connection 23: Worksheet, Areas of Geoboard Figures 83

Home Connection 24: Worksheet, Thinking about Quadrilaterals 87

Home Connection 25: Worksheet, Find the Angle Measure 91

Home Connection 26: Worksheet, Protractor Practice & Clock Angles 93

Home Connection 27: Worksheet, Reflections, Symmetry & Congruence 97

Home Connection 28: Activity, Area Bingo Practice 100

Area Bingo Cards: page 1 of 3 103



Home Connection 29: Worksheet, Drawing Similar Figures 110

Home Connection 30: Activity, Net Picks 113

3-Dimensional Figure Nets: page 1 of 2 115

3-Dimensional Figure Nets: page 2 of 2 117

Home Connection 31: Worksheet, Volume & Surface Area 119

Unit Four: Multiplication, Division & FractionsHome Connection 32: Activity, Estimation Interviews 121

Home Connection 33: Worksheet, More Multiplication Menus 123

Home Connection 34: Worksheet, Multiplication & Division Practice 125

Divisibility Riddles 129

Home Connection 35: Worksheet, The Tangerine Problem 131

Home Connection 36: Worksheet, Lady Liberty 133

Home Connection 37: Worksheet, Fraction & Division Story Problems 135

Home Connection 38: Worksheet, The Mini-Quilt Project 137

Home Connection 39: Worksheet, Egg Carton Fractions & More 141

Home Connection 40: Worksheet, More Fraction Story Problems 145

Home Connection 41: Worksheet, Unit Four Review 147

Unit Five: Probability & Data AnalysisHome Connection 42: Worksheet, Bar & Circle Graphs 151

Home Connection 43: Worksheet, Presidents’ Names 155

Home Connection 44: Worksheet, Briana’s Routes 159

Home Connection 45: Worksheet, Another Spinner Experiment 163

Home Connection 46: Worksheet, Spinner & Dice Probabilities 167

Home Connection 47: Worksheet, Tallies & Graphs 169

Home Connection 48: Worksheet, Reading Survey Data 173

Unit Six: Fractions, Decimals & PercentsHome Connection 49: Worksheet, Interpreting Remainders 177

Home Connection 50: Worksheet, Equivalent Fractions on a Clock 181

Home Connection 50: Activity, Equivalent Fraction Concentration 183

Home Connection 51: Activity, The Smaller the Better Fraction Game 185

The Smaller the Better Fraction Game 1 186

The Smaller the Better Fraction Game 2 187

Home Connection 52: Worksheet, Cafeteria Problems 191

Home Connection 53: Worksheet, Modeling, Reading & Comparing Decimals 195

Home Connection 54: Worksheet, More Decimal Work 197

Home Connection 55: Worksheet, Decimal Sense & Nonsense 201

Home Connection 56: Worksheet, Working with Decimals & Percents 203

Home Connection 56: Activity, Adding Decimals Game 205

Home Connection 57: Worksheet, Finding Percents 207

Home Connection 58: Worksheet, Unit Six Review 211

Unit Seven: Algebraic ThinkingHome Connection 59: Activity, Instructions for The Operations Game 215

The Operations Game Cards: page 1 of 3 217



Home Connection 60: Worksheet, Operations, Equations & Puzzles 225

Home Connection 61: Worksheet, More Tile Patterns 229

Home Connection 62: Worksheet, Thinking About The King’s Chessboard 233

Home Connection 63: Worksheet, The Function Machine Strikes Again! 237

Home Connection 63: Activity, Instructions for The Function Machine Game 238

What’s My Rule? Record Sheet 1 239

What’s My Rule? Record Sheet 2 240

Home Connection 64: Worksheet, The Lemonade Stand 241

Home Connection 65: Worksheet, Picturing Problems 245

Unit Eight: Data, Measurement, Geometry & Physics with Spinning TopsHome Connection 66: Activity, Circle Surround 247

Home Connection 67: Worksheet, Circle Math 251

Home Connection 68: Activity, Circle Explorations 256

Home Connection 69: Worksheet, Unit Eight Review 260

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Bridges in Mathematics 1© The Math Learning Center

Home Connections For use after Unit One, Session 2.

Home Connection 1 H Worksheet

Math Interviews

Select a parent or other adult and ask them the following questions. Record their answers below.

Name of the person interviewed _________________________________________

1 What is mathematics?

2 How do you use mathematics at home or at work?

3 What are your best mathematical abilities?

4 What are your strongest memories about learning math in school?

Home Connections

© The Math Learning Center2 Bridges in Mathematics

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More about Today’s Cube Sequence

1 Here are the first 3 arrangements in the cube sequence we discussed in class. Explain what the pattern is to an adult at home and have the adult initial the sheet to show he or she understands.

Arrangement 1 Arrangement 3 InitialsArrangement 2


2a Here is the fourth arrangement in the sequence. How many cubes are in this arrangement?

Arrangement 4

b Shanda says you don’t have to count the cubes one by one to find out how many are in the 4th arrangement. She says there is 1 cube in the middle and then 5 arms of 3 cubes each.

Write an equation to show how Shanda figured out the number of cubes in the 4th arrangement.

Arrangement 4

3 3

3

1 cube3

3

(Continued on back.)

Home Connections


3 How many cubes are in the 5th arrangement? Use Shanda’s method or come up with one of your own to figure it out without counting one by one. Label the picture of arrangement 5 and write an equation to show your thinking.

Arrangement 5

4 How many cubes would it take to build the 23rd arrangement in this sequence? Show your thinking using numbers, words, and/or labeled sketches.

CHALLENGE

5 A certain arrangement in this sequence takes 631 cubes to build. Which ar-rangement is it? Show your thinking using numbers, words, and/or labeled sketches.

Home Connection 2 Worksheet (cont.)

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Exploring a New Sequence

1 What do you notice about the first three arrangements in the sequence above?

2 Sketch the 4th and 5th arrangements in this sequence.

3 How many cubes would it take to build the 149th arrangement? Explain your answer using words, numbers, and/or a labeled sketch.

4 A certain arrangement takes 124 cubes to build. Which arrangement is it? Ex-plain your answer using words, numbers, and/or a labeled sketch.

Arrangement 1 Arrangement 3Arrangement 2


Home Connections


CHALLENGE

5 There are 8 people on a committee. Each time they meet, they shake hands with each other so that each person shakes everyone else’s hand once.

a Each time they meet, how many handshakes are there?

b Imagine that 3 committee members arrive late. The other 5 members have al-ready shaken hands. How many handshakes will there be when the 3 late mem-bers arrive?


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Story Problems

Solve the problems below and on the next page. Show your work using words, numbers, and/or labeled sketches. Be sure to write your answer in the space provided.

1 Over the summer, Kiyoshi’s neighbor paid him $7 each week to water the flowers in her front yard. By the end of the sum-mer, Kiyoshi earned $56. How many weeks did he water his neighbor’s flowers?

Kiyoshi watered the flowers for _____ weeks.

2 Carlotta has 7 cousins. They are coming to her house for a party. She wants to get each cousin a bracelet that costs $6. How much money will Carlota need to buy a bracelet for all of her cousins?

Carlotta will need $ ______ .

3 Terrell is helping his dad plant a vegetable garden. He is planting seeds in rows. If Terrell plants 8 rows with 6 seeds in each row, how many seeds will he plant in all?

Terrell will plant _____ seeds.



Home Connections


4 Thirty-eight fifth graders at Vernon Elementary are going on a field trip to the zoo. They are riding in vans that each hold 9 students. How many vans will they need for everyone to get to the zoo?

They will need _____ vans.

5 Whitney and Troy baked 38 cookies for the bake sale. They put them in bags of 8 cookies each to sell at the bake sale. When they were done, they had some cookies left over. If they shared the leftover cookies equally, how many cookies did each person get?

Each person got _____cookies.


(Continued on next page.)

Home Connections



6 Brandon and Bethany baked 55 cookies for the bake sale. They put 8 cookies in each bag to sell. When they were done, they had some left over. If they shared the leftovers equally, how many cookies did each person get?

Each person got _____ cookies.

7 Emma and Maggie made brownies for the bake sale. They made 52 altogether and put 4 in each bag. They charged $0.75 per bag and sold 7 bags.

a How much money did they make?

b How many bags of cookies did they have left?


Home Connections



8 When Alex and Marcus went to the store with their mom, she said they could split the change evenly. The total cost of their groceries was $57.32. She gave the cashier three $20 bills.

a How much money did Alex and Marcus get each?

b What coins would they have needed to get in order to split the money evenly?

9 On Friday afternoon, Keira realizes she has put off her reading for too long and that she needs to finish her book by Monday. The book is 265 pages long. She is on page 27. How many will she need to read each night to finish the book before school on Monday morning?

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Primes & Composites

Words in italics are defined at the top of the next page.

1 Make a quick sketch of all the rectangles that can be formed with tile for the numbers 23, 32, 35, and 37.

a 23 b 32

c 35 d 37

2 List all the factors for 23, 32, 35, and 37.

a 23 b 32

c 35 d 37

3a Which of the numbers 23, 32, 35, and 37 are prime? Which are composite?

_________ are prime _________ are composite

b Explain how you made your choices.


Home Connections


When you multiply two whole numbers to get another number, the two num-bers you multiplied are factors of the other number. Example: 3 and 5 are factors of 15 because 3 × 5 = 15.

A prime number only has two factors: 1 and itself. Example: 17 = 1 × 17

A composite number has more than two factors. Example: 6 = 1 × 6 and 6= 2 × 3.

Note The number 1 is neither prime nor composite because it has just one factor: itself.

CHALLENGE


4 On the grid to the right, follow the directions to color in all the composite numbers.

a Color in all the even numbers ex-cept 2 itself.

b Color in all the numbers that end in 5 except 5 itself.

c Color in any numbers you get when you count by 3 except 3 itself. If you land on a number that is already colored, you don’t have to color it in twice.

d Color in any numbers you get when you count by 7 except 7 itself. If you land on a number that is already colored, you don’t have to color it in twice.

100

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

10

20

30

40

50

60

70

80

90

e List at least three mathematical observations about the numbers that never got colored in.

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Using Arithmetic Properties

1 Do not use a calculator for these two problems. Multiply the numbers from left to right.

a 3 × 5 × 7 × 2 = b 5 × 2 × 3 × 7 =

2 In which order was the multiplication above easier? Why?

3a Here are three different ways to add the numbers 97, 48, 3, and 2. Circle the way that seems easiest and explain why it seems easiest to you.

97 + 48 + 3 + 2 48 + 3 + 97 + 2 97 + 3 + 48 + 2

b Now add the four numbers and record the answer.


Home Connections



4 Alonya had 48 stamps in her stamp collection. Then she got 12 more stamps. Which of the following shows a way to find how many stamps Alonya has now?

Divide 48 by 12. Subtract 12 from 48. Multiply 48 by 12. Add 12 to 48.

5 Corrina was planting seeds to grow green beans. She had 36 seeds altogether. She planted 12 on Saturday and decid-ed to plant the rest on Sunday. Which expression could you use to find out how many seeds she had left to plant on Sunday?

36 ÷ 12 36 – 12 36 + 12 36 × 12

6 Domingo baked 60 cookies for the bake sale. He ate 2 cookies and gave his sister 2 cookies. Then he put the cookies in bags of 7 to sell at the bake sale. Which expression below would you use to find out how many bags of cookies Domingo filled?

(60 – (2 + 2)) – 7 (60 – (2 + 2)) ÷ 7 (60 + 2 + 2) ÷ 7 (60 ÷ 7) – (2 + 2)

CHALLENGE

7 Ramona was having a birthday par-ty. She got candy to put in her guests’ party favor bags. She had 72 pieces of candy altogether. Before she could put the candy in the bags, each of her 3 brothers took 4 pieces. Then she divid-ed what was left among the ten party favor bags. Write a single math expres-sion to show how you could figure out how many pieces of candy went in each bag.

8 Write a story problem to match the following expression.

(56 ÷ 7) + (42 ÷ 7)

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NOTE TO FAMILIES

We have been working on order of operations in class. The order of operations is a set of rules telling us what to do first when a problem has more than one operation. (Addition, subtraction, multiplication, and division are all operations.) These are the rules: • Do anything inside parentheses first. • Then do the multiplication or division from left to right. • Then do the addition or subtraction from left to right. Here is how the order of operations works for this problem: (8 + 3) × 3 – 1

1. First add 8 + 3 inside the parentheses: (8 + 3) × 3 – 1 = 11 × 3 – 1

2. Then multiply 11 × 3 because multiplication goes before subtraction: 11 × 3 – 1 = 33 – 1

3. Now subtract: 33 – 1 = 32 If you want to see why the order of operations is important, try doing the operations in another order. We need the order of operations so that we always arrive at the same answer.

Taking Orders

1 You can put parentheses in a problem to show what to do first. See how many different answers you can find for 12 + 2 × 4 – 1 by putting the parentheses in different places. Each time, write 12 + 2 × 4 – 1 with parentheses to show how you got the answer.

example (12 + 2) × (4 – 1) = 42

I found ______ different answers for 12 + 2 × 4 – 1.




Home Connections


c (32 + 48 ÷ 6 × 2) ÷ 12 + 17

d (25 + (5 + 49 ÷ (3 + 4)) – 5) ÷ 4

a (7 × 8 ÷ 2 + 2) ÷ (2 × 5)

b 37 + 12 ÷ 4 – 15


2 Below are three different answers for 8 + 3 × 6 ÷ 2. Add parentheses to make each equation true.

a 8 + 3 × 6 ÷ 2 = 33 b 8 + 3 × 6 ÷ 2 = 13 c 8 + 3 × 6 ÷ 2 = 17

3a Ask up to four family members or friends to find the answer to each of these problems:

12 + 2 × 4 – 1 8 + 3 × 6 ÷ 2

b Record their answers in the table below.

c Write the correct answers using the order of operations at the bottom of the table.

Name of Person 12 + 2 × 4 – 1 8 + 3 × 6 ÷ 2

Using Correct Order of Operations

4 Use what you know about the order of operations to evaluate (find the answers to) the expressions below.


Home Connections



CHALLENGE

5 Write your own expression. Use at least one set of parentheses to ensure an operation is done earlier than it would be otherwise. Also make sure that your answer turns out to be a whole number.

Home Connections


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Tile Sequences

1 What do you notice about the first three arrangements in the tile sequence above?

2 Sketch the 4th and 5th arrangements in this sequence.

3 How many tile would be in the 10th arrangement in this sequence? Use num-bers, words, or labeled sketches to explain how you got your answer.

It would take ________ tile to build the 10th arrangement in the sequence.

4 What do you have to do to figure out how many tile are in any arrangement (or the nth arrangement) in this sequence? You can write an expression using n or explain your thinking in words. Draw a labeled sketch that shows how you ar-rived at your answer.

Arrangement 1 Arrangement 2 Arrangement 3



Home Connections



Note The white squares in the middle of each arrangement do not count as tile.

5 What do you notice about the first three arrangements in the tile sequence above?

6 How many tile would be in the 10th arrangement in this sequence? Use num-bers, words, or labeled sketches to explain how you got your answer.

It would take ________ tile to build the 10th arrangement in the sequence.

7 A certain arrangement in this pattern has 52 tile. Which arrangement is it? Use numbers, words, or labeled sketches to explain how you got your answer.



NAME DATE

Home Connections



8 What do you have to do to figure out how many tile are in any arrangement (or the nth arrangement) in the sequence on the previous page? You can write an expression using n or explain your thinking in words. Draw a labeled sketch that shows how you arrived at your answer.

9 Evaluate the following expressions using what you know about order of opera-tions. Do the operations in this order: • Do anything inside parentheses first, using the order shown below.• Then do multiplication or division from left to right.• Then do addition or subtraction from left to right

a (4 + 56 ÷ 8 × 3) ÷ 5

b (11 + 72 ÷ (2 × 6) – 8) ÷ (32 ÷ 16 + 1)

c (125 ÷ (45 ÷ 9) × 4 × 6) – 33


Home Connections



CHALLENGE

10a Use each of these numbers exactly one time to write an expression equal to 9. You may go through many steps to arrive at a solution, but use what you know about order of operations to write your answer as a single expression.

60 9 3 27 2

b Find at least one more way to do it with the same numbers. Again, write your answer as just a single expression.

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Range, Mode, Median & Mean (Average)

1 Use the information below to help find the range, mode, median, and mean of the numbers 4, 4, 5, 8, and 9.

a The range is the difference between the highest and lowest values in a set of numbers.

4 4 5 8 9

range: 9 – 4 = _____

b The mode is the value that shows up the most in a set of numbers.

4 4 5 8 9

mode: _____


c The median is the middle value in a set of numbers.

4 4 5 8 9

median: _____

d The mean or the average is the value you get when you level off all the num-bers in a set.

mean (average): _____

Home Connections



2a Display the following set of numbers on the grid: 2, 2, 3, 9, 14.

b What is the range of that set of numbers?

c What is the mode of that set of numbers?

d What is the median in that set of numbers?


e What is the mean (average) of that set of numbers?

f Explain how you figured out the mean (average) of those numbers.

NAME DATE

Home Connections


b What is the range of that set of numbers?

c What is the mode of that set of numbers?

d What is the median in that set of numbers?

e What is the mean (average) of that set of numbers?

f Explain how you figured out the mean (average) of those numbers.


3a Display the following set of numbers on the grid: 1, 2, 3, 5, 7, 7, 10.


Home Connections


CHALLENGE

4 Wesley scored 14 points on his first math test. He wants to score enough points on his next math test to have an average of 21 points. How many points will he need to score on his next math test to have an average of 21 points? Use numbers, words, and/or a labeled sketch to show your work. Don’t forget to include the answer!

5a Five numbers have an average of 11. Three of those numbers are 5, 6, and 9. What could the other two numbers be?

b If the range of the set of numbers is 13, what must the other two numbers be?


NAME DATE

Home Connections




Home Averaging

1 Collect at least 5 numbers from objects at home to create a data set. Here are some ideas: the heights of at least 5 different cans of food, the number of boxes of food on at least 5 different shelves, the number of pictures or posters in at least 5 different rooms, the number of chairs in at least 5 different rooms, the number of books on at least 5 different shelves, or the heights of at least 5 different tables. Make sure the numbers relate to each other in some way.

2 When you have collected the numbers for the data set, list them in order from smallest to greatest below.

3 Explain how you collected your numbers. What are they about?

4 Find the range, mode, median, and mean of the numbers you collected.

a range ______ b mode ______ c median ______ d mean ______


Home Connections


5 Now make a display of the numbers in your set. You can display them on the grid below or make your display on another sheet of paper and attach it to this assignment.


4 6 7 8 8 11 14

14 – 4 = 10

4 6 7 8 8 11 13

4 6 7 8 11 11 13

2 7 7 8 6 6 6 6

Words to RememberRange: the difference between the highest and lowest number in a data set

Mode: the number that appears most often in a set of numbers. In any data set, there may be one mode, more than one mode, or no mode.

Median: the middle number when the numbers in a data set are arranged from lowest to highest

Mean: the number you get when you level off or even out all the numbers in a data set. The mean is also called the average.

name date


HomeConnectionsFor use after Unit Two, Session 1.

HomeConnection11HWorksheet

estimatingLengthinmetricUnits

1 Here is a quote from the book we read in class today, Millions to Measure, by David Schwartz:

“Many people believe that the United States will eventually join the rest of the world and measure only in the metric system.”

Do you think this is a good idea or not? Please explain your answer.

2 This chart shows some of the metric units people use to measure length. Use the information to help with the problems on the next page.

metricUnit abbreviation equivalencies Benchmark

millimeter mm –––––––– A dime is about 1 millimeter thick.

centimeter cm 10 millimeters Your little finger is about 1 centimeter wide.

decimeter dm 10 centimetersA new crayon is about 1 decimeter long.

meter m 100 centimetersThe distance from the floor to a doorknob is about a meter.

kilometer km 1000 meters3 times around a football field is about a kilometer.


Home Connections



2a Find 5 things at home that are more than a decimeter long. List them below and estimate the length of each in decimeters.

Item Approximate Length in Decimeters

b Find at least 4 things at home that are about 1 meter long, wide, or high. List them below.

3 In Millions to Measure, David Schwartz says that a flea is about 1 millimeter tall.

1 centimeter = 10 millimeters

close-up of a flea

a What else could you measure in millimeters? List at least 5 ideas below.


NAME DATE

Home Connections


3b Complete this table of equivalent centimeter and millimeter measurements.

1 cm 2 cm 3 cm 4 cm 10 cm 30 cm 100 cm 1,000 cm

10 mm 50 mm 500 mm

4 Cut out the centimeter ruler on page 33. Use it to draw four different rect-angles that each have a perimeter of 24 cm. Then find the area of each rectangle. You can use the back of this page if you need more room.

Words to RememberPerimeter: the total distance around a shape.

Area: the total number of squre units it takes to cover a shape.


3 cm

3 cm

2 cm 2 cm A = 2 × 3 = 6 square cm

3 cm

3 cm

2 cm 2 cm P = 2 + 3 + 2 + 3 = 10 cm

Home Connections



CHALLENGE

5 Use the centimeter ruler to draw some more rectangles with a perimeter of 24. This time, make sure the sides of the rectangles are not whole numbers. 3 and 6 are whole numbers. 3 and 6.25 are not whole numbers.2

1


Home Connections


Cut out this centimeter ruler and use it for problems 4 and 5 on pages 31 and 32.

centimeters81 2 3 4 5 6 7 9 10 11 12 13 14 15


Home Connections


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Home Connections For use after Unit Two, Session 3.

Home Connection 12 H Activity

NOTE TO FAMILIES

We are studying double-digit multiplication in class. One way to solve a problem like 24 × 37 is to think of it as 4 smaller multiplication problems: 20 × 30, 20 × 7, 4 × 30, and 4 × 7. When you break it down this way, you can see that it helps to be able to multiply single and double-digit numbers by 10 and multiples of 10, like 20, 30, and 40. Multiplication Four in a Row and the related worksheet will help stu-dents practice this skill.


You’ll need a partner and 2 small markers, such as paperclips or pennies, to play this game.

Instructions for Multiplication Four in a Row

1 Play Rock, Paper, Scissors or flip a coin to decide who will go first.

2 Put the markers on top of 2 of the multipliers in the row above the game grid. You can choose 2 different multi-pliers, like 20 and 40, or put the mark-ers on the same multiplier, like 30 and 30. Then multiply the 2 numbers and write an x over the answer on the grid.

Home Connections

Bridges in Mathematics � � 45© The Math Learning Center PRE-PUBLICATION DRAFT

Home Connection 12 Activity (cont.)

NAME DATE

Multiplication Four in a Row Record Sheet

Multipliers

10 20 30 40 50 60 70 80 90

Game Grid

100 200 300 400 500 600

700 800 900 1,000 1,200 1,400

1,500 1,600 1,800 2,000 2,100 2,400

2,500 2,700 2,800 3,000 3,200 3,500

3,600 4,000 4,200 4,500 4,800 4,900

5,400 5,600 6,300 6,400 7,200 8,100

Okay, I put the 2 paperclips on 30 and 40. If you multiply those 2 numbers, you get 1,200 so I’ll write an X on that number.

3 The next player moves one of the markers to a different multiplier in the row. Multiply the 2 numbers and circle the answer on the grid.

Home Connections

Bridges in Mathematics � � 45© The Math Learning Center PRE-PUBLICATION DRAFT


NAME DATE


Multipliers

10 20 30 40 50 60 70 80 90

Game Grid

100 200 300 400 500 600

700 800 900 1,000 1,200 1,400

1,500 1,600 1,800 2,000 2,100 2,400

2,500 2,700 2,800 3,000 3,200 3,500

3,600 4,000 4,200 4,500 4,800 4,900

5,400 5,600 6,300 6,400 7,200 8,100

Mom I can only move one of the paperclips. I think I’ll leave the one that’s on 30 and move the other to the 20. 20 x 30 is 600, so I’ll circle that on the grid.

Sam I bet you did that to block me from capturing the numbers on that diagonal!

Home Connections


4 Take turns back and forth. You can only move one marker each time. Continue to play until one partner has captured 4 squares in a row (horizon-tally, vertically, or diagonally).



Home Connections



NAME DATE


Multipliers

10 20 30 40 50 60 70 80 90

Game Grid

100 200 300 400 500 600

700 800 900 1,000 1,200 1,400

1,500 1,600 1,800 2,000 2,100 2,400

2,500 2,700 2,800 3,000 3,200 3,500

3,600 4,000 4,200 4,500 4,800 4,900

5,400 5,600 6,300 6,400 7,200 8,100


NAME DATE

Home Connections



1 Choose 10 different products from the Multiplication Four in a Row grid. Then write 1 or 2 different combinations for each product using only the numbers in the row above the grid.

Product Combination 1 Combination 2

example 1,800 20 × 90 30 × 60

2 Kamala says that 40 × 60 is just like 4 × 6 except that it’s 100 times bigger. Do you agree with her or not? Please explain your answer.


NAME DATE

Home Connections


3 Solve the following problems. Draw a sketch on the base ten grid at the bottom of the page if you need to.

a 10 × 15 b 20 × 15 c 20 × 25

d 10 × 30 e 12 × 30 f 20 × 30

g 10 × 18 h 20 × 18 i 10 × 37



Home Connections


CHALLENGE

4 Write one of these 9 numbers in each blank to make the three multiplication equa-tions true. You can only use each number once, and you have to use all 9 of them.

10 20 30 40 50 60 70 80 90

a ____ × ____ × ____ = 72,000

b ____ × ____ × ____ = 40,000

c ____ × ____ × ____ = 126,000


NAME DATE


a b

15 × 15 = 17 × 13 =


NOTE TO FAMILIES

One way to think of a multiplication problem like 13 × 15 is to picture it in the form of a rectangle. We have been doing this a lot in class recently. When you do this, the two numbers you’re multiplying are the dimensions of the rectangle, and the area of the rectangle is the answer. The advantage of looking at it this way is that you can actually see the pieces or “partial products” that make up the total. This Home Connection provides more practice using this area model to solve double-digit multiplication problems.

Example: 10 + 5

100 + 50 + 30 + 15 = 195

13 × 15 = 195

10

+

3

100

30

50

15

Multiplication Sketches

1 Fill in and label these sketches to solve the multiplication problems. Below each sketch, write an equation to show how you found the total area and fill in the answer to the multiplication problem.



Home Connections



2 Make a labeled sketch to solve each multiplication problem below. For each one, write an equation to show how you got the total and fill in the answer to the multiplication problem.


c

24 × 27 =

a b

14 × 16 = 13 × 18 =

NAME DATE

Home Connections


3 Sometimes you can break a rectangle into two or three partial products, in-stead of four, to solve a multiplication problem. Here are two examples.

10 + 5

150 + 30 + 15 = 195

13 × 15 = 195

10

+

3

150

30 15

10 + 5

150 + 45 = 195

13 × 15 = 195

10

+

3

150

45

Solve the problems below by sketching an array and breaking it into fewer than four partial products. You can use four partial products, though, if you need to. For each one, write an equation to show how you got the total and fill in the an-swer to the multiplication problem.

b

14 × 22 =



a

12 × 17 =

Home Connections


4 Multiply each number in the top row by the number at the left. The first one is done for you as an example.

× 2 4 8 3 6 12 5 10 7 9

10 20

× 2 4 8 3 6 12 5 10 7 9

3

× 2 4 8 3 6 12 5 10 7 9

13

5 Mara says you can use the answers in the first 2 rows of Problem 4 to help figure out the answers in the third row. Do you agree with her? Why or why not?

CHALLENGE

6 Manny has 24 feet of fencing and wants to make the biggest possible rectangu-lar pen for his rabbit to live in outside. What length should he make each side of the pen? Use numbers, words, and/or labeled sketches to solve this problem and show your work.


NAME DATE




Coins & Quick Sketches

Here is an array of quarters.

1 What is the total amount of money in this array? Use numbers, words, and/or labeled sketches to explain your answer.

2 Use the array to help solve these multiplication problems.


a 4 × 25 = _______

b 6 × 25 = _______

c 8 × 25 = _______

d 10 × 25 = _______

e 12 × 25 = _______

f 14 × 25 = _______

3 Rosie says she can solve 24 × 25 using the information above. Do you agree with her? Why or why not?

Home Connections




4 Use what you know about adding and multiplying money to help solve the multiplication problems below.

example 25 I know there are four 25’s in 100 (four quarters in a dollar). × 36 36 is equal to 9 groups of 4. So, 36 × 25 is like 9 × 100. _____ 900

a 25 b 25 c 25 d 25 × 24 × 32 × 40 × 34 _____ _____ _____ _____

e 50 f 50 g 50 h 50 × 2 × 16 × 24 × 32 _____ _____ _____ _____

i 50 j 50 k 75 l 75 × 33 × 17 × 2 × 16 _____ _____ _____ _____

NAME DATE

Home Connections



5 Label the dimensions of each rectangle below and make a quick sketch to find the area. Write an equation to show how you got the total, and then write a multi-plication equation to match your sketch.

Labeled Quick SketchEquation to Find

TotalMultiplication Equation

example

a

b


10 + 10 + 4

10+3

100

30

100

30

40

12

100100403030

+ 12312

13 x 24 = 312

Home Connections



6 Multiply each number in the top row by the number at left. The first one is done for you as an example.

× 2 4 8 3 6 12 5 10 7 9

30 60

× 2 4 8 3 6 12 5 10 7 9

6

× 2 4 8 3 6 12 5 10 7 9

36

CHALLENGE

7 Mr. Mugwump wants to buy a cape for the costume party on October 13th. The cape costs $26.00. He puts 1 cent in the bank on October 1st, 2 cents in the bank on October 2nd, 4 cents on October 3rd, and 8 cents in the bank on October 4th. He continues doubling the amount of money he saves each day until October 13. How much money will he have, counting the money he saves on the 13th? Will it be enough to buy the cape on October 13th?

Use numbers, words, and/or labeled sketches to solve this problem. Show all of your work. You can work on the back of this page if you like.

NAME DATE




Looking for Metric Measures at Home

In his book, Millions to Measure, David Schwartz writes, “Even though the metric system has not been adopted by people in the United States, many Americans use it every day.” Today’s Home Connection will give you a chance to check this out for yourself.

Containers that hold liquids like juice, soda pop, shampoo, or liquid soap may be labeled in milliliters or liters. These are metric units of volume.

Metric Unit Abbreviation Equivalencies Benchmark

milliliter mL or ml –––––––– A milliliter of water is about 10 drops.

liter L or l 1,000 millilitersA liter bottle of water holds just a little more than a quart.

Cans and packages of food may be labeled in grams or even kilograms if they are very heavy. These are metric units of mass, which is similar to weight.

Metric Unit Abbreviation Equivalencies Benchmark

gram g –––––––– A dollar bill has a mass of about 1 gram.

kilogram kg 1,000 gramsAn adult cat might weigh about 3 1/2 kilograms.


Home Connections



1 Find 4 containers at home that hold liquids and are labeled in milliliters or liters. Try looking in your kitchen, bathroom, and garage. List them by name and tell how much they hold in metric units according to their labels.

Item Volume (in Metric Units)

example mouthwash bottle 530 milliliters

2 Find 6 cans or packages of food or other solid materials that are labeled in grams or kilograms. List them by name and tell how much they weigh in metric units according to their labels.

Item Weight or Mass (in Metric Units)

example can of pineapple chunks 567 grams


NAME DATE

Home Connections


3 After the race in Millions to Measure, the snail will be able to quench his thirst with 1 milliliter of water. How many milliliters of water do you think it would take to quench your thirst after a big race? Explain your answer.

4 In Millions to Measure, Sandro and Robert ask to become Olympic wrestlers. When Marvelosissimo grants their wish, they each weigh 118 kilograms. How many grams do the 2 boys weigh altogether? Show your work.

5a The members of Jahara’s soccer team drank a case of 24 bottles of water dur-ing the tournament. Each bottle had 500 ml of water. How many milliliters of water did they drink?

b How many liters of water did they drink?



Home Connections



6 There will be 24 people altogether at George’s birthday party. He wants to serve his grandmother’s special fruit punch. His grandmother lives in England, where they use metric measurements in cooking. This is her recipe.

Grandmother’s Fruit Punch—Serves 10

400 ml pineapple juice 300 ml papaya juice 600 ml orange juice

George can buy papaya juice in 356 ml bottles. How many bottles of papaya juice should he buy to make enough punch to serve all 24 people?

CHALLENGE

7 The snail in Millions to Measure has a mass of 8 grams. This snail has 124 friends and all of them have the same mass as he does. What is their total mass in grams? What is their total mass in kilograms? Show your work.

NAME DATE

Home Connections



Multiplication Interview

You will need an adult to help you do the first page of this assignment.

1 Ask an adult to solve the two multiplication problems below the way he or she learned when he or she went to school. Watch carefully and ask the adult to ex-plain each step. 34 34 × 6 × 26 ____ ____

2 Work the problems below, using the same method the adult just showed you. If you didn’t understand it when he or she showed you the first time, ask the adult to work with you until you can do it on your own. If you’re already familiar with the method, work these on your own, and then write and solve 3 more that seem challenging to you.

32 32 32 32 × 8 × 18 × 28 × 38 ____ ____ ____ ____

43 43 43 43 × 7 × 27 × 37 × 47 ____ ____ ____ ____

Three challenging multiplication problems I’ve written and solved:



Home Connections



3 Most 10- to 13-year-olds need 10 hours of sleep each night, while 9 hours is enough for others. Most adults need 8 hours of sleep each night. Use any method you choose except a calculator to figure out how much sleep you’d get in a week, a 30-day month, and a year if you slept 10, 9, or 8 hours a night. Enter your an-swers on the chart, and use the space below the chart to show your work. The three spaces at the bottom of the chart are for problem 4.

Hours of Sleep

per night per week per 30-day month per year

a 10

b 9

c 8

def

CHALLENGE

4 Choose 1 to 3 animals from the list below. Add them to the chart above and find how many hours of sleep they get in a week, a 30-day month, and in a year.

How many hours per day (or night) some animals sleep:

animal hours slept animal hours slept

brown bat 20 ferret 14 1

python 18 gerbil 13

human infant 16 cat 12

tiger 16 dog 10 1

guppy 7 elephant 4

horse 3 giraffe 2

2

2

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NOTE TO FAMILIES

Over the past two weeks, we have been using many different strategies to multiply larger numbers, some of which are shown below. In this homework assignment, students should try to use more than one of these strategies, but they should always do what makes the most sense to them. Students may have their own variations on the strategies and may write them in different ways than those shown below.

Multiplication Strategies

Review the multiplication strategies on this page. Then solve the problems on the following pages. Use a few of these strategies to solve the problems. Choose the strategies you use based on what makes the most sense for the numbers in the problem. Don’t use a strategy unless it makes sense to you.

Use a Basic Fact Strategy

Strategies for the basic facts can be used with larger numbers too.

example Use the half-decade strategy to multiply by 5. 86 × 5 = (86 × 10) ÷ 2 = 860 ÷ 2 = 430

Break One of the Numbers into Parts and Then Multiply and Add

Especially when the digits are small, you can break one of the numbers into tens and ones, multiply by the other number, and add the two products.

example 21 × 32 = 21 × 30 + 21 × 2 = 630 + 42 = 672

Use a Sketch of the Area Model (a Rectangular Array)

You can make a quick sketch of an array to show the multiplication problem and then solve it. You can divide the array into as many parts as you like to compute the total product.

example

27×14

2007080

+ 28378

20 7

10 × 20 = 200 10 × 7 = 70

4 × 20 = 80 4 × 7 = 28

10

4



Home Connections


10×27 = 270

4×27 = 108

20 7

10

4

270+ 108

378

Use an Algorithm

An algorithm is a step-by-step procedure for solving a problem. Algorithms can be the most sensible way to solve some problems, especially when the numbers are very large. We have talked about the two algorithms shown below in class. In the one at left, all the multiplication is done before the addition. In the one at right, we alternate between multiplying and adding.

example 27 27 × 24 × 24 _____ _____ 20 × 20 = 400 108 20 × 7 = 140 + 540 _____ 4 × 20 = 80 648 4 × 7 = + 28 _____ 648

Use any of the strategies on the previous page, or a strategy of your own, to solve the following problems. Do what makes the best sense to you, but try not to use just one strategy the whole time. Please show all of your work.

1 33 2 22 × 12 × 8 _____ _____


2 1


NAME DATE

Home Connections


3 42 4 26 × 21 × 17 _____ _____

5 42 6 69 × 15 × 11 _____ _____


Home Connections



7 132 8 35 × 31 × 24 _____ _____

9 142 10 4583 × 16 × 271 _____ ______

NAME DATE




Agree or Disagree?

Choose 5 of the 6 problems on this page and the next. For each one you choose, write whether you agree or disagree. Then explain your thinking using numbers, words, and/or labeled sketches.

Do you agree or disagree? Explain your thinking.

1 The 5th graders set up 20 rows of chairs with 25 chairs in each row for the assembly. Mrs. Lord asked if they’d set up enough chairs for all 552 students. Kamil said he could skip count to find out how many chairs there were in all, and then they’d know if they had enough.

2 The track at the high school is 400 meters. After she ran 6 times around the track, Isuko said she’d gone more than 2 kilo-meters.

3 Mr. Madison needs 175 granola bars for the 5th grade field trip. The bars come in boxes of 10. He’ll need to buy 17 boxes to have enough.


Home Connections



Do you agree or disagree? Explain your thinking.

4 To multiply 247 × 4 you can do these smaller problems and add them together:

200 × 4

4 × 4

7 × 4

5 Mrs. Gonzalez ordered four super-size pizzas for $9.97 each. If she gives the delivery person two $20 bills, she’ll get some change back.

6 There are 46 kids in the After-School Club. Today they’re go-ing to the pool at the Community Center. If each mini-van can take 6 kids, they’ll need 8 mini-vans for all the kids.


NAME DATE

Home Connections



Remember that the perimeter of a figure is the total distance around it and that area is the total number of square units it takes to cover a shape.

Perimeter the total distance around a shape.

3 cm

3 cm

2 cm2 cm

P = 2 + 3 + 2 + 3 = 10cm

Area the total number of square units it takes to cover a shape.

3 cm

3 cm

2 cm2 cm

A = 2 × 3 = 6 sq. cm

Find the area and perimeter of the figures below. Be sure to include the units.

7 8 m

13 m

Perimeter ________________

Area ________________

8 17 cm

17 cm

Perimeter ________________

Area ________________


Home Connections


CHALLENGE

9

12 in.

3 in.6 in.

6 in.

Perimeter ________________

Area ________________

10

10 ft.

10 ft.

4 ft.

2 ft.

2 ft.

3 ft.

Perimeter ________________

Area ________________


NAME DATE




NOTE TO FAMILIES

One way to solve a long division problem is to picture it in the form of a rectangle. When you do this, the number you’re dividing by is one of the dimensions and the number being divided is the area of the rectangle. Quotients Win will help students practice using this strategy to sketch and solve such problems as 150 ÷ 10 and 220 ÷ 22. Your fifth grader can show you how to make the sketches, and there is an example below for your reference. There are two record sheets so you can play the game twice. This Home Connection includes a second division game, Go for Zero, if you and your fifth grader want to play a more challenging game.

You’ll need 2 pencils, colored pencils or markers in 2 different colors, and a paperclip. Use your pencil and the paperclip as a spinner as shown to the right. If you want to play the second game, Go for Zero, you’ll need a calculator, pencils, and the 2 spinners on page 65.

Instructions for Quotients Win


1 Take turns spinning the spinner one time each. The player with the higher number gets to pick his or her color marker or colored pencil and go first.

2 Spin the spinner to see which prob-lem on the game sheet you will solve.

3 Make a labeled sketch of the prob-lem on the game sheet and fill in the answer. Be sure to use your colored pencil or marker to sketch the dimen-sions and a regular pencil for the rest of the work. You can build a model with your base ten pieces first, but you don’t have to.

Home Connections


Quotients Win Game Sheet 2Player 1 _________________ Color _________ Player 2 _________________ Color _________

1

280 ÷ 10 = ______

2

190 ÷ 19 = ______

3

300 ÷ 20 = ______

4

400 ÷ 20 = ______

5

160 ÷ 10 = ______

6

220 ÷ 20 = ______

Player 1’s Score _____________________ Player 2’s Score _____________________

100 60

16

Theo I spun a 5, so I have to do problem 5 on the game sheet. That’s 160 ÷ 10. First I’ll show 10 on the side and then start filling in the array until I get to 160. My rectangle turned out to be 16 along the other side, so that’s the answer.

4 Take turns spinning and solving problems until you have each gone 3 times. If you spin the number of a problem that has already been solved, spin again until you get the number of a problem that has not been solved yet.

Home Connections



4 (cont.) (You have to use the first number that has not been solved.) When it’s the other player’s turn, be sure to watch, help, and double-check his or her work.

5 At the end of the game, add your quotients and record your score at the bottom of the sheet. The player with the higher score wins.

CHALLENGE

Instructions for Go for Zero

1 Take turns spinning the spinner once. The person with the higher number goes first.

2 Choose any 3-digit number that is less than or equal to 900. Enter it into the calculator and then give the calcu-lator to your partner.

3 Player 2 uses the calculator to re-duce the number to 0 by adding, sub-tracting, multiplying, or dividing by single-digit numbers other than zero. You can make as many as 5 calculations (but no more) to get the original num-ber down to zero. Do your work on the calculator, but record each move on the record sheet.


4 Play back and forth until you have each had 3 turns. Then count up the total number of calculations you made and use the more or less spinner to determine the winner. If the spinner lands on “more,” the player who made more calculations wins. If the spinner lands on “less,” the player who made fewer calculations wins.

example

Player 1 chooses 334.

Player 2: • divides 334 by 2 to get 167 (calcula-tion 1) • subtracts 7 from 167 to get 160 (cal-culation 2) • divides 160 by 8 to get 20 (calculation 3) • divides 20 by 4 to get 5 (calculation 4) • subtracts 5 from 5 to get 0 (calcula-tion 5)

Starting Number (Chosen by Player 1) 334

Calculation 1 334 ÷ 2 = 167

Calculation 2 167 – 7 = 160



Calculation 5 5 – 5 = 0

NAME DATE

Home Connections



Game Spinners

Rip this page carefully out of your book to play Quotients Win and/or Go for Zero.

Use this spinner for Quotients Win and also to decide which player starts first in Go for Zero.

Use this spinner to determine the winner in Go for Zero.

1

25

3

6

4


Home Connections


NAME DATE

Home Connections



Quotients Win Game Sheet 1

Player 1 _________________ Color _________ Player 2 _________________ Color _________

1

120 ÷ 12 = ______

2

230 ÷ 10 = ______

3

180 ÷ 18 = ______

4

240 ÷ 10 = ______

5

110 ÷ 10 = ______

6

150 ÷ 15 = ______

Player 1’s Score _____________________ Player 2’s Score _____________________(Continued on back.)

Home Connections



Quotients Win Game Sheet 2Player 1 _________________ Color _________ Player 2 _________________ Color _________

1

280 ÷ 10 = ______

2

190 ÷ 19 = ______

3

300 ÷ 20 = ______

4

400 ÷ 20 = ______

5

160 ÷ 10 = ______

6

220 ÷ 20 = ______

Player 1’s Score _____________________ Player 2’s Score _____________________



Player 1 __________________________________________ Player 2 __________________________________________

Round 1

Starting Number (Chosen by Player 1) Starting Number (Chosen by Player 2)

Calculation 1 Calculation 1





Round 2







Round 3







Total number of calculations made by player 1 ______

Total number of calculations made by player 2 ______

The winner of this game is ________________________



Go for Zero Record Sheet

NAME DATE

Home Connections


NAME DATE




Area & Perimeter

Perimeter is the distance all the way around the rectangle. It is measured in linear units (centimeters, in this case).

Area is the number of square centimeters it takes to cover the shape.

Measure and then label the length and width of each rectangle in centimeters. If you don’t have a centimeter ruler at home, cut out the one on page 73 and use it instead. Find the area and perimeter of each rectangle using the most efficient method you can. Show your work.

example

1


2 cm

4 cm Perimeter = 12 cm

Work: 2 + 2 + 4 + 4 = 12 cm

Area = 8 sq. cm

Work: 2 × 4 = 8 sq. cm


2

3


Home Connections

Home Connection 20 Worksheet (continued)



centimeters81 2 3 4 5 6 7 9 10 11 12 13 14 15

Home Connections


Home Connections


NAME DATE

Home Connections



4 Ali made a card for her grandma. The card has a perimeter of 20 inches and an area of 24 square inches. Which of these is a picture of Ali’s card? Fill in the bubble to show, and then explain your choice.

I chose rectangle ______ because

CHALLENGE

5 Micah’s garden is 6 feet wide and 12 feet long. He wants to use the whole gar-den for roses. If each rose bush needs exactly 9 square feet of space, how many rose bushes can he plant? Show all your work. Please also make a labeled sketch to show the solution.

2"

12"

6"8"

cba

4" 3"

Home Connections


NAME DATE




Unit Review

1 Alexis is going to measure the distance from her classroom to the school office. Fill in one of the bubbles to show which unit of measure would work best for the job.

millimeters centimeters meters kilometers

2 How much does Maria’s new puppy weigh? Fill in the bubble below that makes the most sense.

1 gram 10 grams 3 kilograms 100 kilograms

3 Hugh is looking for a container that will hold about 1 liter of water. Fill in the bubble below to show which would be the best choice.

a coffee cup a water bottle a bathtub a swimming pool

4 Write the answer to each of these combinations. 12 15 30 50 40 50 × 10 × 10 × 20 × 20 × 40 × 60 ____ ____ ____ ____ ____ ____

5 The pet store just got 42 tropical fish. They want to put 9 fish in each tank. How many tanks will they need? Use numbers, words, and/or labeled sketches to solve the problem. Show your work.


Home Connections



6 Choose one multiplication problem below and circle it. Pick the one that seems best for you—not too hard and not too easy.

13 14 24 25 28 × 13 × 12 × 23 × 26 × 28 ____ ____ ____ ____ ____

a Write a story problem to match the multiplication problem you just circled.

b Solve the problem below. Show all of your work.


NAME DATE

Home Connections



7 Choose one division problem below and circle it. Pick the one that seems best for you—not too hard and not too easy. 180 ÷ 10 220 ÷ 20 440 ÷ 22 520 ÷ 26

a Write a story problem to match the division problem you just circled.

b Make a labeled sketch on the grid below to show the problem you chose.

c Find the answer to the problem you chose using your sketch. Show all of your work.


Home Connections



CHALLENGE

8 The Chocolate Factory packs their chocolate bars in boxes of 5 or boxes of 12. What is the smallest number of full boxes they would need to pack exactly 2005 chocolate bars?

NAME DATE


Home Connections For use after Unit Three, Session 2.


Shape Puzzles

1 Use a ruler and a pencil to divide each polygon below into 2 congruent figures. Remember that congruent figures have to be exactly the same shape and the same size. You may not always be able to use a single line segment, and there is more than one way to do it for some of these shapes. One of the figures can’t be divided into 2 congruent shapes. Can you find out which one it is?

CHALLENGE

2 Label each polygon with its name. The first one is done as an example.(Continued on back.)

Triangle

Home Connections


3 See how many different ways you can divide the hexagon on the geoboard below into 2, 3, 4, or more congruent shapes. (Remember that a hexagon is any closed figure that has 6 sides.) Record below all the different ways you can find to divide this shape into congruent parts. What is the greatest number of congruent parts you can break it into?

number of congruent number of congruent number of congruent parts ________ parts ________ parts ________




NAME DATE




Areas of Geoboard Figures

1 Find and record the area of each figure on this page and the next. Be sure to show your work. Each small square on the geoboard is 1 square unit.

11

1 1

1 2

example ______ square units a ______ square units b ______ square units

c ______ square units d ______ square units e ______ square units

f ______ square units g ______ square units h ______ square units(Continued on back.)



example ______ square units i ______ square units j ______ square units

This triangle is half of a bigger rectangle. The area of the rectangle is 6, so the area of the triangle must be 3.

k ______ square units l ______ square units m ______ square units

Home Connections

3


NAME DATE


2 This star is an example of a decagon, a shape with 10 sides. In two stars, there are 20 sides altogether.

a In 5 stars, there are _____ sides altogether.

b Fill in the missing numbers on this chart about stars and sides.

Number of Stars 10 12 16 25 33 43 100

Number of Sides 100 210 370 1,500

CHALLENGE

3 Draw a decagon (a 10-sided polygon) that is not a star.


Home Connections

Home Connections


NAME DATE




Thinking about Quadrilaterals

1a Study the diagram above and then circle the quadrilaterals in the row of shapes below:

b How do you know that the shapes you circled are quadrilaterals?

c Draw 2 examples of quadrilaterals.

d Draw 2 examples of shapes that are not quadrilaterals.

Quadrilaterals Not Quadrilaterals


Home Connections


2 There are several different types of quadrilaterals. Study the descriptions be-low and draw a line from each to the picture that matches it best. There are pic-ture definitions for the words in italics at the bottom of the page.

Trapezoid a quadrilateral with exactly 1 pair of parallel sides

Parallelogram a quadrilateral with 2 pairs of parallel sides

Rectangle a quadrilateral with 4 right angles

Rhombus a quadrilateral with 4 congruent sides

Square a quadrilateral with 4 congruent sides and 4 right angles

3 Roberto says that all quadrilaterals have at least 1 pair of parallel sides. Do you agree with him or not? Explain your answer.

4 Rebekkah says that a square can be called a rhombus, but a rhombus cannot be called a square. Do you agree with her or not? Explain your answer.

Parallel Not Parallel Congruent Not Congruent



NAME DATE

Home Connections


5 If you cut this cube along some of its edges, you could unfold it into a flat shape that looks like Figure A. This would be one way to see that a cube has 6 faces, and all of them are square.

If you counted all the faces on 2 cubes, you’d get 12.

a If you counted all the faces on 5 cubes, you’d get _____.

b Fill in the missing numbers on this chart about cubes and faces. Do the gray box problems in your head or on a piece of scratch paper.

Number of Cubes

10 12 16 25 32 40 75

Number of Faces

60 126 234 750

6 Choose one of the gray box problems and show how you figured it out.

CHALLENGE

7 Find one example of a quadrilateral at home that is not a square or a rectangle. Make a labeled sketch of it below or on the back of this page.


Cube Figure A

Home Connections


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Find the Angle Measure

1 The sum of the angle measures in a triangle is 180 degrees. Below are 4 trian-gles, each with a missing angle measure labeled n. For each one, choose the value of n.

2a The 4 angles marked n below are congruent and have been put together to form a straight angle. Using sketches, numbers, and words, determine the value of each angle marked n. Show your work below.

b The value of each angle marked n is _______ degrees.

60°

30°

90°

20°


a 20 degrees

30 degrees

50 degrees

60 degrees

b 10 degrees

20 degrees

30 degrees

40 degrees

c 130 degrees

140 degrees

150 degrees

160 degrees

d 30 degrees

45 degrees

50 degrees

60 degrees

70°

90°

80°


Home Connections


3a The 5 angles marked n below are congruent and have been put together to form a straight angle. Using sketches, numbers, and words, determine the value of each angle marked n. Show your work below.

b The value of each angle marked n is _______ degrees.

4 The sum of the angle measures in a convex quadrilateral is 360 degrees. Below are 2 convex quadrilaterals, each with a missing angle measure labeled n. Deter-mine the value (in degrees) of n for each convex quadrilateral.

CHALLENGE

5 Can a triangle have 2 right angles? If so, draw it; if not, explain why not.


a 80 degrees

90 degrees

100 degrees

110 degrees

b 80 degrees

100 degrees

120 degrees

140 degrees

90°

110° 70°

80°

70°80°

90°

110° 70°

80°

70°80°

NAME DATE




Protractor Practice & Clock Angles

When you measure an angle you usually have to choose between two numbers because protractors are designed to measure angles that start on either the right or left side. There are two angles to measure in each of the problems on this sheet and the next. The angle on the left-hand side is angle A. The angle on the right-hand side is angle B. Find and record the measure of both angles in each prob-lem.

1 The measure of angle A is ______ degrees.

The measure of angle B is ______ degrees.

9 0

0 180 1800

0 1 2 33 2 1

1701016020

1503014040

13050

12060

11070

10080

10 170

20 160

30 150

40140

50130

60120

70110

80100

A B



9 0

0 180 1800

0 1 2 33 2 1

1701016020

1503014040

13050

12060

11070

10080

10 170

20 160

30 150

40140

50130

60120

70110

80100

A B


Home Connections





9 0

0 180 1800

0 1 2 33 2 1

1701016020

1503014040

13050

12060

11070

10080

10 170

20 160

30 150

40140

50130

60120

70110

80100

A B



9 0

0 180 1800

0 1 2 33 2 1

1701016020

1503014040

13050

12060

11070

10080

10 170

20 160

30 150

40140

50130

60120

70110

80100

A B

5 Go back and add each pair of angle measures in Problems 1 through 4. What do you notice? Why do you think it works this way?


NAME DATE


c Draw a line from the point above the 12 to the center of the clock and a line from the center to the point be-side the 1.

Angle = ____º

Here’s how I know:

d Draw a line from the point above the 12 to the center of the clock and a line from the center to the point be-side the 4.

Angle = ____º


b Draw a line from the point above the 12 to the center of the clock and a line from the center to the point below the 6.

Angle = ____º


a Draw a line from the point above the 12 to the center of the clock and a line from the center to the point be-side the 3.

Angle = ____º


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6 Follow the directions below to construct an angle on each clock face. Use a ruler or a note-card so your lines are straight. For each one, give the measure of the angle and explain how you know it’s that many degrees. (Hint: There are 360º in a circle.)

Home Connections


NAME DATE




Reflections, Symmetry & Congruence

1 Reflect each of these shapes over the dark line in the center of the grid. Use a ruler or a straight edge to help make your lines straight.

example

original reflection

b

original reflection

a

original reflection

c

original reflection

2 What did you do to make sure that the reflections you drew are accurate?


Home Connections



3 Preston says that when you reflect a figure over a line, the reflection is always congruent to the original. Do you agree or disagree with him? Explain your answer.

4 Tasha says that this shape has 4 lines of symmetry. Do you agree or dis-agree with her? Explain your answer and be sure to draw in any lines of sym-metry you can find. (Hint: Trace the figure, cut it out, and fold it before you make your decision.)

5 Draw a design or picture that has exactly 2 lines of symmetry. Draw and label the lines of symmetry when you’re finished. (If you prefer, you can use a picture from a newspaper or magazine instead of drawing one, but it has to have exactly 2 lines of symmetry.)

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This page is meant to be blank.

NAME DATE




Area Bingo Practice

1 Cut out the 2 pages of Area Bingo Cards.

2 For each card listed below, graph the points on page 101 and connect them to form a polygon. Use a ruler so your lines are straight and label the polygon with its card letter.

When you graph points, the first number tells you how far over and the second number tells you how far up to go. To find (3,9), for example, go over 3 on the x-axis and then up 9 on the y-axis.

3 Then write the name of the polygon along with its area on the chart below. The first one is done for you as an example.

Card Polygon Name Area

Card C example Rectangle 3 square units

Card E

Card G

Card H

Card I

Card L


Home Connections



0

123456789

1011121314151617181920212223242526272829303132

2 4 6 8 10 12 14 16 18 20 22 24 26 281 3 5 7 9 11 13 15 17 19 21 23 25 27


Home Connections


NAME DATE

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Cut out the cards on this page. Put them in a small envelope or plastic sandwich bag and bring them back to school when you return this assignment.

(4,

13)

(6,

13)

(4,

15)

(6,

15)

(25,

18)

(25,

20)

(23,

20)

(15,

19)

(15,

22)

(16,

22)

(16,

19)

(18

, 14

)

(18

, 16

)

(10,

16)

(12

, 2

0)

(15,

20)

(13,

22)

(10,

22)

(10,

4)

(17,

4)

(17,

5)

(10,

5)

(2,

4)

(2,

6)

(7,

5)

(2,

14)

(3,

14)

(4,

15)

(3,

15)

HC

28

Are

a Bi

ngo

Car

d

AB

CD

EF

GH

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

Home Connections


NAME DATE

Home Connections




(22

, 18

)

(22

, 21

)

(25,

21)

(25,

18)

(20,

5)

(23,

5)

(20,

9)

(17,

9)

(21,

8)

(25,

8)

(25,

3)

(7,

12)

(6,

13)

(17,

13)

(18

, 12

)

(7,

5)

(15,

5)

(10,

8)

(2,

8)

(14,

21)

(25,

21)

(14,

25)

(10,

32)

(13,

22)

(16,

32)

(5,

20)

(8,

20)

(8,

27)

(5,

27)

IJ

KL

MN

OP

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

Home Connections


NAME DATE

Home Connections




(9,

19)

(10,

19)

(10,

32)

(9,

32)

(0,

20)

(4,

20)

(0,

28)

(17,

24)

(17,

26)

(24,

26)

(24,

24)

(2,

9)

(8,

9)

(2,

5)

(0,

28)

(8,

28)

(8,

32)

(0,

32)

(17,

27)

(19,

32)

(25,

32)

(23,

27)

(27,

1)

(28

, 1)

(28

, 32

)

(27,

32)

(20,

0)

(27,

0)

(20,

8)

QR

ST

UV

WX

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

HC

28

Are

a Bi

ngo

Car

d

Home Connections


Home Connections


This page is meant to be blank.

NAME DATE



Drawing Similar Figures

1 Graph the following points in order on the next page. Remember that the first number in each pair tells you how far to go over, and the second number tells you how far to go up. Then use a ruler or straight-edge to connect them in the same order: (1, 0), (1, 9), (3, 9), (5, 7), (7, 9), (9, 9), (9, 0), (7, 0), (7, 6), (5, 4), (3, 6), (3, 0) and back to (1, 0).

2 Describe the figure you got when you connected the points in order.


Original coordinates

Coordinates multiplied by 3

(1, 0) (3, 0)

(1, 9) (3, 27)

(3, 9) (9, 27)

(5, 7)

(7, 9)

(9, 9)

(9, 0)

(7, 0)

(7, 6)

(5, 4)

(3, 6)

(3, 0)

(1, 0)

3a Multiply each pair of coordinates by 3. Write the answers in the table below.

4a Divide each pair of coordinates by 2. Write the answers in the table below.

Original coordinates

Coordinates divided by 2

(1, 0) ( 1 2 , 0)

(1, 9) ( 1 2 , 4 1

2 )(3, 9) ( 1 1

2 , 4 1 2 )

(5, 7)

(7, 9)

(9, 9)

(9, 0)

(7, 0)

(7, 6)

(5, 4)

(3, 6)

(3, 0)

(1, 0)

b Now graph these points in order on the next page and use your ruler or straight-edge to connect them.

b Now graph these points in order on the next page and use your ruler or straight-edge to connect them.


Home Connections


0

123456789

10111213141516171819202122232425262728

2 4 6 8 10 12 14 16 18 20 22 24 26 281 3 5 7 9 11 13 15 17 19 21 23 25 27


5 Write any observations you can make about the 3 figures. How are they alike? How are they different? How do they compare to one another in size and shape?

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NAME DATE




Net Picks

A net is a 2-dimensional figure that can be cut and folded to form a 3-dimensional figure. On pages 115 and 117, you’ll find five different nets. Each one will form one of the 3-dimensional figures shown below.

RectangularPrism

TriangularPrism

HexagonalPrism

Square-BasedPyramid

Cube

1 Predict which 3-dimensional shape each net represents and record your predic-tion on the chart below.

2 Cut out each net along the heavy outline and fold it on the thin lines to form a 3-dimensional shape.

3 Use the shapes you just folded to help fill in the rest of the chart. (Write in the figures you really get when you fold each net if they’re different than your predictions.)

NetPrediction/Actual

FigureNumber of

FacesNumber of

EdgesNumber of

Vertices

a

b

c

d

e

Vertex

Face

Edge


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CHALLENGE

4 In his famous book The Phantom Tollbooth, Norton Juster invented a character with 12 different faces. He based his idea on a 3-dimensional figure known as a dodecahedron. Here’s a picture of a dodecahedron with its net.

Dodecahedron Net for a Dodecahedron

a Choose your favorite of the 5 figures you just cut out and folded. Unfold it and use crayons, colored pencils, or felt markers to turn it into some kind of charac-ter. Then fold it back up and use a little tape along the edges so it stays together.

b In the space below, write a descriptive paragraph about the character you just invented. Bring your character and your paragraph back to school to share with the class.


NAME DATE


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a

b

c

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NAME DATE

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d

e

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NAME DATE


Volume & Surface Area

The volume of a solid figure tells you how many cubes of a given size it takes to build that figure. Volume is measured in cubic units or cubes.

The surface area of a solid figure is what you get when you find the area of every surface, including the top and the bottom, and then add all the areas together. Surface area is measured in square units or squares.

This figure took 2 centimeter cubes to build, so its volume is 2 cubic cm (also written cm3). There is 1 square on the top, 1 on the bottom, and 2 more squares on each of the 4 sides, so its surface area is 10 square cm (also written cm2).

1 Find the volume and surface area of each cube building shown below and on the back of this page (building d is an optional challenge.) Use labeled sketches, numbers, and/or words to show how you got your answers for each building.

Volume = 2 cubic cm

Surface Area = 10 square cm

a

Volume = _____________

Surface Area = ____________

Explanation:

b

Volume = _____________


Explanation:


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2 Nguyen says it’s easier to find the surface area of a cube than of other kinds of rectangular solids. Do you agree or disagree with him? Explain your answer.

1c

Volume = _____________


Explanation:

CHALLENGE

d

Volume = _____________


Explanation:


NAME DATE


Home Connections For use after Unit Four, Session 2.


Estimation Interviews

Estimate the answer to each problem below (or solve it in your head) and explain your thinking. Then ask an adult to do the same. Record his or her responses on your sheet.

Signature of the adult I interviewed for this assignment:

________________________________________

1 The Carpenter family’s car can drive 24 miles on the freeway using 1 gallon of gas. The car’s tank holds 20 gallons of gas. If they fill up at a gas station outside of town and stay on the freeway, how far can they drive before the tank is empty?

Our estimates (or mental solutions) and explanations:

Student: _______________ Adult: _______________

2 The family stops for lunch at the Sandwich Station. They buy 4 sandwiches for $3.49 each, 2 salads to share for $1.49 each, and 4 yogurt smoothies for $2.59 each. If these prices include sales tax, what is their total?


Student: _______________ Adult: _______________


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3 If the Carpenters are driving at 55 miles per hour, about how long will it take them to get from Atlanta, Georgia, to Durham, North Carolina, a distance of 384 miles?


Student: _______________ Adult: _______________

4 When do people use estimation in their daily lives? What are some situations in which it’s just as good (or better) to make an estimate than to find the exact answer? Ask the adult with whom you’re working to help you think of at least 4 different examples.

NAME DATE




More Multiplication Menus

Use mental strategies instead of a calculator to solve the problems on this page and the next.

1a Write the answers to the combinations in the left column. Then use the infor-mation to help solve the combinations in the right column.

1 × 14 = _____ 3 × 14 = ______

2 × 14 = _____ 5 × 14 = _____

10 × 14 = _____ 30 × 14 = _____

20 × 14 = _____ 15 × 14 = _____

b Use the information above to solve the problem below. Use numbers and words to explain how you got your answer.

25 × 14 = _____

2a Write the answers to the combinations in the left column. Then use the in-formation to help solve the combinations in the right column.

1 × 23 = _____ 3 × 23 = _____

2 × 23 = _____ 5 × 23 = _____

10 × 23 = _____ 30 × 23 = _____

20 × 23 = _____ 15 × 23 = _____

b Use the information above to solve the problem below. Use numbers and words to explain how you got your answer.

24 × 23 = _____





1 × 32 = _____ 3 × 32 = _____

2 × 32 = _____ 5 × 32 = _____

10 × 32 = _____ 30 × 32 = _____

20 × 32 = _____ 15 × 32 = _____

b List 4 combinations you can solve using the information above. Then find the answer to each of your own problems and explain your thinking. Be creative! You can make your combinations as hard as you want, as long as you can solve them accurately and show your thinking.

Combination Explanation

example: 12 x 32 = 384 10 x 32 = 320

2 x 32 = 64

Home Connections

320+ 64384

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NOTE TO FAMILIES

We have been practicing long division at school over the past week or so. First we used sketches to help, and now we are practicing using a numerical method that probably looks somewhat similar to the way you learned to do long division. Look at the comparison below, and then talk to your child as he or she completes this assignment. You might enjoy solving some of the problems yourself with this new way. If so, your child can help you.

A Familiar Way A New, Similar Way

13 48137

– 3991

– 910

× Menu for 13

10 x 13 = 130 20 x 13 = 260 5 x 13 = 65

13 481 – 260

221

– 6526

– 260

20

37 10 5 2

– 1 3091

Multiplication & Division Practice

Solve the following division problems. For each one, complete a multiplication menu first. Then you can solve the problem using only numbers, or you can use sketches and numbers together. The first one is done for you as an example.

example× Menu for 15

10 × 15 = 15020 × 15 = 3005 × 15 = 75

15 240

15

1016

– 15090

– 7515

– 150


15015 75 15

10 5 1 10 + 5 + 1 = 16so, 240 ÷ 15 = 16


Home Connections


1× Menu for 16

10 × 16 = 20 × 16 = 5 × 16 =

16 272

2× Menu for 12

10 × 12 = 20 × 12 = 5 × 12 =

12 216

3× Menu for 17

10 × 17 = 20 × 17 = 5 × 17 =

17 408

4× Menu for 22

10 × 22 = 20 × 22 = 5 × 22 =

22 330



NAME DATE

Home Connections



5× Menu for 26

10 × 26 = 20 × 26 = 5 × 26 =

26 598

Use numbers, words, and/or labeled sketches to solve the story problems below. Do not use a calculator.

6 Josh and his dad are baking chocolate chip cookies for his boy scout troop’s jamboree. There will be 98 people at the event and Josh wants everyone to be able to eat 2 cookies.

a How many cookies will they need to bake?

b How many dozens of cookies will that be?


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7 Mr. Elliot wants to build a fence around a yard that is 50 feet wide and 100 feet long. The fencing he wants to use comes in ready-made sections that are 6 feet long. Each section costs $26.

a How many feet of fencing does he need in all?

b How many fence sections does he need to buy?

c How much will it cost to build this fence?

NAME DATE

Home Connections



CHALLENGE

Divisibility Riddles

8 Here are two number riddles. Use the clues to solve each riddle. Show all of your thinking and work below each riddle. If you need more space to work, at-tach an extra piece of paper to this assignment.

Riddle 1

My number is between 1 and 25 When you divide my number by 1, the remainder is 0. When you divide my number by 2, the remainder is 1. When you divide my number by 3, the remainder is 2. When you divide my number by 4, the remainder is 1. When you divide my number by 5, the remainder is 2. When you divide my number by 6, the remainder is 5. When you divide my number by 7, the remainder is 3.

My number is ______

Riddle 2

My number is between 1 and 50 When you divide my number by 1, the remainder is 0. When you divide my number by 2, the remainder is 0. When you divide my number by 3, the remainder is 1. When you divide my number by 4, the remainder is 2. When you divide my number by 5, the remainder is 1. When you divide my number by 6, the remainder is 4. When you divide my number by 7, the remainder is 4.

My number is ______

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The Tangerine Problem

1 Estimate the results of 360 ÷ 24 and explain your thinking.

2 Fill in the menu and then solve 360 ÷ 24. You can make a sketch, or you can work with numbers only.

3 Ali says that if you divide 360 by 12 instead of 24, the answer will be twice as large. Do you agree with her or not? Why?

NAME DATE

MultiplicationMenu

1 × 24 = _____2 × 24 = _____10 × 24 = _____20 × 24 = _____5 × 24 = _____Other usefulcombinations:



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4 Holly and her brother Max got permission to pick tangerines from the trees in their yard and sell them to their friends and neighbors. In all, they collected 360 tangerines.

Holly thinks they should put the tangerines in bags of 24 and sell each bag for $1.50.

Max thinks they should divide the tangerines equally among 24 bags and sell each bag for $1.50.

Whose plan is better? Why? Show all of your your work below.


NAME DATE



Lady Liberty

1 Write the answers to the combinations in the left column. Then use the infor-mation to help solve the combinations in the right column without a calculator.

1 × 8 = _____ 3 × 8 = _____

2 × 8 = _____ 5 × 8 = _____

10 × 8 = _____ 30 × 8 = _____

20 × 8 = _____ 15 × 8 = _____

2 Use the information from the multiplication menu above to estimate the an-swer to 168 ÷ 8. Explain your estimate and then solve the problem. You can use any strategy you want, including a sketch or just numbers.

a Estimate for 168 ÷ 8: ______________

b Explanation of estimate:

c Solve the problem and show all of your work below.



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3 The Statue of Liberty was a gift to the United States from the people of France in 1884. It is a world known symbol of freedom, democracy, and international friendship.

Data:Statue height, from feet to torch: 151 feet Total height including pedestal: 305 feet Number of steps inside the statue: 168

Today, people can tour a museum at the base of the statue and climb to the top of the pedestal. There they find a glass ceiling that allows them to look through the inside of the statue.

Imagine you were allowed to climb the steps inside the statue itself. (They go from the feet to the head, not up the arm.)

Label both sides of the number line on this page to show the trip up all those stairs divided into fourths and eighths. On the left side of the num-ber line, show the fractions and on the right side show how many steps you must climb to reach those fractions. The mark at the halfway point has already been done except for the number of eighths and the number of steps. You’re respon-sible for labeling the rest of the marks.

CHALLENGE

4 When you are done, go back and show where you would be at 1

3 and 2 3 of the way up the steps.

Include the number of steps at each of those fractions.

168 steps

____ =steps

0 steps

4 4

= 8 8

1 2

= 2 4

= 8 8

0 4

NAME DATE




Fraction & Division Story Problems

On Tuesday, David and three friends shared a large pizza for an after-school treat. Each of the four boys ate the same amount of pizza. On Thursday, David shared two large pizzas with 7 friends from his soccer team. Each of the eight team members got equal amounts.

1 Use the circles below to draw labeled models showing how much pizza David got to eat on both days.

a Tuesday’s Pizza Shares b Thursday’s Pizza Shares

2 What fraction of a large pizza did David eat on Tuesday? _____

3 What fraction of a large pizza did David eat on Thursday? _____

4 Did David eat more pizza on Tuesday or on Thursday? _____

5 Write at least 3 mathematical observations that you can make from your sketches for this situation.



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6 Write a story problem to match each of the equations below:

a 37 ÷ 4 = 9 R1

b 37 ÷ 4 = 9 1 4

c $37.00 ÷ 4 = $9.25

d 40 ÷ 4 = 10

CHALLENGE

7 LaToya had a large collection of basketball cards. She decided to give half of them to her friend, Erin, and a fourth of them to her brother. She still has 150 cards left. How many cards did she start with?

NAME DATE




The Mini-Quilt Project

1 Choose one of the quilt blocks you designed on page 123 or 124 in your Bridges Student Book. Use your colored pencils to copy the block 12 times on the grid below.

2 Give your Mini-Quilt a title: __________________________________



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3 Write at least 3 different mathematical observations about your Mini-Quilt.

4 Each of the small squares measures 1 centimeter by 1 centimeter. What is the area of the entire mini-quilt in square centimeters? Do this problem without a calculator and show your work below.

5 If the entire quilt is assigned an area of 1, what fraction of the quilt is covered by each of the colors you used? Show your thinking.


NAME DATE

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CHALLENGE

6 Give your quilt block a title that relates to American history. Then write a short explanation or story about what your quilt block title means. To help come up with ideas, think about what you have studied in American history class, and remember the book The Seasons Sewn. It might help to talk about your ideas with someone at home first and then do the writing.

a Title _______________________________

b Write your story below and on the back of this page. (You can type it if you prefer.)

Home Connections


NAME DATE




Egg Carton Fractions & More

1 In each problem below, there are 2 identical pictures. Label each with a differ-ent fraction name and draw in yarn lines to show your thinking. In all problems, one egg carton is always worth 1.

b

a

c

d

e

example 26

13


Home Connections



12

14

12

12

12

13

16

Eggs in a carton ___

Minutes in an hour ___

Inches in a foot ___

14

14

14Eggs in

a carton ___Minutes in an hour ___


13

13

13Eggs in



16

16

16Eggs in



6 630

example

a

b

c

2 Show each fraction below on the egg carton, the clock, and the ruler.


NAME DATE

Home Connections


3 List at least three things that a 12-egg carton, a clock, and a ruler have in common mathematically.

CHALLENGE

4 Ravi gave 2 (two and one-half thirds) as one fraction name for the part of a dozen shown here:

Explain how you think he decided this.

5 In a 12-egg carton, 1 3 equals 4 eggs. Use the grids below to help you imagine

and draw cartons where:

a 1 3 is 7 eggs b 2

3 is 10 eggs


1 2

3


Home Connections



CHALLENGE

6 Use 4 straight lines to divide this square into 11 sections. The sections don’t have to be congruent. (Hint: Use scratch paper to try out different ideas before you record your solution here.)




More Fraction Story Problems

1 When Annie went to get her hair cut she asked the stylist to cut her hair so that it stopped 1

4 of an inch above her shoulders. When it was all over, her hair was 4 inches above her shoulders. Annie was shocked. If her hair grows 3

4 of an inch per month, how many months will it take for Annie’s hair to grow to the length she wanted?

Solve this problem by making a sketch in the first box and writing an equation (or more than one equation) in the second box.

It will take _______ months for Annie’s hair to grow to the length she wanted.

NAME DATE


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2 Jamal’s house is 40 miles from Loon Lake and 80 miles from Crescent City.

a Label the map below to show how far it is from Loon Lake to Crescent City.

b Label the map to show about where Jamal’s house is.

c Explain how you knew where to put Jamal’s house.

CHALLENGE

3 16-year-old Marybeth has a regular after-school babysitting job. This is a record of the number of hours she worked last week:Monday 2 1

3 hoursTuesday 3 1

2 hoursWednesday 2 1

4 hoursThursday 3 2

3 hours

She gets paid $6 per hour. How much money did Marybeth earn babysitting last week? (Show your work.)



Unit Four Review

1 Draw and label a sketch to show 2 3 .

2 Write two different names for each collection of eggs below.

a b

_______ _______ _______ _______

3a Circle the fraction that is greater.

1 4 2

6

b Make a labeled sketch to show your thinking.

4 Add each pair of fractions below. Use a labeled sketch to show your thinking for each one.

a 5 8 + 2

8 = b 1 6 + 1

3 =

NAME DATE



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5 Find the difference between each pair of fractions below. Use a labeled sketch to show your thinking for each one.

a 4 8 – 1

8 = b 2 3 – 1

6 =


1 × 22 = _____ 3 × 22 = _____

2 × 22 = _____ 5 × 22 = _____

10 × 22 = _____ 30 × 22 = _____

20 × 22 = _____ 15 × 22 = _____

b Solve the combination shown below. Use numbers and words to explain how you got your answer.

28 × 22 = _____

NAME DATE

Home Connections



7 Choose one division problem below and circle it. Pick the one that seems best for you—not too hard and not too easy.

112 ÷ 8 156 ÷ 12 210 ÷ 14 572 ÷ 22

a Estimate the answer to the problem you circled and explain your thinking.

b Use this space to solve the problem. Show all your work using labeled sketch-es, numbers, and/or words.

Home Connections


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Bar & Circle Graphs

1 100 students were surveyed about their favorite music. The results are shown on the circle graph at the right.

a How many students chose hip-hop as their favorite music?

15 25 50 90

b How did you choose your answer?

2 Another class like yours did a pet survey. Their results are shown on the graph below.

a How many students are represented on the graph?

25 26 27 28

Number of pets (per family)

Number of Pets Owned

Num

ber

of

stud

ents

9

7

5

3

1

0 1 2 3 4 5 or more

b Based on this data, list 2 different things you might guess about the students in this fifth grade class.

Home Connections For use after Unit Five, Session 3.

Rock

Jazz

Country Hip-Hop



4 Two students in Mr. Madison’s class did a survey to find out what kind of snacks their classmates liked best, and then they showed the results on a circle graph. Here’s what they found out:

peanuts: 4 kids pretzels: 8 kids

popcorn: 10 kids potato chips: 8 kids

a What fraction of the class said they liked popcorn best?

1 4 1

3 1 2 5

8

b How did you choose your answer?


3 An election for 7th grade Class President was held at Hastings Middle School. The vote results are presented in the bar graph below.

a How many more votes did the winning candidate get than the 2nd place candidate?

10 15 30 50

Candidates

Class President Election Results

Num

ber

of

vote

s

50

40

30

20

10

A B C D

b Write 3 more questions you could ask someone about this graph:

Pretzels8 kids

Peanuts4 kids

Potato Chips8 kidsPopcorn

10 kids

Home Connections


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Home Connections




Complete the following multiplication problems using the strategy that makes the best sense to you. Do not use a calculator.

example 33 5 33 × 27 × 25 _____ _____ 20 × 30 = 600 20 × 3 = 60 7 × 30 = 210 7 × 3 = + 21 _____ 891

6 63 7 56 × 22 × 28 _____ _____

8 132 9 844 × 23 × 25 _____ _____

Home Connections



Complete the following division problems using the strategy that makes the best sense to you. Do not use a calculator. You can make a multiplication menu for the divisor before you start (as in the example below), but you do not have to. Please circle your answer to each problem, as in the example below.

example 12 276276– 240

36– 36

3 12 × 10 = 12012 × 20 = 24012 × 2 = 2412 × 5 = 60

20

0

23

10 15 345

11 17 714 12 21 903

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Presidents’ Names

Do you think U.S. presidents tended to have longer or shorter first names in the old days? Test your hypothesis by counting and graphing the length of some presi-dents’ names from the nineteenth and twentieth centuries. Write the number of letters in each president’s first name on this chart. Then use the information to complete the next 2 pages. Presidents’ nicknames are included in parentheses af-ter their full names. Some presidents like Grover Cleveland went by their middle names; Grover Cleveland’s first name was actually Stephen. For this assignment, use the first names by which the presidents were known, but don’t use nicknames.

Name

Dates of

term(s)

served

Number of

letters in

first name

Name

Dates of

term(s)

served

Number of

letters in

first name

Thomas Jefferson 1801–1809 6 Theodore Roosevelt 1901–1909

James Madison 1809–1817 5 William Taft 1909–1913

James Monroe 1817–1825 (Thomas) Woodrow Wilson 1913–1921 7

John Adams 1825–1829 Warren Harding 1921–1923

Andrew Jackson 1829–1837 Calvin Coolidge 1923–1929

Martin Van Buren 1837–1841 Herbert Hoover 1929–1933

John Tyler 1841–1845 Franklin Roosevelt 1933–1945

James Polk 1845–1849 Harry Truman 1945–1953

Franklin Pierce 1853–1857 Dwight Eisenhower 1953–1961

James Buchanan 1857–1861 John Kennedy 1961–1963

Abraham Lincoln 1861–1865 Lyndon Johnson 1963–1969

Andrew Johnson 1865–1869 Richard Nixon 1969–1974

Ulysses Grant 1869–1877 Gerald Ford 1974–1977

Rutherford Hayes 1877–1881 James Carter (Jimmy) 1977–1981

Chester Arthur 1881–1885 Ronald Reagan 1981–1989

(Stephen) Grover Cleveland 1885–1889 6 George Bush 1989–1993

Benjamin Harrison 1889–1893 William Clinton (Bill) 1993–2001

Note The following presidents from the nineteenth century were left out so that the two samples would contain exactly the same number of presidents: William Harrison (1841), Zachary Taylor (1849–1850), Millard Fillmore (1850–1853), James Garfield (1881), Grover Cleveland (1893–1897), and William McKinley (1897–1901).



1a List the number of letters in each of the nineteenth century (1800’s) U.S. pres-idents’ first names in numeric order. Be sure to include every name on the list, so if there are 4 presidents with 4 letters in their first name, you’ll list 4, 4, 4, 4.

b Determine the range, mode, and median of this data set.

range = ________ mode = ________ median = ________

2a List the number of letters in the twentieth century (1900’s) U.S. presidents’ first names in numeric order.

b Determine the range, mode, and median of this data set.

range = ________ mode = ________ median = ________

3 Find the mean (average) of each data set, and show your work for each.

a Mean number of letters in first names of nineteenth century presidents = ___

b Mean number of letters in first names of twentieth century presidents = ___

Words to RememberRange the difference between the highest and lowest number in a set

Mode the number that appears most often in a set of numbers. In any set, there may be 1 mode, more than 1 mode, or no mode.

Median the middle number when the numbers in a set are arranged from lowest to highest

Mean the number you get when you level off or even out all the numbers in a set. The mean is also called the average.

4 6 7 8 8 11 14

14 – 4 = 10

4 6 7 8 8 11 13

4 6 7 8 11 11 13

2 7 7 8 6 6 6 6

Home Connections


Home Connections

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4 Using the data from the first page, make a double bar graph of the numbers of letters in the presidents’ first names. Use one color to make bars for the nine-teenth century presidents and another color to make bars for the twentieth cen-tury presidents.

Graph Title

Num

ber

of

pre

sid

ents

Number of letters in name

5 Do you think there’s enough evidence to say that one group of presidents had, on average, longer first names than the presidents in the other? Why or why not?




Home Connections

6 Isaac says that the two groups had names that were just about the same length and that there is not much difference. Do you agree or disagree? Why or why not?

NAME DATE



Briana’s Routes

Briana’s Home

Road 1

Road 2

Road 3

Road 4

StoreSchool

4th

Ave

.

3rd

Ave

.

2nd

Ave

.

1st

Ave

.

Briana is in fifth grade and she walks to school every day. Here is a map of her neighborhood. She lives with her family at the intersection of Road 4 and 1st Avenue. Her school is at the intersection of Road 1 and 4th Avenue. Here are 2 of the routes she takes to get to school:

Briana likes to take a different route each day, but she’s only allowed to go EAST and SOUTH on the roads and avenues in her neighborhood. How many differ-ent routes are there? Use the mini-grids on the next two pages to find out. When you’ve drawn all the different routes you can find, ask someone in your family to check your work to see if they think that:• all the routes you’ve found are different, and• there aren’t any other routes to be found. (If they think there are more, they

can help you find them.)

Have your helper sign the mini-grid sheet before you bring it back to school.


Home

Store School

Home

Store School

Home Connections



Home

Store School

Home

Store School

Home

Store SchoolHome

Store SchoolHome

Store School

Home

Store School

Home

Store School

Home

Store SchoolHome

Store SchoolHome

Store School

Home

Store School

Home

Store School

Home

Store SchoolHome

Store SchoolHome

Store School

Home

Store School

Home

Store School

Home

Store SchoolHome

Store SchoolHome

Store School

Use these mini-grids to find routes before recording them on page 161.

NAME DATE

Home Connections



Home

Store School

Home

Store School

Home

Store SchoolHome

Store SchoolHome

Store School

Home

Store School

Home

Store School

Home

Store SchoolHome

Store SchoolHome

Store School

Home

Store School

Home

Store School

Home

Store SchoolHome

Store SchoolHome

Store School

Home

Store School

Home

Store School

Home

Store SchoolHome

Store SchoolHome

Store School

Signature of my homework helper ________________________________________

Home Connections


NAME DATE



Another Spinner Experiment

1 Color 2 3 of the spinner below red. Leave the other 1

3 white.

2 If you spin this spinner once, what are your chances of landing on red? What are your chances of landing on white? Explain your answers.

3 If you spin this spinner 24 times, about how many times do you expect to land on red? About how many times do you think you’ll land on white? Explain your answers.



Home Connections



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4 Use a paperclip for a spinner arrow and a pencil to anchor it, as shown here. Spin the spinner on page 163 24 times, and make a chart below to show your results.

5 How do the results of your experiment compare with your expectations?

6 Make 24 more spins and show your results on a chart below.

7 Counting all 48 spins, how many times did you get red? ______ How many times did you get white? _______

8 Lara told her mom about this experiment. She said, “I was sure I’d get red 32 times and white 16 times, because 1

3 of 48 is 16. But I got 25 reds and 23 whites. That’s more like half and half. I don’t get it.”

What would you say to Lara to help her understand her experimental results?

Home Connections

Home Connections


NAME DATE



Spinner & Dice Probabilities

1 Refer to the spinner at the right.

a On a single spin, what is the probability of getting a 3? Justify your answer using words, numbers, or a labeled sketch.

b What is the probability of spinning a 7 on the spinner above? Justify your answer using words, numbers, or a labeled sketch.

2 Refer to the spinner at the right.

a On a single spin, what is the probability of spinning an odd number? Justify your answer using words, numbers, or a labeled sketch.

b If you spun this spinner twice, you might get the same number twice, like 1 and 1, or two different numbers, like a 1 and a 2. On the chart below, list all the possible combinations.

Spin 1 1 1

Spin 2 1 2

c Sam says that the likelihood of spinning two numbers on this spinner that add up to 4 is 3

9 or 1 3 . Do you agree with him? Why or why not?


2

3

2

1

2

3

1 3

1

2 3




3a On a single roll of a die numbered 1 through 6, what is the probability of getting a 3?

b On a single roll of a die, what is the probability of getting a number equal to or greater than 3?

c Explain why the answers to the two questions above are different.

4 Refer to the spinner at the right, and think of an ordinary die numbered 1–6.

a If you spun the spinner once and rolled the die once, you’d get 2 numbers. They might be the same, like a 1 and a 1, or they might be different, like a 2 and a 6. Make a table to show all the different combinations of two numbers you could get.

b If you spin the spinner and roll the die (numbered 1 through 6) at the same time, what is the probability that both the spinner and the die will show a 1? How do you know?

61

2

1

2 3

53

4

Home Connections

NAME DATE



Tallies & Graphs

1 On the grid below, make a bar graph that accurately represents the election data shown at the right.

Choose a scale for your graph that will accommodate all of the data.

Give your bar graph a title and label both of the axes.

Graph Title

2 Explain who would be interested in reading the graph you just made and why.

Number of Votes for Student CouncilStudent AStudent BStudent CStudent D




3 Use this double bar graph to answer the questions below.

Mr. Wu’sClass

Mr. Dye’sClass

Carrots & Celery

Cherry Tomatoes

Mrs. Brown’sClass

Ms. Ozuna’sClass

Survey of Favorite Vegetable Snacks

Num

ber

of

vote

s

24222018161412108642

a Mr. Dye has 30 students in his class. According to this graph, how many of his students did not vote in this survey? ________

b In all, how many students participated in this survey? ________

c In these 4 classes, the following number of students voted for carrots and cel-ery: 16, 18, 12, and 14. Find the mean (average) number of votes for carrots and celery, and show your work.

d Find the mean (average) number of votes for cherry tomatoes and show your work.

e Who would be interested in the results of this survey?


Home Connections


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Home Connections





example 33 4 65 × 27 × 50 _____ _____ 20 × 30 = 600 20 × 3 = 60 7 × 30 = 210 7 × 3 = + 21 _____ 891

5 73 6 48 × 21 × 36 _____ _____

7 52 8 157 × 33 × 24 _____ _____

Home Connections




example

23 r7

12 283– 240

36– 36

3 12 × 10 = 12012 × 20 = 24012 × 2 = 2412 × 5 = 60

20

7

9 24 648

10 32 463 11 17 454

name date


HomeConnection48HWorksheet

ReadingSurveydata

Below is a bar graph giving the results of a survey about fifth-graders’ favorite va-cation activities. Use the information to answer the questions below.

Favorite Vacation Activities

Visiting Beaches

Camping

Entertainment Activities

Shopping

Visiting Theme Park

1 How many more fifth-graders in this survey would rather visit a theme park than do other entertainment activities? Show how you got your answer.

2 How many students participated in this survey? Show how you got your answer.

3 Do you think this survey would give someone a good idea of what fifth graders all over the whole country like to do when they go on vacations? Why or why not?

0 2 4 6 8 10 12 14 16 18 20Number of fifth graders


HomeConnections For use after Unit Five, Session 18.


4a A school official wants student opinions about a new class schedule. Where would this official take a survey to get the most representative group of students?

an assembly a language arts class a math class the school office

b Explain the reason for your choice.

5 A class was surveyed about when they liked to do homework. These were the results.• 9 students preferred in the evening• 6 students preferred in the afternoon• 3 students preferred on the weekend

a Which of the following unlabeled circled graphs best pictures this data?

� � � �

b Use numbers, words, and/or a labeled sketch to explain how you made your choice above.


Home Connections


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Home Connections





example 33 6 68 × 27 × 25 _____ _____ 20 × 30 = 600 20 × 3 = 60 7 × 30 = 210 7 × 3 = + 21 _____ 891

7 41 8 59 × 33 × 46 _____ _____

9 201 10 147 × 32 × 45 _____ _____

Home Connections




example

23 r7

12 283– 240

36– 36

3 12 × 10 = 12012 × 20 = 24012 × 2 = 2412 × 5 = 60

20

7

11 15 398

12 38 884 13 27 923

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Interpreting Remainders

Solve each division problem below. Handle the remainder in the way that makes the best sense:• leave it as a whole number• show it as a fraction• show it as a decimal

Show your work for each problem and explain why you handled the remainder the way you did.

example Two kids are sharing 39 animal crackers. How many does each child get?


Home Connections For use after Unit Six, Session 2.

a 39 ÷ 2 = ______ cookies

b How I handled the remainder:

There was 1 cookie left over and I gave each kid half of it.

1 75 books have been donated for 4 classroom libraries. How many books are there for each room?

a 75 ÷ 4 = ______ books


19 1

Multiplication Menu

10 x 2 = 2020 x 2 = 40

Multiplication Menu

2 39

910

19 R1

– 2019

– 181

2

4 75

Home Connections




2 Dave drove his car 109 miles on 4 gallons of gas. How many miles can his car drive on one gallon of gas (miles per gallon)?

a 109 ÷ 4 = ______ miles per gallon


Multiplication Menu

3 Four kids earned a total of $63.00 washing cars. How much money does each kid get?

a $63 ÷ 4 = $ _______


Multiplication Menu

4 Kim had 47 marbles. She shared them evenly with 2 of her friends. How many marbles did each of the 3 friends get?

a 47 ÷ 3 = _______ marbles


Multiplication Menu

4 109

4 63

3 47

NAME DATE

Home Connections



5 Write a story problem to match each equation below:

a 55 ÷ 4 = 13 R3

b 55 ÷ 4 = 13 3

c $55.00 ÷ 4 = $13.75

6 Write and solve your own division problem with a remainder. Be sure it’s chal-lenging enough to be interesting to you.

7 Solve the following multiplication problems in the way that makes the best sense to you. Do not use a calculator. Show your work.

a 86× 5____

b 73× 22_____

c 57× 38_____

d 66× 28_____

4


Home Connections


CHALLENGE

8 The figure below has an area of 575 square units. What is its perimeter? Use numbers, words, and/or labeled sketches to solve the problem and show how you got the answer. You can use a calculator to help solve the problem if you want to.


NAME DATE



Equivalent Fractions on a Clock

This clock is broken! The hour hand is stuck at the 12, but the minute hand can still move.

1 Marcus looked at the clock shown above and said, “ 1 of an hour has passed.” Sierra said, “ 3 of an hour has passed.” Ali said, “ 15 of an hour has passed.” Their teacher said they were all correct. Explain how this could be possible.

2 Label each clock with at least 2 equivalent fractions to show what part of an hour has passed. On the clocks marked with stars, write at least 3 equivalent fractions.

a

_______ _______

Hb

_______ _______ _______

Hc

_______ _______ _______


4

12 60


Home Connections



Hd

_______ _______ _______

e

_______ _______

Hf

_______ _______ _______

g

_______ _______

Hh

_______ _______ _______

Hi

_______ _______ _______

Hj

_______ _______ _______

k

_______ _______

Hl

_______ _______ _______


NAME DATE

Home Connections



Equivalent Fraction Concentration

Use your fraction cards to play a game of concentration with an adult. Here are the instructions:

1 Sort your cards into four piles, and check to be sure there are six cards in each pile. The four piles will be:• the ones with no mark in the corner • the star cards• the lightening bolt cards • the cards you made

2 Choose two stacks (12 cards in all). Put them together and mix them up. Then lay them out in a 3 × 4 array, face down, like this:

3 Take turns turning two cards face up. If the two cards you get are equivalent fractions, like 1⁄2 and 6⁄12, you get to keep them. If they’re not equivalent, you have to turn them face down again and put them back in exactly the same spot.

4 Each time either player gets a pair of equivalent fractions, you have to explain to the other person how you know they are equivalent. You can use sketches, numbers, or words to do this, and you can help each other.

5 The person with the most cards at the end of the game wins.

6 When you are finished, play the game again with the other two sets of cards, and then have the adult sign the bottom of this page.

CHALLENGE

7 If you want to play a more challenging game, use all 24 of your cards at the same time.

Signature of the adult who played this game with me: _________________________

Home Connections


name date


HomeConnection51HActivity

note to Families

We are learning to compare, add, and subtract fractions in class. The Smaller the Better Fraction Game will help your student practice these skills.

theSmallertheBetterFractionGame

You’llneedapartner,apencil,andapapercliptoplaythisgame.

InstructionsfortheSmallertheBetterFractionGame

1PlayRock,Paper,Scissorsorflipacointodecidewhowillgofirst.

2Player1spinsbothspinnersonpage186.(Useyourpencilandthepaperclipforthespinnerarrow,asshownonpage186.)Decidehowtousethetwonumbersto make the smallestfractionpossible,andrecorditinyourRound1box.NowPlayer2doesthesame.

3Worktogethertocomparethefractions,andwritethesignforgreaterthan(>),lessthan(<),orequalto,inthecirclebetweenthetwofractions.Youcanusethefractionchartonthelastpagetohelpcompareyourfractions.Cutthepiecesoutandmovethemaroundifyouneedto.Youcanalsorenamebothfractionssotheyhavethesamedenominator.Here’sanexampleusing3 and 2 . First find the leastcommonmultipleofthedenominators,4and3,andthenmultiplythefrac-tions as shown here.

3, 6, 9, 12 3 × 3 = 9 2 × 4 = 8 9 > 8 4, 8, 12 4 × 3 12 3 × 4 12 12 12

When you rename the fractions so they have the same denominator, it’s really easy to compare them.

4Theplayerwhomadethesmallerfractionearns1pointforthatround.Ifthefractionsyoumadewereequal(equivalent),bothplayersearn1pointfortheround.Recordyourscoresfortheround.

5Playanewround.Theplayerwhowonthepreviousroundgetstostartfirst.Theplayerwiththemostpointsafter5roundswinsthefirstgame.

6Playthegameasecondtimeandthendotheproblemsonpage188.

(Continuedonback.)

HomeConnectionsFor use after Unit Six, Session 6.

4 3

Home Connections



1 2

5 4

6 3

1 2

8 4

10 3

Game 1

Player 1 Player 2 Player 1 Points Player 2 Points

Roun

d 1

Roun

d 2

Roun

d 3

Roun

d 4

Roun

d 5

Totals


NAME DATE

Home Connections




Game 2

Player 1 Player 2 Player 1 Points Player 2 Points

Roun

d 1

Roun

d 2

Roun

d 3

Roun

d 4

Roun

d 5

Totals

Home Connections


example 2 + 2 = 4

4 = 11


1 3 + 4 =

4 1 + 3 =

7 2 – 2 =

2 3 – 2 =

5 3 – 1 =

3 6 – 4 =

6 2 + 4 =

5 4

4 6

5 10

8

4

4

3 6

10

2 2

8 Find two different ways to show that 1 + 1 does not equal 2 . You can use num-bers, words, and labeled sketches.

2 4 6

3 3 3

3 3

Solve the problems on this page. Use the fraction chart on the next page to help or cut the pieces out and move them around if you need to. If you get an improp-er fraction, change it to a mixed number.

Think 4 is an improper fraction because the numerator is bigger than the denominator. When expressed as a mixed number, 4 = 1 1 .

3

3 3


Home Connections


Unit (1) 1

Halves 1 1

Thirds 1 1 1

Fourths 1 1 1 1

Fifths 1 1 1 1 1

Sixths 1 1 1 1 1 1

Eighths 1 1 1 1 1 1 1 1

Tenths 1 1 1 1 1 1 1 1 1 110 10 10 10 10 10 10 10 10 10

8 8 8 8 8 8 8 8

666666

5 5 5 5 5

4444

3 3 3

2 2


Home Connections


NAME DATE



Cafeteria Problems

1 The cafeteria at King Elementary asked the students to vote on their favorite main dishes. The circle graphs below show the results. Use the information to complete this Home Connection.

18

Fourth Grade Favorites Fifth Grade Favorites Key

Cheese Pizza

Turkey Burgers

Chicken Nuggets

Super Salad

13

13

12

14

16

16

18

a What fraction of the fourth graders did not vote for super salad? Show your work.

b What fraction of the fifth grade voted for turkey burgers or chicken nuggets? Show your work.

c 192 fourth graders voted. How many of them voted for turkey burgers? Show your work.



Home Connections




1d 174 fifth graders voted. How many of them voted for chicken nuggets?

2 Solve the story problems below. Don’t use a calculator, and show all of your work.

a The cafeteria bought 36 bags of frozen chicken nuggets for $15 a bag. How much did they pay in all?

b The cafeteria bought 13 cartons of frozen cheese pizzas. If there were 24 piz-zas in each carton, how many pizzas did they get in all?

c Use the information from problem 2b to help solve this problem. If they cut each pizza into 6 slices, how many slices was that in all?

CHALLENGE

d Use the information from problem 2c to help solve this problem. If the cafeteria serves 72 slices of pizza a day, how many days will the 13 cartons of pizza last?

NAME DATE

Home Connections



3 Choose the expression you’d need to solve each of the problems below.

a The cafeteria bought 29 bags of carrots for $3.50 each. How much did they pay in all?

29 + $3.50 29 × $3.50 29 – $3.50 29 ÷ $3.50

b There are 576 students at King School. 24 kids can sit at each cafeteria table. How many tables does the school need to seat all the students in the cafeteria if no one is absent and they all come in at the same time?

576 – 24 576 × 24 576 ÷ 24 576 + 24

c Bags of fruit are on sale at the Warehouse store for $8.95 each. The cafeteria bought 28 bags of apples and 19 bags of oranges.

(28 + $8.95) + (19 + $8.95) (28 × $8.95) + (19 × $8.95)

(28 + $8.95) × (19 + $8.95) (28 × $8.95) × (19 × $8.95)

4 Solve problem 3b above. Show all your work.


Home Connections


5 Solve the following division problems. Use a multiplication menu if you find it helpful.

a 33 528 b 27 867

c 33 735 d 27 486


NAME DATE



Modeling, Reading & Comparing Decimals


1 This mat has an area of 1.

a Color 0.35 of the mat purple.

b Color 0.40 of the mat green.

c Color 0.05 of the mat red.

d Color the rest of the mat yellow.

e What decimal represents the part of the mat that is colored yellow? ______

2 The full name of 0.2 written out in words is “two tenths.” The full name of 0.20 written out in words is “twenty hundredths.” The full name of 4.05 written out in words is “four and five hundredths.” Use this information to help complete the chart below.

Number Number Name Written Out in Words

a 0.6

b 1.5

c 1.03

d two and two hundredths

e 0.37

f forty hundredths

3 List the decimals from the boxes above on these lines. Write them in order from least to greatest.

_______ < _______ < _______ < _______ < _______ < _______


Home Connections



4 Mr. Mugwump doesn’t know which is greater, 1.5 or 1.05. Use numbers, words, and/or labeled sketches to help him understand which number is greater. You can use the grids below to help if you want.

5 Write four decimal numbers that are less than 1.4 on the lines below.

_________ _________ _________ _________

6 Write four decimal numbers that have an even digit in the tenths place and an odd digit in the hundredths place.

_________ _________ _________ _________

CHALLENGE

7 Robbie babysits the kids next door every day after school for 1.5 hours. He earns $3.50 an hour. How much money will he earn in 6 weeks if school is in ses-sion 5 days a week the whole time? Show your work.

NAME DATE



More Decimal Work

1 Label each digit in the numbers below with its place value name. The first one is done for you as an example.

3 2 . 0 3 7 1 . 0 6 1 3 4 . 7 5 3 1 4 2 . 0 0 5

2 Complete the chart below.

Number Number Name Written Out in Words

a 0.540

b 1.503 one and five hundred three thousandths

c 11.07

d one and four hundred twenty-nine thousandths

e 7.005

f zero and four thousandths

3 Mr. Mugwump is still confused. He doesn’t know which is more, 5.200 or 5.002. Draw or write something that will help him understand which number is greater and why.



7 th

ousa

ndth

s

3 hun

dred

ths

0 te

nths

2 one

s

3 ten

s

Home Connections



4 Lightly shade in half of this decimal grid.

5 Use the shaded grid to help fill in the missing values on the chart below.

Tenths Hundredths Thousandths Ten-Thousandths

Fraction 5

Decimal 0.50


Note This grid has an area of 1.

10

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Home Connections



6 When do people actually use decimal numbers?

• Weather stations measure temperature in tenths of a degree. A weather report-er might say, “The temperature in Seattle today at noon was 65.7º F.”

• Weather stations measure rainfall in hundredths of an inch. A weather report-er might say, “Portland got one and six hundredths (1.06) of an inch of rain today.”

• People use thousandths to talk about baseball players’ batting averages. A sports reporter might say, “Babe Ruth had a lifetime batting average of 0.324.” This means Babe Ruth got a base hit about a third of the time, which is pretty amazing.

Look in your kitchen cupboards, on the Internet, or in a magazine or newspaper to find some other ways people use decimals in their lives. List at least one exam-ple of each type of decimal number and where it came from in each box below. You can paste in some of the examples you find if you like.

Tenths

example Temperatures (65.7ºF)

Hundredths

example Rainfall (1.06 inches)

Thousandths

example Batting Averages (0.324)

Ten-Thousandths

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Decimal Sense & Nonsense

1 In each of the following statements, place a decimal point so the statement makes sense.

a Martin’s Grandpa is 6 7 0 0 years old.

b Tara’s older sister is 5 4 0 0 feet tall.

c Normal body temperature for a healthy human is 9 8 6 degrees Fahrenheit.

d By age 14, most people have 2 8 0 teeth.

e Frank went outside without a coat today because the weather report said it was 7 4 5 0 degrees Fahrenheit.

2 Use the decimal numbers below to fill in the blanks so that the story below makes sense.

1.1 7.46 2.4 4.25 3.21

Three kids from the track team ran in a big road race this spring. The race was

______ miles long. Danny ran ______ miles, more than half way, but then he had

to stop because he got cramps. He stopped ______ miles before the finish line.

Katy was the first of the other two to cross the finish line. It took her ______

hours. Akiko walked most of the way, so it took her more than an hour longer

than Katy to cross the finish line. She took ______ hours to finish.



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3a Write a short story (5 or 6 sentences) that has at least 4 or 5 decimal numbers in it, but put the decimal points in the wrong places.

b Write the correct numbers in the key at the bottom of the sheet and cover them up with a little piece of paper.

c Give your silly story to an adult. Have him or her write the correct numbers in the answer box, and then check your key to see how many he/she got right. Have the person who read your story sign the bottom of the page.

Key Answer Box

Adult’s Signature

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Working with Decimals & Percents

1 This quilt has 100 patches. Determine the fraction, percent, and decimal value (when the whole quilt is 1) for each kind of patch. The first one is done as an example.

Fraction Percent Decimal

a 20 20% 0.20

b

c

d

e

f Total

2 Explain how the totals above can help you know if you counted the patches correctly.



100

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3 When do people use percents in their daily lives? Look in a magazine, newspa-per, or on the Internet to find out. Write or paste in at least 4 different examples below, and write a sentence to explain each one.

example People in stores use percents to tell you how much you save when something is on sale.


NAME DATE

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Adding Decimals Game

1 Practice adding decimals by playing this game with an adult. You’ll need two different colors of crayon, marker, or colored pencil. Please don’t use a calculator. If you can get the answers in your head, that’s fine. If you need to do some paper and pencil work, show it below the game board. Have the adult sign the bottom of the sheet when you’re finished.

Instructions:

a Choose 2 numbers from the box at the right and add them.

b Mark the sum on the game board with your color.

c The first player to get 4 in a row, column, or diagonal wins.

d There is one number on the board that can’t be marked because it’s a mistake. As you play, see if you can tell which number is the mistake and circle it. The sooner you find it, the easier it will be to get 4 in a row!

3.26 5.16 7.12 8.050.5

2.76

3.12

2.4

4.05

4

6.4 4.55 3.62 4.5

6.81 1.27 2.9 6.45

5.88 7.17 5.52 6.76

Our work:

Adult signature _________________________________________

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Finding Percents

1 Circle the fraction that means the same as 25%.

1 1 1 1

2 Write the fraction that means the same as 75%. ________

3 The number lines below show 4 different percents. Notice that each line ends with a different number. Use what you know about division to help fill in the empty boxes above each line.

a

Percents (%) 10 25 50 75

Fractions 1 1 1 310 4 2 4

2002 5

b

Percents (%) 10 25 50 75

600

c

Percents (%) 10 25 50 75

2000

d

Percents (%) 10 25 50 75

3000



Hint If 1 of 20 is 5, what’s 3 of 20?

Hint What’s half of 20?

4

4

2 3 4 6

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4 Complete the table so it shows the prices of the items when they are on sale. Use the blank space below the table to show your work. You can use a calculator to help with this problem if you want.

Item Regular Price Sale Price at 50% off Sale Price at 25% off

Bicycle $600.00 a b

Ping-Pong Table $180.00 c d

Trampoline $160.00 e f

Hiking Boots $80.00 g h

Bicycle Lights $30.00 i j

5 There’s a big sale at the shopping mall this weekend. You can get 25% off on a $52 jacket at the Skate Shack. Dudley’s Department Store is selling the same jack-et for $76, but it’s 50% off. Which is the better deal? Use numbers, words, and/or labeled sketches to explain your answer.


NAME DATE

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CHALLENGE

6 When people go out to eat at a restaurant, they leave a tip for the waiter or waitress. Sometimes they decide to leave a tip that is 15% of the cost of their meal and sometimes they leave a 20% tip. Ask an adult to tell you how they figure out 15% and 20% (without using a calculator). Describe their method below, and then use it to figure the tip on amounts a–e. Show your math work.

Here’s how the adult I interviewed finds 20% without a calculator:

Here’s how the adult I interviewed finds 15% without a calculator:

a Breakfast for four at Sheri’s: $18.00

15% tip = ______ 20% tip = ______

b Dinner for three at Mike’s Place: $32.00

15% tip = ______ 20% tip = ______

c Pizza with the family: $19.00

15% tip = ______ 20% tip = ______

d Special occasion dinner: $28.50

15% tip = ______ 20% tip = ______

e Ice cream party at Farrell’s: $37.50

15% tip = ______ 20% tip = ______

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Unit Six Review

1 Find and label the location of these numbers on the number line. It’s okay to add more marks to the line if you need to.

1.4 0.75 1.25 0.2 1.95 0.58

0 1.0 2.0

2 Write the following numbers in order from the smallest to the largest:

94.67 94.64 94.51 94.59 94.50 94.05

_______ < _______ < _______ < _______ < _______ < _______

3 When the odometer of a car reads 35,467.219 the 5 stands for 5000 miles. What does each of the other digits stand for?

a 1: _______________________ of a mile b 2: ______________________ of a mile

c 3: _________________________ miles d 4: _________________________ miles

e 6: _________________________ miles f 7: _________________________ miles

g 9: ______________________ of a mile



4 This whole grid is worth 1. Write at least 3 different fractions and 3 different decimal numbers to name the part that is shaded.

5 What percent of the grid is shaded?

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6 Here is a chart showing the amount of rain they got in Bookerville over the last four days.

Monday 1.35 inches

Tuesday 2.50 inches

Wednesday 3.06 inches

Thursday 2.49 inches

Bookerville has a record of 12 inches of rain in 5 days. How much will it have to rain on Friday to beat the record by one-tenth of an inch? Show all of your math below.

7a Circle the number below that is not equivalent to 1 .

25% 2 0.25 5 5

b Use numbers, words, and/or labeled sketches to explain why the number you circled is not equivalent to 1 .

8 Mr. Mugwump is still confused about fractions. Use numbers, words, and/or labeled sketches to show him why 1 + 1 does not equal 2 .

4

4

3 52

8 16 20

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9 The librarian at our school asked the fourth and fifth graders to vote on their favorite kind of book. The circle graphs below show the results. Use the informa-tion to answer the questions below.

Fourth Grade Favorites Fifth Grade Favorites Key

Fiction

Fantasy

Non-Fiction34

18

12

14

a What percent of the fourth graders said they liked non-fiction books best? How do you know?

b If there are 96 fourth graders, how many like fantasy books best? Show your work.

c What fraction of the fifth graders said they like fantasy books best? How do you know?

d If there are 112 fifth graders, how many like non-fiction books best? Show your work.

e What percent of the fifth graders said they liked fiction books best? How do you know?

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10 After the librarian did her survey, she decided to buy some more books. She got 48 new fiction books for $16 each. How much did she have to pay in all? Show your work.

CHALLENGE

11 Mrs. Longchamp spent exactly $224 when she bought 28 more books for the li-brary. She spent $96 on non-fiction books and $128 on fantasy books. The price of each non-fiction book was the same as the price of each fantasy book. How many of each did she buy? Show your work.

12a If 6 is 5% of a number, what is 40% of that number?

b What is the number?

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The Operations Game

Cut out the cards on pages 217–221. Fasten the cards to this assignment with a paperclip. Follow the directions below to play the game twice at home and then bring the record sheets back to school.

Instructions for The Operations Game

Home Connections For use after Unit Seven, Session 1.

Use the order of operations.

Do the operations in any order.

1 Mix up the cards and place them face down in a stack. Then decide which player will start.

2 The first player draws a card from the top of the stack and copies the equation on his or her side of the Game 1 Record Sheet.

3 Then the second player follows step 2.

4 Player 1 uses a pencil and paperclip to spin the spinner above. If the pa-perclip lands on top, both players will have to use the order of operations. If the paperclip lands on the bottom, players can do the operations in any order to get the largest possible result.

5 Both players solve their equations at the same time, following the guide-lines set by the spinner. If you get to do the operations in any order, mark your equations with parentheses to show how you did it. Either way, the answer is your score for this turn. You can do your figuring on the record sheet or use a piece of scratch paper.

6 Share your answers with each other to make sure you both agree they are correct.

7 Continue to take your turns at the same time until you’ve filled the re-cord sheet. When you’re finished, each player adds up his or her answers and enters his or her total score at the bot-tom of the sheet. The player with the highest score wins.

Note Once you’ve used a card, do not return it to the stack. You should be able to use all of the cards once by playing two games.

Order of Operations

1. If there are parentheses, do what-ever is inside them first.

2. Multiply and divide from left to right.

3. Add and subtract from left to right.


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The Operations Game Cards page 1 of 3

Home Connections Cut out all the cards on this sheet. Mix them up before you play the game.

HC 59 The Operations Game Card








7 × 6 – 4 × 2 =

15 ÷ 3 + 2 × 5 =5 + 9 × 3 =

10 × 7 – 12 × 5 =

4 + 2 × 5 – 12 ÷ 6 = 12 – 4 × 3 =

48 ÷ 4 – 3 + 1 × 5 =13 – 6 ÷ 2 + 1 =

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36 ÷ 4 + 2 × 7 =

7 × 8 – 6 × 9 =24 + 8 ÷ 4 – 6 + 14 =

6 + 4 × 5 =

5 × 6 – 3 = 8 × 8 – 6 × 6 =

25 – 3 × 7 =7 + 7 × 5 =

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14 × 3 + 7 × 3 =

12 ÷ 6 – 3 + 2 × 6 =17 – 4 × 3 =

6 × 3 + 7 – 1 × 4 =

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Game 1 Record Sheet

Player 1: Player 2:

Player 1 Total Score: Player 2 Total Score:

NAME DATE


Home Connections

NOTE TO FAMILIES

Here are two ways to solve 8 × 5 – 3 × 6. Using order of operations, you can only get one answer for 8 × 5 – 3 × 6. You have to do the multiplication first and then the subtraction, so 8 × 5 = 40 and 3 × 6 = 18, and then subtract to get 40 – 18 = 22.

If you get to do the operations in any order you want, you can get lots of different answers for 8 × 5 – 3 × 6. Try to find the highest answer to get the best score. Remember to use parentheses to show what order you used. Example: ((8 × (5 – 3)) × 6 = 8 × 2 × 6 and 8 × 2 × 6 = 96


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Game 2 Record Sheet

Player 1: Player 2:

Player 1 Total Score: Player 2 Total Score:

NAME DATE



Operations, Equations & Puzzles

Order of Operations

1. If there are parentheses, do whatever is inside them first.2. Multiply and divide from left to right.3. Add and subtract from left to right.

1 Find the answer to each problem below. Use the standard order of operations, and show the steps you use.

example 3 + 4 × 2 – 1 3 + 8 – 1 = 10

a 15 ÷ 5 + 4 b 14 + 5 × 3

c (9 – 3) × 5 + 8 d 2 + 24 ÷ 12 – 3

e 17 – 2 × 7 + 21

2 Circle the word to show whether each equation below is true or false.

a 29 + 7 = 6 × 6 True False

b 5 × 2 × 4 = 4 × 5 × 2 True False

c 12 × (10 – 2) = (12 × 10) – 2 True False

d 20 = 2n + 10 if the value of n is 5. True False



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3 Write the correct number in each box to complete the equations. Find at least two different ways to complete equations b and e.

a 18 = 1 × 12 +

b 4 × = 2 × 4 × = 2 ×

c 3 × – 8 = 2 × 2

d 15 ÷ = 7 – 4

e 24 ÷ = 16 ÷ 24 ÷ = 16 ÷

4 A ÷ 2 = 6

A – B = 8

( A + B ) ÷ C = 2

5 60 – A = 20

A ÷ B = 8

( A – B ) ÷ C = 5

A = _____ B = _____ C = _____ A = _____ B = _____ C = _____

6 A × 3 = 21

A – B = 3

( A + B ) × C = 66

7 75 + 25 = A

A ÷ B = 10

( A – B ) × C = 45

A = _____ B = _____ C = _____ A = _____ B = _____ C = _____



Solve the problems below without a calculator.

8 65× 32_____

9 132× 56_____

10 112× 87_____

11 16 589

12 16 412 13 25 928


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CHALLENGE

14 3 × A = 39

A × B = 65

( A – B ) × C = 96

( A + B – C ) × D = 120

15 A + 15 = 30

A × B = 45

( A + B ) ÷ C = 3

( A + B ) – ( C × D ) = 0

A = _____ B = _____ C = _____ D = _____ A = _____ B = _____ C = _____ D = _____


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More Tile Patterns

Below are parts of two different tile sequences. For each sequence, sketch the missing arrangement. Then use words, numbers, and your sketches to describe how the arrangements change from one to the next. (Or give a rule that tells how to make any arrangement in the sequence.)

1a Sketch the first arrangement.


b Description or Rule:

2a Sketch the fourth arrangement.

Arrangement 1 Arrangement 2 Arrangement 3 Arrangement 4 Arrangement 5

b Description or Rule:



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Below are descriptions of two different tile sequences. For each, you are given the first arrangement and then a rule that tells you how to make the rest of the arrangements in the sequence. Sketch arrangements 2 through 4 for each sequence.

3 Rule: Add 3 to the arrangement number. (It takes 4 tile to make the first arrangement because 1 + 3 = 4.)

Arrangement 1 Arrangement 2 Arrangement 3 Arrangement 4

4 Rule: Multiply the arrangement number times 2. (It takes 2 tile to make the first arrangement because 2 × 1 = 2.)

Arrangement 1 Arrangement 2 Arrangement 3 Arrangement 4



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Solve the problems below without a calculator.

5 36× 27_____

6 113× 62_____

7 207× 35_____

8 62 1146

9 62 826 10 31 843



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CHALLENGE

Think carefully about order of operations when doing the following puzzles.

11 12

+ 12

= 1

A × A + B = 55

A × B ÷ C = 14

( ( B + C ) × A ) ÷ D = 7

12 2 × 25 + A = 98

A ÷ B + 3 = 7

A + B × C = 120

( A ÷ C + B ) × D = 200

A = _____ B = _____ C = _____ D = _____ A = _____ B = _____ C = _____ D = _____

13 3 × 15 + A = 85

A ÷ B + 4 = 24

A + B × C = 76

( C ÷ B + A ) ÷ D = 7

14 A + 7 × 7 = 54

( A × A ) – ( B × B ) = 9

A × B + ( C × C ) = 56

( C × A + B ) + ( D × D ) = 98

A = _____ B = _____ C = _____ D = _____ A = _____ B = _____ C = _____ D = _____

15 In this box, make up your own algebra puzzle for someone else in your class to solve. Double check to make sure your puzzle works and write the answers in the key box. Then cover the key by taping a little flap over it.

Key

5A

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Thinking About The King’s Chessboard

Here are the number of grains of rice that appeared on the first row of the king’s chessboard.

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8

1 2 4 8 16 32 64 128

1 Using the information above, complete the following table. (The first part is filled out for you.)

a Total number of grains on days 1 and 2

Grains on day 3 b Total number of grains on days 1, 2 and 3

Grains on day 4

3 4

c Total number of grains on days 1–4

Grains on day 5 d Total number of grains on days 1–5

Grains on day 6

e Total number of grains on days 1–6

Grains on day 7 f Total number of grains on days 1–7

Grains on day 8

2 List at least 2 different patterns you notice when you look at the numbers in the tables above.



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3 By the 12th day, the Weigher of the King’s Grain got tired of counting out grains of rice and simply weighed out an ounce of rice to send to the wise man. On what day did the wise man get a full pound of rice? (There are 16 ounces in a pound.) Show your work.

4 There are 2 cups of rice in a pound. When you cook rice, it swells up to 3 times its volume. Fill in the table below to show how many cups of cooked rice you get as the number of pounds increases.

Pounds of rice 1 2 3 4 5 6 10 20 100

Cups of raw rice 2 6 12 40 100

Cups of cooked rice 6 30 300

5 What do you have to do to figure out how many cups of cooked rice you’ll get from cooking any number of pounds? Give your answer in words, and then write an equation to match.


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Home Connections


6 It wasn’t long before the wise man started receiving 128-pound sacks of rice from the king. How many cups of cooked rice would you get if you cooked the whole 128 pounds? Show your work.

7 The wise man gave his sacks of rice to the people in the villages all around. In one village, they cooked one whole sack, all 128 pounds of it, and had a big party. Every single person in the whole village got 3 cups of cooked rice to eat. How many people were there in the village? Show your work.

CHALLENGE

8 Near the end of the story, the Chief Mathematician figured out that to keep his promise, the king would have to give the wise man 274,877,906,944 tons of rice. A modern 18-wheeler truck can carry 45 tons at the most. How many 18-wheelers would it take to carry the promised amount of rice? Do your calculations by hand on the back of this page and bring them in to share with the class.


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b The value of the output number is:

c Here’s how to write the rule as an equation:

b The value of the output number is:

c Here’s how to write the rule as an equation:

The Function Machine Strikes Again!

Here’s the function machine with some more puzzles for you to solve. Use the clues to fill in the missing numbers on each chart. Describe a rule the machine could use to get the numbers in the chart. Then write an equation to describe that rule.

1a 2a

10 5

8 3

4

7 2

0

32

15 10

47

2 5

5 14

7

10

6 17

20

100 299

23

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The Function Machine Game

Play this game with an adult. You’ll need a record sheet and a pencil to play.

I played this game with ____________________________________

Instructions for The Function Machine Game

1 Think of a mathematical rule for transforming numbers. Examples of rules would be add 5, multiply by 3, or divide by 2 and then add 1. You can get even more complicated if you want, as long as you think your partner can figure out your rule.

2 On your record sheet, create a chart of input and output numbers. Fill in the first 3 lines. You get your output numbers by applying the rule to each input number. You don’t have to start with 1 as your first input number and it is fine to skip numbers. Make sure you follow your own rule to get all the output numbers.

3 Write an input number on the fourth line. If your partner guesses the output number correctly, he or she scores a point. If your partner guesses incorrectly, write the correct number yourself. Repeat this on the fifth line. Your partner scores a point if he or she guesses the output number correctly.

4 Then ask your partner to guess your rule. If the guess is correct, your partner scores 5 points. If the guess is not correct, ask your partner to write his or her second guess on the record sheet. If it’s correct, your partner scores 2 points. If it’s not correct, write your rule on the third line for your partner to see. Keep in mind that your partner might see the rule differently than you do. If the rule he or she guesses works for every pair of input and output numbers, he or she gets the points.

5 Now switch and try to guess your partner’s rule. The player with the most points after 3 rounds is the winner. Record your scores at the bottom of the sheet. There is an extra record sheet if you want to play the game a second time before you bring the assignment back to school.

(your partner’s signature)


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What’s My Rule? Record Sheet 1

Round 1Player 1's T-chart Player 2's T-chart

In Out In Out

Guess 1 (5 points) Guess 1 (5 points)Guess 2 (2 points) Guess 2 (2 points)Player 1's Rule: Player 2's Rule:Round 2

Player 1's T-chart Player 2's T-chartIn Out In Out



Guess 1 (5 points) Guess 1 (5 points)Guess 2 (2 points) Guess 2 (2 points)Player 1's Rule: Player 2's Rule:

Player 2's Score _______________________ Player 1's Score _______________________

PLAYER 1 DATE

PLAYER 2

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What’s My Rule? Record Sheet 2

Round 1Player 1's T-chart Player 2's T-chart

In Out In Out





Guess 1 (5 points) Guess 1 (5 points)Guess 2 (2 points) Guess 2 (2 points)Player 1's Rule: Player 2's Rule:

Player 2's Score _______________________ Player 1's Score _______________________

PLAYER 1 DATE

PLAYER 2

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The Lemonade Stand

Troy and his little sister are going to sell lemonade to earn money for the wildlife refuge near their home. Troy’s parents have agreed to pay for the ingredients and the cups. The kids are going to charge 50¢ a glass for their lemonade.

1 Fill in the table below to show how much money they’ll earn.

Number of glasses sold 1 2 3 5 7 8 9

Money earned $0.50 $1.50 $3.00 $5.00

2 Use the grid below to graph the amount of money they’ll earn as they sell glasses of lemonade. Give your graph a good title.

8.50

8.00

7.50

7.00

6.50

6.00

5.50

5.00

4.50

4.00

3.50

3.00

2.50

2.00

1.50

1.00

.50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Number of Glasses Sold (Continued on back.)

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3 Why do the points on the graph form a straight line?

4 The first day they opened their lemonade stand it was really hot. Troy and his sister sold 24 glasses of lemonade between noon and 3:00 pm. How much money did they make? Show your work.

5 Between 1:00 pm and 5:00 pm on the second day, they made $14.50. How many glasses of lemonade did they sell during those 4 hours? Show your work.

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6 What do you have to do to figure out how much money they’ll earn for selling any number of glasses of lemonade? Give your answer in words, and then write an equation to match.

7 Their goal is to earn $75.00 for the wildlife refuge. How many glasses of lem-onade will they need to sell to reach their goal? Show your work.

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8 Here is a recipe for 1 glass of lemonade:

1 1 2 tablespoons lemon juice

1 4 cup sugar

1 cup of water

The pitcher the kids were using held 8 glasses of lemonade. How much lemon juice, sugar, and water did it take to make enough lemonade to fill the pitcher? Show your work.

CHALLENGE

9 Use your answer to problem 7, along with the information below to figure out how much it cost Troy’s parents to buy the ingredients for all the lemonade they sold. (The kids did reach their goal of earning $75.00 exactly.) Show all of your work.• A 1-quart bottle of lemon juice costs $2.95.• There are 16 tablespoons in a cup and 4 cups in a quart.• A 5-pound bag of sugar costs $3.29.• There are 111

4 cups of sugar in a 5-pound bag.


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Picturing Problems

Here is the model we’ve been using to solve story problems in class for the last few days. The longer line segment is like the coffee stirrer and represents any number or a secret number. The shorter line segment is like the red linear unit, and always represents 1.

secret number 1

example Draw a collection below that is 4 more than a secret number.

1 Draw a collection below that is 7 more than the secret number.

2 Draw a collection below that is 2 times the secret number.

3 Draw a collection below that is 3 times the secret number plus 2.

4 Pretend that the secret number is worth 15. How would 17 look if you used the model shown above? Sketch it below.

5 The sum of two secret numbers is 24. Their difference is 6. What are the two secret numbers? Show all of your work below. See if you can use a strategy that is not random guess and check to solve this problem.

The two secret numbers are _____ and _____. (Continued on back.)

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6a A square has a perimeter of 72 centimeters. Make a labeled sketch of the square.

b Determine the length of each side of the square. Use words, numbers, and/or a labeled sketch to show how you got the answer.

c Each side of the square is ___ centimeters.

7a In the Brown family, the oldest sister is 2 years older than the middle sister. The middle sister is 3 years older than the youngest sister. The ages of all three sisters total 26 years. Make a labeled sketch to model this situation.

b Determine the ages of each sister. Use words, numbers, and/or a labeled sketch to show how you got the answer.

c The youngest sister is ____. The middle sister is ____ years old. The oldest sister is ____ years old.

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Circle Surround

1 Estimate how many circles of the same radius will fit around the small circle in the center of this figure.

Home Connections For use after Unit Eight, Session 2.

2 Cut out the circles at the bottom of the page. Be sure you don’t cut off the heavy black line that forms the cir-cumference of each circle.

3 Arrange the cut out circles around the central circle without any gaps or overlapping. How many fit? ______

4 Carefully glue or tape those circles that fit around the central circle. It’s okay if you have some extra circles left over.

5 Then go on to the activities on page 249.


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6 Look around your home for circular objects. Find as many circular objects as you can that your family has many copies of. See how many of those objects fit around one of the same object. Use the chart below to make a list of the objects you tested and the number that fit around each. Some common items have been listed to get you started.

Circular Object How many fit around one?

pennies

tuna cans

cylindrical drinking glasses

7 What do you notice?

8 Explain your results. Why is this happening? (Hint: Use your knowledge of circles to develop an explanation.)

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Circle Math

1 Imagine drawing a circle using a cardstock compass as it is shown in this diagram.

a The radius will be:

b The diameter will be:

2 Draw a line from each description to the drawing it describes:

a Intersecting circles cross each other at two points along their circumferences.

b Tangent circles touch each other but they do not intersect.

c Concentric circles have the same center point.


0 cm 1 2 3 4 5 6 7


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3 Mark and label each of the following terms on the circle below. Use a ruler to make sure your work is accurate.

a Center

b Radius

c Diameter

d Circumference

4 How many centimeters long is the radius, diameter, and circumference of the circle? Use the string and ruler to measure the circumference. Add this informa-tion to your labels.



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Each circle below has a line segment going through its diameter and a point marked on its circumference.

5 Draw a triangle in each circle by connecting the endpoints of each diameter line segment to the point on the circumference. (Use a ruler.)

example

6 Look at each angle that has the point on the circumference as its vertex. What do you notice?

7 How many degrees do the 3 angles in each triangle add up to?

8 How does this compare to the total number of degrees in a circle?

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This page meant to be blank.

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110

56

29

47

38

110

56

29

47

38


Circle Explorations

See directions on the next page.

Circle A Observations about circle A:

Circle B Observations about circle B:

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Directions for Circle A

1 Use a ruler to draw line segments to connect each numbered point on the cir-cumference of circle A. Draw a line from point 1 to point 2, from point 2 to point 3, and so on.

2 The polygon you have just drawn is called a decagon because it has 10 sides.

3 Each numbered point on this circle has a partner right across the circle from it. Draw line segments to connect each point to the points on either side of its partner.

example Point 1’s partner across the circle is point 6. You will draw a line seg-ment connecting point 1 to point 5. Then draw another line segment connecting point 1 to point 7.

4 Do this for all ten points on the circumference of circle A.

5 Write at least 3 mathematical observations about the figure you’ve just drawn.

Directions for Circle B

6 Now use a ruler to draw line segments to connect only the even-numbered points on the circumference of circle B. Do not connect the odd-numbered points. Draw a line from point 2 to point 4, from point 4 to point 6, from point 6 to point 8, and so on.

7 How many sides are in the polygon you have just drawn inside circle B? ____. What is the name of a polygon with this many sides? _____________________


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Directions for Circle B (cont.)

8 Each numbered point on circle B has a partner right across the circle from it. Draw line segments to connect each even-numbered point to the points on either side of its partner.

example Point 2’s partner is point 7. You will draw a line segment connecting point 2 to point 8. Then draw another line segment connecting point 2 to point 6.

9 Do this for all five even-numbered points on the circumference of circle B.

10 Write at least 3 mathematical observations about the figure you’ve just drawn.

Coloring the Figures

11 Design a color scheme and color both figures with colored pencils or felt pens.

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Unit Eight Review

Tanya and Patrick investigated how the size of a top’s radius affects its spin time. They made two tops that were identical except that top A had a radius of 3 cm and top B had a radius of 6 cm. Both tops were made from 3 layers of tagboard.

Top A Top B

Then they spun each top 10 times and recorded the number of seconds for each spin. Here is their raw data:

Trial NumberTop A

Duration of Spins in SecondsTop B

Duration of Spins in Seconds

1 15 312 14 313 13 344 12 345 10 336 10 347 9 338 10 319 11 3010 12 32



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1a List all 10 spin durations for top A in order from least to greatest.

b Determine the following statistics for top A, using the list above.

Range ______ Mode ______ Median ______ Mean ______

2a List all 10 spin durations for top B in order from least to greatest.

b Determine the following statistics for top B, using the list above.

Range ______ Mode ______ Median ______ Mean ______

3 Use the grid below to make a line plot of the data for both tops.

a Label your line plot along the side and the bottom.

b Number it to fit your data.

c Give your line plot a title and make a key to show which top is which.

Key

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4 What conclusion can you make about this experiment? Describe a possible ex-planation for Tanya and Patricks' results.

5 Partway through the investigation Tanya realized that they had actually changed two attributes instead of just one. She said when the radius changed the mass also changed. Please explain Tanya’s thinking.

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written by Raven Deerwater Anne E. Fischer Allyn Fisher