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LESSON 3 1 Name Date Time General Patterns and Special Cases 71 Copyright © Wright Group/McGraw-Hill 1. You are describing a general number pattern for a special case when you write a rule for a “What’s My Rule?” table. Write a rule for each table shown below. in out 813 11 16 20 25 105 110 Rule: Rule: 2. You are writing special cases for a general number pattern when you complete a “What’s My Rule?” table. Complete. Rule:Add the opposite of the number.Rule:Divide by the number. (xx0) (yy1) in out 12 4 21 7 60 20 300 100 Use the values from the table above to write special cases for the following general number patterns: xx0. Special cases Example:3 3 0 in out 30 25 7 53 yy1. Special cases Example:8 8 1 in out 81 9 1 4 100 103, 253

LESSON 3 1 Name Date Time Number Patterns 72 Copyright © Wright Group/McGraw-Hill Triangular, square, and rectangular numbers are examples of number patterns that can be shown by geometric arrangements of dots. Study the number patterns shown below. 1. Use the number patterns to complete the table. Number of Dots in Arrangement 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th Triangular Number 13 610 Square Number 14 916 Rectangular Number 2 6 12 20 2. What is the 11th triangular number? How does the 11th triangular number compare to the 10th triangular number? Triangular Numbers 1st 2nd 3rd 4th Square Numbers 1st 2nd 3rd 4th Rectangular Numbers 1st 2nd 3rd 4th

LESSON 3 1 Name Date Time Number Patterns continued 73 Copyright © Wright Group/McGraw-Hill 3. Describe what you notice about the sum of 2 triangular numbers that are next to each other in the table. 4. Add the second square number and the second rectangular number; the third square number and the third rectangular number. What do you notice about the sum of a square number and its corresponding rectangular number? 5. Describe any other patterns you notice. 6. You can write triangular numbers as the sum of 4 triangular numbers when repetitions are allowed. For example: 6 1 1 1 3 Find 3 other triangular numbers that can be written as sums of exactly 4 triangular numbers.            

STUDY LINK 3 1 Variables in Number Patterns Copyright © Wright Group/McGraw-Hill 74 Name Date Time 1. Following are 3 special cases representing a general pattern. 17 0 1743 0 43 7 80  7 8 a. Describe the general pattern in words. b. Give 2 other special cases for the pattern. For each general pattern, give 2 special cases. 2. (2 m) m3 m 3. s0.25 0.25 s For each set of special cases, write a general pattern. 4. 323 33 5 5. 7 0.1  17 0 6. 201 5 25 35 5 3 0.1  13 0 146 01 13 213 313 5 4 0.1  14 0 (1 2)01 103 Practice Complete. 7. 11 0 0.10 8. 1 4 ——— 0. 9. 1 50.20 10. 3 4  0.75 11. 4 50. 12. 17 0 0. 100 100 100 25 100

STUDY LINK 3 2 General Patterns with Two Variables 75 Name Date Time Copyright © Wright Group/McGraw-Hill For each general pattern, write 2 special cases. 1. (6 b) c6 (bc) For each set of special cases, write a number sentence with 2 variables to describe the general pattern. 4. 7 5 7 (5) 5. 4 6 4 6 3 3  12 8 12 (8) 1 2 1 2 3 3  9 1 9 (1) 2 5 2 5 3 3  General pattern: General pattern: 6. 16 0  16 0 2 2  7. 1 51 2 1 5 1 2  14 2 14 2 2 2  2 31 2 2 3 1 2  2 4  2 4 22  3 41 2 3 4 1 2  General pattern: General pattern: Write each fraction as a decimal. 8. 2 15 00 0  9. 1 10 06 0  10. 1 10 00 0  3. x yx 1 y (yis not 0) 2. a b 2(2 a) b Practice 103

LESSON 3 2 Name Date Time True and Not True Special Cases 76 Copyright © Wright Group/McGraw-Hill For each of the following, write one special case for which the sentence is true. Then write one special case for which the sentence is not true. 1. mnmn True Not true 2. a 2bab True Not true For each of the following, write at least 2 special cases for which the sentence is true. Circle each sentence that you think expresses a general pattern that is always true. 3. a22 a 4. If ais not 0, then a am n  = a mn 5. (ab) (ab) a 2b 2

STUDY LINK 3 3 General Patterns with Two Variables 77 Name Date Time Copyright © Wright Group/McGraw-Hill Write an algebraic expression for each situation. Use the suggested variable. 1. Kayla has xCDs in her music collection. If Miriam has 7 fewer CDs than Kayla, how many CDs does Miriam have? CDs 2. Chaz ran 2.5 miles more than Nigel. If Nigel ran dmiles, how far did Chaz run? miles 3. If a car dealer sells cautomobiles each year, what is the average number of automobiles sold each month? automobiles First translate each situation from words into an algebraic expression. Then solve the problem that follows. 4. The base of a rectangle is twice the length of the height. If the height of the rectangle is hinches, what is the length of the base? inches If the height of the rectangle is 4 inches, what is the length of the base? inches 240 5. Monica has 8 more than 3 times the number of marbles Regina has. If Regina has rmarbles, how many marbles does Monica have? marbles If Regina has 12 marbles, how many does Monica have? marbles 6. 2.75 m cm 7. 3.5 cm mm 8. 500 m km Try This Practice

1. When you cut a circular pizza, each cut goes through the center. Fill in the missing numbers in the table. Then write an algebraic expression that describes how many pieces you have when you make ccuts. pieces 2. Fold a sheet of paper in half. Now fold it in half again. And again. And again, until you can’t make another fold. After each fold, count the number of rectangles into which the paper has been divided. Fill in the missing numbers in the table. Write an algebraic expression to name the number of rectangles you have after you have folded the paper ktimes. rectangles 3. Below are the first 4 designs in a pattern made with square blocks. Draw Design 5 in this pattern. 4. How many square blocks will there be in a. Design 10? b. Design n? Design 5 Design 4 Design 3 Design 2 Design 1 LESSON 3 3 Name Date Time “What’s My Rule?” for Geometric Patterns 78 Copyright © Wright Group/McGraw-Hill Cuts Pieces 12 24 3 4 12 16 Folds Rectangles 01 12 2 3 4 5 6 1 cut 2 cuts 3 cuts

LESSON 3 3 Name Date Time More Algebraic Expressions 79 Copyright © Wright Group/McGraw-Hill Write each word phrase as an algebraic expression. 1. tincreased by 5 2. the product of wand 3 3. 7 less than g 4. mhalved 5. kshared equally by 8 people 6. 24 less than xtripled 7. bdecreased by 12 Evaluate each expression when y9.05. 8. y4.98 9. y8.9 10. y10 2 Write an algebraic expression for each situation. Then solve the problem that follows. 11. Talia earns ddollars per week. How much does Talia earn in 10 weeks? dollars If Talia earns $625.75 per week, how much does she earn in 10 weeks? dollars 12. Michelle is 5 years younger than Ruby, who is ryears old. Kyle is twice as old as Michelle. a. Using Ruby’s age, r,write an expression for: Michelle’s age years old Kyle’s age years old b. Suppose Ruby is 12 years old. Find: Michelle’s age years old Kyle’s age years old

STUDY LINK 3 4 “What’s My Rule?” Part 1 Copyright © Wright Group/McGraw-Hill 80 253 Name Date Time mn 4.56 4.34 10 9.78 0.010.21 12 04 0 0.02 7.80 7.58 rt 20 10 15 7.5 1 0.5 1.5 0.75 3.4 1.7 pq 7 12 10 18 10 15 28 30 58 Practice 1. a. State in words the rule for the “What’s My Rule?” table at the right. b. Which formula describes the rule? Fill in the circle next to the best answer. A nm0.22 B mn0.22 C mn0.22 2. a. State in words the rule for the “What’s My Rule?” table at the right. b. Which formula describes the rule? Fill in the circle next to the best answer. A r0.25 tB t0.12 rC r0.5 t 3. Which formula describes the rule for the “What’s My Rule?” table at the right? Fill in the circle next to the best answer. A q13 pB q(2 p) 2C q2 (p2) 4. 180 in. feet 5. 31 2minutes seconds 6. 5,280 ft yards 7. 51 2miles feet

LESSON 3 4 Name Date Time Special Cases for Formulas 81 Copyright © Wright Group/McGraw-Hill A formula is an example of a general pattern. When you substitute values for the variables in a formula, you are writing a special case for the formula. Area Formulas Example: To find the area of a rectangle, use the formula Ab h. Write a special case for the formula using b12 cm and h3 cm. First substitute only the value of b. A12 cmh Next substitute the value of h. A12 cm 3 cm Now find the value of Aand write the special case. 36 cm 212 cm 3 cm 1. To find the area of a triangle, use the formula A 1 2(bh). Find the value of Aand write a special case for the formula using b4.5 cm and h4.8 cm. cm 2 1 2( cm cm) 2. To find the area of a square, use the formula As 2. Find the value of Aand write a special case for the formula using b2.5 ft and h2.5 ft. ft 2ft 2 s b h h b

LESSON 3 4 Name Date Time Formula for a Brick Wall 82 Copyright © Wright Group/McGraw-Hill Suppose you were going to build a brick wall. It would be useful to estimate the number of bricks you would need. You could do this if you had a formula for estimating the number of bricks for any size wall. Study the following information. Then follow the instructions for measuring an actual brick wall. Try to devise a formula for estimating the number of bricks needed to build any size wall. A brick wall is built by putting layers of bricks on top of one another. The space between the bricks is filled with a material called mortar,which hardens and holds the bricks in place. The mortar between the bricks forms the mortar joint. A standard building brick is 2 1 4inches by 8 inches by 3 3 4inches. The face that is 2 1 4inches by 8 inches is the part of the brick that is visible in a wall. Equivalents: 1 ft 12 in. 1 ft 212 in. 12 in. 144 in. 2 1. Find a brick wall in your school, home, or neighborhood. Using a ruler or tape measure, measure the length and height of the wall or part of the wall. Count the bricks in the area you measured. a. Length b. Height c. Number of bricks d. Measure the width of the mortar joint in several places. Decide on a typical value for this measurement. The mortar joints are each about inch(es) wide. 2. Devise a formula for calculating the number of bricks needed to build a wall. Let lstand for the length of the wall in feet. Let hstand for the height of the wall in feet. Let Nstand for the estimated number of bricks needed to build the wall. a. The area of this wall (the side you see) is square feet. b. My formula for the estimated number of bricks: N 3. Test your formula. Use the length and width you measured in Problem 1. Does the formula predict the number of bricks you counted? mor tar joint width mortar 8 in. 4 12 in. 4 33 in. l (ft) h (ft) (unit) (unit)

1. Rule:Subtract the in number from 11 1 2. 2. Formula: r4 s 3. Rule:Triple the innumber and add 6. STUDY LINK 3 5 “What’s My Rule?” Part 2 83 253 Name Date Time Copyright © Wright Group/McGraw-Hill in out bd 1.5 0.5 63 4 21 4 24 8 81 27 9.75 3.25 in out xy in out x(3x) (6) 13 2 15 8 6 4. For the table below, write the rule in words and as a formula. Rule: Formula: 5. Make up your own. Rule: Formula: 6. 3 6  7. 17 5  8. 8 (2) (9)  9. 5 3 (5) 7  in out n11 1 2n 1 2 81 2 5 12 in out sr 12 24 0.3 1 1 2 Practice

LESSON 3 5 Name Date Time Rates 84 Copyright © Wright Group/McGraw-Hill Solve the rate problems. You can use tables similar to “What’s My Rule?” tables to help you find the answers, if needed. 1. Renee reads 30 pages per hour. a. At this rate, how many pages can she read in 3 hours? (unit) b. Would she be able to read a 220-page book in 7 hours? 2. Wilson was paid $105 to cut 7 lawns. At this rate, how much was he paid per lawn? 3. Gabriel blinks 80 times in 5 minutes. a. At this rate, how many times does he blink in 2 minutes? (unit) b. In 4 minutes? (unit) 4. Michael can bake 9 batches of cookies in 3 hours. At this rate, how many batches can he bake in 2 hours? (unit) 5. Elizabeth can run 5 miles in 2 3of an hour. At this rate, how long does it take her to run 1 mile? (unit) Hours Pages 130 2 3 Lawns Dollars 7 105 6 5 Minutes Blinks 580 4 3 Hours Batches 39 2 1 Hours Miles 5 1 2 3  1 3

LESSON 3 6 Name Date Time When an Object Is Dropped 85 Copyright © Wright Group/McGraw-Hill 0 0 900 800 700 600 500 400 300 200 100 1,0001,100 1,200 1,300 123456789 Time in Seconds (t) Distance in Feet (d)

STUDY LINK 3 6 Area and Perimeter Copyright © Wright Group/McGraw-Hill 86 212, 214, 215 Name Date Time 1. Use the perimeter and area formulas for squares to complete the table. Use the table above to complete the graphs on Math Masters,page 87. Length of side (in.) Perimeter (in.) Area (in. 2) 1 2 3 4 5 P4 º sss As 2 s s Perimeter Area

STUDY LINK 3 6 Name Date Time Area and Perimeter continued 87 Copyright © Wright Group/McGraw-Hill 2. Graph the perimeter data from the table on page 86. Use the grid at the right. Use the graph you made in Problem 2 to answer the following questions. 3. If the length of the side of a square is 2 1 2inches, what is the perimeter of the square? (unit) 4. If the length of the side of a square is 4 1 4inches, what is the perimeter of the square? (unit) 5. Graph the area data from the table on page 86. Use the grid at the right. Use the graph you made in Problem 5 to answer the following questions. 6. If the length of the side of a square is 1 1 2inches, what is the approximate area of the square? About (unit) 7. If the length of the side of a square is 3 1 4inches, what is the approximate area of the square? About (unit) Find the missing dimension for each rectangle. 8. b5.5 cm; h 9.9 cm; Acm 2 9. b36 in.; hin.; A151.2 in. 2 0 2 4 6 8 10 12 14 16 18 20012345 Length of Side (in.) Perimeter (in.) 2 4 6 8 10 12 14 16 18 20 22 0 24 1234 05 Length of Side (in.) Area (in. 2) Practice

LESSON 3 6 Name Date Time Using Graphs to Make Predictions 88 Copyright © Wright Group/McGraw-Hill Radio station WSUM has a contest in which listeners call in to win money. The contest begins with a $200 jackpot. One caller each hour can win the jackpot by correctly answering a math question. If the caller does not give a correct answer, $25 is added to the jackpot for the next hour. 1. Some available jackpot amounts for callers appear in the table below. Complete the table. Then graph the data values from the table. 12345678910 150 200 250 300 350 400 450 500 Caller Number (n) Jackpot Amount ($) WSUM Contest Caller Jackpot Number (n) Amount ($) 1 200 2 225 3 275 5 2. Suppose you were the eighth caller to WSUM and you answered correctly. Extend your graph to predict the amount of money you would win. 3. The formula (n 1) º $25 $200 can be used to express the jackpot amount for any caller. Use this formula to complete the table below. Refer to page 247 of the Student Reference Bookif you need to review the order of operations. Rule:(n 1) º $25 $200 in out n(n1) º $25 $200 2 $225 4 15 $825 101 Predict the number of the caller who would win a jackpot of $1,000,000. Use the formula (n 1) º $25 $200 to check your prediction. Try This

STUDY LINK 3 7 Spreadsheet Practice 89 142–144 Name Date Time Copyright © Wright Group/McGraw-Hill Ms. Villanova keeps a spreadsheet of her monthly expenses. Use her spreadsheet to answer the questions below. 1. What is shown in cell B1? 2. What is shown in cell C4? 3. Which cell contains the word Rent? 4. Which cell contains the amount $58.50? 5. Ms. Villanova used column E to show the total for each row. Find the missing totals and enter them on the spreadsheet. 6. Write a formula for calculating E3 that uses cell names. 7. Write a formula for calculating E5 that uses cell names. 8. Ms. Villanova found that she made a mistake in recording her March phone bill. Instead of $25.35, she should have entered $35.35. After she corrects her spreadsheet, what will the new total be in cell E3? ABCDE 1 January February MarchTotal 2 Groceries $125.25 $98.00 $138.80 $362.05 3 Phone Bill $34.90 $58.50 $25.35 4 Car Expenses $25.00 $115.95 $12.00 5 Rent $875.00 $875.00 $875.00 Practice Find the missing dimension for each square. 9. s12 cm; Acm 2 10. sin.; A81 in. 2 11. s8.6 mm; Amm 2 12. sft; A289 ft 2

STUDY LINK 3 8 Copyright © Wright Group/McGraw-Hill 90 95 96 Name Date Time Solve. 1. b9 3; b 2. 5 a1; a 3. m(5) 4; m 4. k3 3; k Add. 5. 13 (5)  6. (10) 12  7. (7) (8) 8. (15) 10 9. (4) (9)  10. 7 (19) 11. Complete the “What’s My Rule?” table. Adding Positive and Negative Numbers xy 82 42 24 6 8 15 a. Give the rule for the table in words. b. Circle the formula that describes the rule. x6 yxº (6) yx(6) y 6xy 12. Evaluate when k5. a. k2 b. 2k c. 10k d. 24 k 13. Evaluate when x1. a. 10 x b. 2x c. (1 2)x d. x(8) Practice

LESSON 3 8 Name Date Time Spreadsheet ScrambleProblems 91 Copyright © Wright Group/McGraw-Hill Study the completed Spreadsheet Scramble game mat at the right. Player 1 gets 1 point each for F3, F4, and C5. Player 2 gets 1 point each for F2 and E5. Player 1 wins the game, 3 points to 2 points. Notice that if the numbers in cells C2 and B4 were interchanged and new totals were calculated, Player 2 would win the game, 4 points to 2 points. Can you switch the values of two other cells so that Player 2 would win the game? 1. Which cells would you interchange? 2. What would be the new score of the game? Player 1 Player 2 3. Fill in the new game mat. Total Total 1 2 3 4 5ABCDE F 16 3 5 9 42 46 8 351 2 1 0 10 1 Total Total 1 2 3 4 5ABCDE F 163 5 9 42 46 8 351 2 1 0 10 1 Total Total 1 2 3 4 5ABCDE F 133 56 42 46 8 651 2 2 340 1 Total Total 1 2 3 4 5ABCDE F

LESSON 3 9 Name Date Time A Time Story 92 Copyright © Wright Group/McGraw-Hill Satya runs water into his bathtub. He steps into the tub, sits down, and bathes. He gets out of the tub and drains the water. The graph shows the height of the water in the tub at different times. Time Height of Water in Tub

STUDY LINK 3 9 Ferris Wheel Time Graph 93 140 Name Date Time Copyright © Wright Group/McGraw-Hill The time graph below shows the height of Rose’s head from the ground as she rides a Ferris wheel. Use the graph to answer the following questions. 0 0 10 20 30 40 50 60 Time (sec) Height (ft) 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 1. Explain what is happening from 0 to 95 seconds. 2. How long is Rose on the Ferris wheel before she is back to the position from which she started? About (unit) 3. After the Ferris wheel has been completely loaded, about how long does the ride last before unloading begins? (unit) 4. After the Ferris wheel has been loaded, how many times does the wheel go around before unloading begins? (unit) 5. When the ride is in full swing, approximately how long does one complete revolution of the wheel take? (unit) 6. Rose takes another ride. After 130 seconds, the Ferris wheel comes to a complete stop because of an electrical failure. It starts moving again 2 minutes later. Complete the graph to show this event. 0 20 0 10 20 30 40 50 60 40 60 80 100 120 140 160 Time (sec) Height (ft) 180 200 220 240 260 280 300 320 340 Try This

LESSON 3 9 Name Date Time Matching Events, Tables, and Graphs Copyright © Wright Group/McGraw-Hill Cut out the situations, tables, and graphs. After you match each situation with one table and one graph, tape or glue them onto a separate sheet of paper. When you are finished, you will have one table and one graph left over. A fern was growing rapidly in its pot for a while until it didn’t get enough water. The fern then stopped growing. A fern was growing slowly in its pot due to a lack of sunlight. When the fern was moved to a nearby windowsill, it began to grow more rapidly. A fern was growing rapidly in its pot for a while until it was knocked over and a dog bit off the top. It stopped growing for a while before it eventually began to grow again. Table 1 Week Height 1 4 in. 2 6 in. 3 8 in. 4 9.5 in. 5 7 in. 6 7 in. 7 8 in. Table 3 Week Height 14 in. 2 4.5 in. 35 in. 4 5.5 in. 56 in. 68 in. 7 10 in. Table 4 Week Height 1 4 in. 2 6 in. 3 8 in. 4 10 in. 5 12 in. 6 12 in. 7 12 in. Table 2 Week Height 1 4 in. 2 5 in. 3 6 in. 4 7 in. 5 8 in. 6 9 in. 7 10 in. Time Height Graph A Time Height Graph B Time Height Graph C Time Height Graph D 94

LESSON 3 9 Name Date Time Mystery Graphs 95 Copyright © Wright Group/McGraw-Hill Make a mystery graph on the grid below. Be sure to label the horizontal and vertical axes. Describe the situation that corresponds to your graph on the lines provided.

STUDY LINK 3 10 Comparing Pet-Sitting Profits Copyright © Wright Group/McGraw-Hill 96 254 Name Date Time Jenna and Thomas like to pet-sit for their neighbors. Jenna charges $3 per hour. Thomas charges $6.00 for the first hour and $2 for each additional hour. 1. Complete the table below. Use the table to graph the profit values for each sitter. 1 0 23456 0 2 4 6 8 10 12 14 16 18 Time (Hours) Profit ($) Time Jenna’s Profit ($) Thomas’s Profit ($) (hours) 1 2 3 4 5 2. Extend both line graphs to find the profit each sitter will make for 6 hours. Jenna (6 hours) Thomas (6 hours) 3. Which sitter, Jenna or Thomas, earns more money for jobs of 5 hours or more? 4. Which line graph rises more quickly? 5. Complete each statement. For every hour that passes, Jenna’s profit increases by ; Thomas’s profit increases by . 6. At what point do the line graphs intersect? Practice 7. Evaluate when m3. a. m4 b. 20 m c. 4m 4m d. 10 m 5 m e. m m 3 2 

LESSON 310 Name Date Time Reviewing Rules, Tables, and Graphs 97 Copyright © Wright Group/McGraw-Hill Rule: 0 0 (Label for x-axis) (Label for y-axis) in out

LESSON 3 10 Name Date Time Rate of Change Experiment 98 Copyright © Wright Group/McGraw-Hill Using a metric measuring cup, pour 100 mL of water into each of 4 bottles of different shapes. Each time you add water to a bottle, measure the height of the water level in centimeters. On a separate sheet of paper, make a table to record each change in volume and water height. Use your table to make a graph for each bottle on the grids below. Volume (mL) Height of Water (cm) 0 0 Volume (mL) Height of Water (cm) 0 0 Volume (mL) Height of Water (cm) 0 0 Volume (mL) Height of Water (cm) 0 0 Bottle 1 Bottle 2 Bottle 3 Bottle 4

LESSON 3 10 Name Date Time 99 Copyright © Wright Group/McGraw-Hill 1 2 3 4 5 Volume (mL) Height of Water (cm) 0 0 Graph A Volume (mL) Height of Water (cm) 0 0 Graph C Volume (mL) Height of Water (cm) 0 0 Graph D Volume (mL) Height of Water (cm) 0 0 Graph E Assume the bottles are filled with water at a constant rate. Match the graphs with their bottles. Write the letter of the graph under the bottle it represents. The Shape of Change 0 0 Volume (mL) Height of Water (cm) Graph B

STUDY LINK 3 11 Unit 4: Family Letter Copyright © Wright Group/McGraw-Hill 100 Name Date Time Rational Number Uses and Operations One reason for studying mathematics is that numbers in all their forms are an important part of our everyday lives. We use decimals when we are dealing with measures and money, and we use fractions and percents to describe parts of things. Students using Everyday Mathematicsbegan working with fractions in the primary grades. In Fifth Grade Everyday Mathematics,your child worked with equivalent fractions, operations with fractions, and conversions between fractions, decimals, and percents. In Unit 4, your child will revisit these concepts and apply them. Most of the fractions with which your child will work (halves, thirds, fourths, sixths, eighths, tenths, and sixteenths) will be fractions that they would come across in everyday situations— interpreting scale drawings, following a recipe, measuring distance and area, expressing time in fractions of hours, and so on. Students will be exploring methods for solving addition and subtraction problems with fractions and mixed numbers. They will look at estimation strategies, mental computation methods, paper-and-pencil algorithms, and calculator procedures. Students will also work with multiplication of fractions and mixed numbers. Generally, verbal cues are a poor guide as to which operation (, , º, /) to use when solving a problem. For example, moredoes not necessarily imply addition. However, many ofand part ofgenerally involve multiplication. At this point in the curriculum, your child will benefit from reading and understanding 1 2º12 as one-half of 12,rather than one-half times 12;or reading and understanding 1 2º 1 2as one-half of one-half,rather than one-half times one-half. Finally, students will use percents to make circle graphs to display the results of surveys and to learn about sales and discounts. Please keep this Family Letter for reference as your child works through Unit 4. Jambalaya Recipe 1 8teaspoon salt 3 4cup rice 4 ounces each of chicken and sausage 4 cups peppers 1 cups chopped onions 2 3 1 tablespoons chopped thyme1 2

101 Copyright © Wright Group/McGraw-Hill Math Tools The Percent Circle,on the Geometry Template, is used to find the percent represented by each part of a circle graph and to make circle graphs. The Percent Circle is similar to a full-circle protractor with the circumference marked in percents rather than degrees. This tool allows students to interpret and make circle graphs before they are ready for the complex calculations needed to make circle graphs with a protractor. Vocabulary Important terms in Unit 4: common denominator A nonzero number that is a multiple of the denominators of two or more fractions. For example, the fractions 1 2and 2 3have common denominators 6, 12, 18, and other multiples of 6. Fractions with the same denominator already have a common denominator. common factor A factor of two or more counting numbers. For example, 4 is a common factor of 8 and 12. discount The amount by which a price of an item is reduced in a sale, usually given as a fraction or percent of the original price, or a percent off. For example, a $4 item on sale for $2 is discounted by 50%, or 1 2. A $10.00 item at “10% off!” costs $9.00, or 11 0less than the usual price. equivalent fractions Fractions with different denominators that name the same number. greatest common factor (GCF) The largest factor that two or more counting numbers have in common. For example, the common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12, and their greatest common factor is 12. improper fraction A fraction whose numerator is greater than or equal to its denominator. For example, 4 3, 5 2, 4 4, and 2 14 2are improper fractions.InEveryday Mathematics,improper fractions are sometimes called top-heavy fractions. interest A charge for the use of someone else’s money. Interest is usually a percentage of the amount borrowed. least common denominator (LCD) The least commonmultiple of the denominators of every fraction in a given collection. For example, the least common denominator of 1 2, 4 5, and 3 8is 40. least common multiple (LCM) The smallest number that is a multiple of two or more given numbers. For example, common multiples of 6 and 8 include 24, 48, and 72. The least common multiple of 6 and 8 is 24. mixed number A number that is written using both a whole number and a fraction. For example, 2 1 4is a mixed number equal to 2  1 4. percent (%) Per hundred, for each hundred, or out of a hundred. 1%  11 00 0.01. For example, 48% of the students in the school are boysmeans that out of every 100 students in the school, 48 are boys. proper fraction A fraction in which the numerator is less than the denominator. A proper fraction is between 1 and 1. For example, 3 4,  2 5, and 2 21 4are proper fractions. Compare toimproper fraction. Everyday Mathematicsdoes not emphasize these distinctions. Unit 4: Family Letter cont. STUDY LINK 311 5% 15% 30% 35% 40% 45% 55% 60% 65% 70%80%85%90%95%0% 10% 20% 25% 50% 75% 1/5 1/6 1/101/8 1/3 1/4 2/3

Copyright © Wright Group/McGraw-Hill 102 Do-Anytime Activities Try these ideas to help your child with the concepts taught in this unit. 1.Consider allowing your sixth grader to accompany you on shopping trips when you know there is a sale. Have him or her bring a calculator to figure out the sale price of items. Ask your child to show you the sale price of the item and the amount of the discount. If your child enjoys this activity, you might extend it by letting him or her calculate the total cost of an item after tax has been added to the subtotal. One way to calculate the total cost is simply to multiply the subtotal by 1.08 (for 8% sales tax). For example, the total cost of a $25 item on which 8% sales tax is levied would be 25 º1.08 25 º(1 0.08) (25 º1) (25 º0.08) 25 2 27, or $27. 2.On grocery shopping trips, point out to your child the decimals printed on the item labels on the shelves. These often show unit prices (price per 1 ounce, price per 1 gram, price per 1 pound, and so on), reported to three or four decimal places. Have your child round the numbers to the nearest hundredth (nearest cent). 3.Your child’s teacher may display a Fractions, Decimals, Percents Museum in the classroomand expect students to contribute to this exhibit. Help your child look for examples of the ways in which printed advertisements,brochures, and newspaper and magazine articles use fractions, decimals, and percents. In Unit 4, your child will work on his or her understanding of rational numbers by playing games like the ones described below. Fraction Action, Fraction FrictionSeeStudent Reference Book,page 317 Two or three players gather fraction cards that have a sum as close as possible to 2, without going over. Students can make a set of 16 cards by copying fractions onto index cards.Frac-Tac-ToeSee Student Reference Book, pages 314–316 Two players need a deck of number cards with 4 each of the numbers 0–10; a game board, a 5-by-5 grid that resembles a bingo card; a Frac-Tac-ToeNumber-Card board; markers or counters in two different colors, and a calculator. The different versions of Frac-Tac-Toehelp students practice conversions between fractions, decimals, and percents. Building Skills through Games Unit 4: Family Letter cont. STUDY LINK 311 quick common denominator (QCD) The product of the denominators of two or more fractions. For example, the quick common denomina- tor of 3 4and 5 6is 4 º6, or 24. In general, the quick common denominator of baand dcis bºd.As the name suggests, this is a quick way to get a common denominatorfor a collection of fractions, but it does not necessarily give the least common denominator. simplest form of a fraction A fraction that cannot be renamed in simpler form. Also called“lowest terms.” A mixed number is in simplest form if its fractional part is in simplest form. Simplest form is not emphasized in Everyday Mathematicsbecause other equivalent forms are often equally or more useful. For example, when comparing or adding fractions, fractions with a common denominator are likely to be easier to work with than fractions in simplest form.

103 Copyright © Wright Group/McGraw-Hill As You Help Your Child with Homework As your child brings assignments home, you may want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through some of this unit’s Study Links. Study Link 4 1 Sample answers for problems 1–16. 1. 18 0 2. 1 24 0 3. 2 8 4. 4 6 5. 1 80 6. 4 4 7. 3 4 8. 1 5 9. 1 4 10. 5 2 11. 1 5 12. 2 3 13. 2 6, 3 9, 14 2 14. 3 4, 1 25 0, 1 25 00 0 15. 6 1, 1 22, 1 38 16. 2 14 0, 3 16 5, 4 28 0 17. 1 2 18. 2 3 19. 1 5 20. 2 5 21. 3 8 22. 2 7 23.x324.y1225.m30 26.27 1 4 27.29 1 5 28.29 2 7 Study Link 4 2 1. 2. 3. 4. 5. 6. 7. 1 3, 2 5, 1 22 5 8. 11 2, 1 5, 1 3, 2 5, 17 4, 16 0, 1 15 6, 4 59 0 9.9.89710.3.83211.0.82312.4.357 Study Link 4 3 1. 1 2 2.1 11 6 3.2 1 23 0 4. 2 3 5. 1 11 2 6.1 1 6 7.1 48 5 8.2 9. 3 8 10.1 14 5 11. 1 3 12. 1 2 13.1 3 4 14. 11 0 15.2.716.0.58 17.1.98 Study Link 4 4 1. a.Sample answer: They may have added only the numerators. b.Sample answer: Both fractions are close to 1, so their sum should be close to 2. 2.1 1 4inches 3.Sample answer: He can use three 1 2-cup measures and one 1 4-cup measure. 4.4 1 2 5.1 3 4 6.2 1 3 7.1 7 4, 1 41 8.909.24610.432 11.315 Study Link 4 5 1. a.8 1 2in.b.1 1 2in.; 1 4in. 2. a.2 1 2bushelsb.30 quarts 3.44. 2 3 5.5 1 6 6. 5 9 7.1 5 8 8.69.6 3 5 10.1 15 2 11.2 1 21 0 12.1413.17.914.$21.99 15.20 Study Link 4 6 1. 26 0 2. 1 65 3 3. 1 85or 1 7 8 4. 1 41 8 5. 3 45 8 6. 12 01 0 7. 1 44 5 8. 3 72or 4 4 7 9. 9 16 1, or 8 18 1 10. 1 5of the points 11.2 1 4cups12. 17 2of the sixth graders 13. a. 1 2the girlsb.6 girls 14.915.0.116.0.1 Unit 4: Family Letter cont. STUDY LINK 311

Copyright © Wright Group/McGraw-Hill 104 Unit 4: Family Letter cont. STUDY LINK 311 Study Link 4 7 1. 9 5 2. 1 68 3. 1 37 4. 7 2 5.36.4 1 8 7.2 1 2 8.6 2 3 9.310.4 1 5 11.2 11 2 12.5 4 9 13.7 3 31 2 14.2015.2816.63 17.63 Study Link 4 8 1. 18 0, 80%2. 17 05 0, 75% 3. 13 00 0, 13 0 4.0.55.0.756.0.257.1.8 8. 2 5 9. 11 0 10. 1 27 5 11. 1 4 12.50%13.25%14.60%15.95% 16. 15 00 0, 1 2 17. 14 00 0, 2 5 18. 1 10 00 0, 119. 1 18 00 0, 1 4 5 Study Link 4 9 1.65%2.33.4%3.2%4.40% 5.270%6.309%7.0.278.0.539 9.0.0810.0.6011.1.8012.1.15 13.0.88, 88%14.0.42, 42% Study Link 4 10 Problems 1– 4 are circle graphs. Study Link 4 11 1.Table entries: 150, 100, 125, 125 students 2.Table entries: 18, 12, 15, 15 students 3. a.3.3b.8.8c.22