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STUDY LINK 71 Outcomes and Probabilities 217 Name Date Time Copyright © Wright Group/McGraw-Hill Complete the table. Use the problems from the table to answer the following questions. Express each probability as a percent. 3. What is the probability of selecting a quarter from the coins in Problem 1? 4. What is the probability of choosing a factor of 20 from the cards in Problem 2? 5. Suppose you spin the spinner from the Example in the table. Complete the number sentence below to determine the probability of the spinner landing on A or C.  Probability of A Probability of C Probability of A or C Simplify the expression using the order of operations. 6. 3.8 6.4 0.2 1.8 º 2.6 3.2 0.8 Possible Outcomes Experiment Outcomes Equally Likely? Example: Spin the spinner. 1. Choose a coin. 2. Choose a factor of 20. 12010 24 5 D D D D N Q Q Q A CB No. The area for C is twice as large as each of the other 2 areas. A, B, C Practice 150–153

Booth 1 Two in a Row Flip a coin twice. If the coin lands on the same side both times, you win a prize coupon. Booth 3 Roll It Up Roll a die twice. If the second roll is a greater number than the first, you win a prize coupon. Booth 5 Make the Call Predict the roll of a die. If that number comes up, you win a prize coupon. Booth 2 Odd Tail Toss Flip a coin once and roll a die once. If you get TAILS and an odd number, you win a prize coupon. Booth 4 10 or More Roll a die twice. If you get 5 or greater both times, you win a prize coupon. Booth 6 7 or More Roll a die twice. If the total of the rolls is 7 or greater, you win a prize coupon. LESSON 71 Name Date Time Carnival Games 218 Copyright © Wright Group/McGraw-Hill At the carnival, you will play 10 games and will try to win as many prize coupons as possible. You must visit at least three different booths.

LESSON 71 Name Date Time Carnival Games Records 219 Copyright © Wright Group/McGraw-Hill Below, record the number of each booth you visit. Make a tally mark for each prize coupon you win during your 10 games. 1. Describe a strategy for winning the greatest number of prize coupons in 10 games if you must visit at least 3 different booths. 2. At which booths does it seem easy to win? 3. Describe how you would change the rules of one game to make it easier to win. Booth Number Number of Prize Coupons Won Total Number of Prize Coupons Won

LESSON 72 Name Date Time Random-Number Results 220 Copyright © Wright Group/McGraw-Hill 1 2 3 4 5 Total 100% Outcome Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 All Groups % of Total

STUDY LINK 72 Using Random Numbers 221 Name Date Time Copyright © Wright Group/McGraw-Hill 1. A gym teacher is dividing her class into two teams to play soccer. Do you think she should choose the teams at random? Explain. 2. The entire school is going to a baseball game. Some seats are better than others. Should the principal select the section where each class will sit at random? Explain. 3. The spinner at the right has landed on black 5 times in a row. Renee says, “On the next spin, the spinner is more likely to land on white than on black.” Do you agree or disagree with Renee? Explain. 4. The spinner at the right has landed on black 5 times in row. Matthew says, “On the next spin, the spinner has a better chance of landing on white than on black.” Do you agree or disagree with Matthew? Explain.

LESSON 72 Name Date Time Predict Which Blocks Are in a Bag 222 Copyright © Wright Group/McGraw-Hill 1. Pick one person in your group to be the Director. 2. The Director selects 5 blocks and hides them in a bag. The blocks should NOT all be the same color. The group members should NOT see the blocks. 3. Group members take turns drawing one block out of the bag without looking. Each time a block is drawn, group members tally the color. Example(for first 5 draws): 4. The person who drew the block puts it back into the bag, shakes the bag, and gives it to the next person to draw. 5. After 5 draws, each person writes a prediction for how many blocks of each color are in the bag. 6. Discuss the group’s predictions. If everyone has the same prediction, the Director shows the contents of the bag and checks the prediction. 7. If your group does not agree on a prediction, take turns making 5 more draws (for a total of 10). Everyone predicts again and compares predictions. 8. Continue until the group agrees on a prediction. Then the Director shows the contents of the bag. Repeat this experiment with a different number of blocks in the bag. Try it with 3 blocks. Try it with 7 blocks. 9. Does the number of blocks in the bag make a difference? Explain. 10. Do you think there must be a minimum number of draws to make an informed decision about the contents of the bag? Explain. red //// blue /

LESSON 72 Name Date Time A Table of Random Digits 223 Copyright © Wright Group/McGraw-Hill This is a table of 500 random digits, which includes the digits 0 through 9. Sometimes statisticians generate random numbers for projects or studies they are conducting by using a random digits table. 1. About what percent of the time would you expect each digit to appear? About 2. Use the table at the right to make a tally of the digits. Use a calculator to find what percent of the total each digit appears. 3. Are the digits random in the table of 500 digits? 9 4 0 1 5 4 6 8 7 4 3 2 4 4 4 4 8 2 7 7 5 9 8 2 0 9 6 1 6 3 6 4 6 5 4 2 5 8 4 3 4 1 1 4 5 4 2 8 2 0 7 4 1 0 8 8 8 2 2 2 8 8 5 7 0 7 4 0 1 5 2 5 7 0 4 9 1 0 3 5 0 1 7 5 5 1 4 7 5 0 4 8 9 6 8 3 8 6 0 3 6 2 8 8 0 8 7 8 7 3 9 5 1 6 0 5 9 2 2 1 2 2 3 0 4 9 0 3 1 4 7 2 8 7 7 1 7 3 3 4 3 9 2 8 3 0 4 1 4 9 1 1 7 4 8 1 2 1 0 2 8 0 5 8 0 4 1 8 6 7 1 7 7 1 0 5 9 6 2 1 0 6 5 5 4 0 7 8 5 0 7 3 9 5 0 7 9 5 5 2 1 7 9 4 4 0 5 6 0 0 6 0 4 7 8 0 3 3 4 3 2 5 8 5 2 5 8 9 0 5 5 7 2 1 6 3 9 6 1 8 4 9 8 5 6 9 9 3 2 6 6 6 0 6 7 4 2 7 9 2 9 5 0 4 3 5 2 6 8 0 4 6 7 8 0 5 6 4 8 7 0 9 9 7 1 5 9 4 8 1 3 7 0 0 6 2 2 1 8 6 5 4 2 4 4 9 1 0 3 0 4 5 5 4 7 7 0 8 1 8 5 9 8 4 9 9 6 1 6 9 6 1 4 5 9 2 1 6 4 7 8 7 4 1 7 1 7 1 9 8 3 0 9 4 5 5 7 5 8 9 3 1 7 3 2 5 7 2 6 0 4 7 6 7 0 0 7 6 5 4 4 6 3 7 6 2 5 3 6 6 9 4 7 4 6 4 9 5 8 0 6 9 1 7 0 3 7 4 0 3 8 6 9 9 5 9 0 3 0 7 9 4 3 0 4 7 1 8 0 3 2 6 8 2 5 0 5 5 1 1 1 2 4 5 9 9 1 3 1 4 0 8 3 4 5 8 8 9 7 5 3 5 8 4 1 8 5 7 7 1 0 8 1 0 5 5 9 9 8 7 8 7 1 1 2 2 1 4 7 6 1 4 7 1 3 7 1 1 8 1 DigitTally of Number of Percent of Appearances Appearances Total 0 1 2 3 4 5 6 7 8 9 Total 500 500 100%

STUDY LINK 7 3 Making Organized Lists Copyright © Wright Group/McGraw-Hill 224 Name Date Time Solve each problem by making an organized list. The list in Problem 1 has been started for you. 1. In how many ways can you make $0.60 using at least 1 quarter? You can only use quarters, dimes, and nickels. D D D N Q 3 6 10 QDN 131 10 6 3 Total pts pts pts pts 2. You throw three darts and hit the target at the right. List the different total points that are possible. Use what you know about angle measures of sectors to find the probabilities in Problem 3. Example: Probability of landing on striped sector  1 35 60 0   15 241.67% 3. Find the probability of the spinner landing on a. white. b. black. 156

LESSON 7 3 Name Date Time Coin-Toss Experiment 225 Copyright © Wright Group/McGraw-Hill Step 1Working alone, toss a coin 10 times for Round 1. Enter a tally mark for each time a HEAD or a TAIL occurs in Round 1. Step 2Repeat Step 1 for Rounds 2–5, for a total of 50 tosses. Step 3 a. Record the total number of HEADS and TAILS for your 50 tosses from the frequency table above. My Totals HEADS 50 TAILS 50 b. Record your partner’s HEADS and TAILS totals for all 5 rounds. My Partner’s Totals HEADS 50 TAILS 50 c. Combine your totals with those of your partner. Partnership Totals HEADS 100 TAILS 100 (Step 3a Step 3b) d. Now combine your partnership totals with those of the others in your group. Group Totals HEADS TAILS (Step 3c Step 3d) Coin-Toss Data Round HEADS TAILS 1 2 3 4 5 Totals

LESSON 7 4 Name Date Time Tree Diagrams 226 Copyright © Wright Group/McGraw-Hill BB AA AA AB BBA AB

LESSON 74 Name Date Time Maze 227 Copyright © Wright Group/McGraw-Hill Room A Enter Room B 4 3 2 1 2 1 2 2 2 1 1 1

STUDY LINK 74 Lists and Tree Diagrams Copyright © Wright Group/McGraw-Hill 228 Name Date Time Suppose members of the hiking club are served a breakfast bag whenever they have a Saturday morning meeting. Members use the form at the right to place their orders. Breakfast Order Form Beverage  Milk Water Bagel  Plain Raisin Fruit  Apple  Banana  Orange 1. Complete the organized list of the possible breakfast bags. 2. Use your organized list to complete the tree diagram. Beverage Bagel Fruit MPA MPB Beverage Bagel Fruit WP A WP B 3. How many different breakfast bags are possible? 4. Suppose 60 members fill out an order form. About how many people would you expect to order milk and a plain bagel? people 5. Suppose each of the 60 members brings 2 guests to the next Saturday meeting. About how many people would you expect to order water, a raisin bagel, and an orange? people P R M W

LESSON 7 4 Name Date Time An Amazing Contest 229 Copyright © Wright Group/McGraw-Hill The sixth graders at Bailey School want to raise money to buy a microscope. Students have created the maze shown below, which they will use for a contest. Each contestant pays a fee and tries to go from Start to Exit without retracing any steps. Anyone not ending up at a dead end wins a prize. The paths at each intersection are numbered. When a contestant reaches an intersection, the contestant chooses the next path at random, using number cards. Suppose you are going to try the maze. There are 3 different paths at Start. To decide which path to follow, pick a card, without looking, from a set of cards having 1, 2, and 3. If the card you draw is 1, follow Path 1. This leads to a dead end, so you lose. If the card you choose at Start is 2, follow Path 2. This leads to an intersection that divides into 4 different paths. Pick from a set of cards having 1, 2, 3, and 4 to see which path to follow next. You win if you follow Path 3. If you choose the number 3 at Start, follow Path 3. This leads to an intersection that divides into 2 different paths. Pick from a set of cards having 1 and 2 to see which path to follow next. You win if you follow Path 2. Work with a partner. Take turns trying to get through the maze. Each of you should try a total of 6 times. What fraction of the time did you and your partner reach Exit? I reached Exit of the time. My partner reached Exit of the time. Start Exit 11 1 22 2 33 4

LESSON 7 4 Name Date Time Analyzing the Amazing Contest 230 Copyright © Wright Group/McGraw-Hill Make a tree diagram of the contest maze to help you solve the following problems. 1. If 60 people enter the maze, how many would you expect to reach the exit? 2. Suppose the class charges $5 per person to enter the maze. How much money would the class collect from the contestants? 3. If the prize for winning the Amazing Contest is $12, how much can the class expect to make? 4. If the goal for the class is to make $150, how much should the prize be? 5. If the class wants to break even, how much should the prize be? 6. Explain how you found the answer to Problem 4.

STUDY LINK 75 A Random Draw and a Tree Diagram 231 Name Date Time Copyright © Wright Group/McGraw-Hill Boxes 1, 2, and 3 contain letter tiles. Suppose you draw one letter from each box without looking. You lay the letters in a row—the Box 1 letter first, the Box 2 letter second, and the Box 3 letter third. 1. Complete the tree diagram. Fill in the blanks to show the probability for each branch. T P Box 1 I O A Box 2 N E Box 3 I Box 2 Box 3 NE NE NEOT Box 1 A I E NNENEOP A 2. How many possible combinations of letter tiles are there? 3. What is the probability of selecting: a. the letters P and I ? b. the letter I, O, or A? c. the letter combinations TO or PO ? d. two consonants in a row? Practice 4. 657 18  5. 858.8 38  6. 1,575 125  154 155

LESSON 75 Name Date Time A Coin-Flipping Experiment 232 Copyright © Wright Group/McGraw-Hill 1. Suppose you flip a coin 3 times. What is the probability that the coin will land a. HEADS 3 times? b. HEADS 2 times and TAILS 1 time? c. HEADS 1 time and TAILS 2 times? d. TAILS 3 times? e. with the same side up all 3 times (that is, all HEADS or all TAILS )? Make a tree diagram to help you solve the problems. 2. One trial of an experiment consists of flipping a coin 3 times. Suppose you perform 100 trials. For about how many trials would you expect to get HHH or TTT? What percent of the trials is that?

STUDY LINK 7 6 Venn Diagrams 233 Name Date Time Copyright © Wright Group/McGraw-Hill There are 200 girls at Washington Middle School. 30 girls are on the track team. 38 girls are on the basketball team. 8 girls are on both teams. 1. Complete the Venn diagram below to show the number of girls on each team. Girls’ Sports at WMS 140 a. c.b. e. d. b. c.a. 70 20 10 f. How many girls are on one team but not both? girls g. How many girls are on the track team but not the basketball team? girls 2. Write a situation (2d) for the Venn diagram below. Complete the diagram by adding a title (2a) and labeling each ring (2b and 2c). d. Practice 3. 7 8 29 0 4. 71 34 15 2 5. 92 51 1 4 263 264

LESSON 7 6 Name Date Time Reviewing Venn Diagrams 234 Copyright © Wright Group/McGraw-Hill Marco’s Friends Own a Dog Wear Glasses Germaine Nolan MarcusColleen JonKeo TyroneAaron Sam Madison A Venn diagram shows how data can belong in more than one group. The diagram is made up of rings that sometimes overlap. Study the Venn diagram below. 1. Use a yellow highlighter or pencil to outline and lightly shade the Own a Dog ring. 2. List the names of Marco’s friends who own a dog. 3. Use a blue highlighter or pencil to outline the Wear Glasses ring. 4. List the names of Marco’s friends who wear glasses. 5. Using your blue highlighter, lightly shade the Wear Glasses ring. a. Which names are in the area of the diagram that is shaded both yellow and blue (green)? b. What can you tell about the friends whose names appear in the green area of the diagram? 6. Explain why Jon’s name is outside the rings of the diagram.

LESSON 7 6 Name Date Time Frequency Tables and Venn Diagrams 235 Copyright © Wright Group/McGraw-Hill Suppose researchers chose 1,000 adults at random and tested them to find out whether they were right- or left-handed. People who showed no preference were classified according to the hand they used more often when writing. Each person was also tested to determine which eye was dominant.* Possible results are shown in the table at the right. For example, the table shows that 30 people were left-handed and right-eyed. Refer to the table to answer the following questions. 1. The sum of the numbers in the table is . 2. a. How many people in the sample were right-handed and right-eyed? people b. How many people were right-handed? people 3. a. How many people in the sample were left-handed and left-eyed? people b. How many people were left-handed? people c. How many people were left-eyed? people 4. Use your answers from Problem 3 to complete the Venn diagram. Fill in the missing numbers. 5. What percent of the people in the sample have their dominant hand and dominant eye on the same side? *Eye dominance refers to the tendency to use one eye more than the other in certain tasks involving precise hand-eye coordination and a reasonably distant target. Your dominant eye is the eye you use to aim when you throw darts, for example. Dominant Hand Left Right 70 200 30 700 Dominant Eye Right Left Adults Left-eye Dominance 700 Left-hand Dominance

STUDY LINK 77 More Tree Diagrams Copyright © Wright Group/McGraw-Hill 236 Name Date Time Denise has 3 red marbles and 1 green marble in a bag. She draws 1 marble at random. Then she draws a second marble without putting the first marble back in the bag. 1. Find the probabilities for each branch of the tree diagram below. R3 G R1 R2 a. What is the probability that Denise will select 2 red marbles? % b. What is the probability that Denise will first draw a green marble and then a red marble? % 2. Three coins are tossed. H H T H T T H H H T H T T T Outcomes HHH TTT a. Complete the table of possible outcomes at the right. b. What is the probability of tossing exactly2 HEADS ? % c. What is the probability of tossing at least1 TAIL ?% Coin 1 Coin 2 Coin 3 R2 R3R1 G R1 R3R2 G R1 R2R3 G R1 R2G R3

LESSON 77 Name Date Time A Coin-Flipping Experiment 237 Copyright © Wright Group/McGraw-Hill 1. Draw a tree diagram to show all possible outcomes when you flip a coin 4 times. 2. How many possible outcomes are there? 3. What is the probability that the coin will land TAILS once and HEADS 3 times? 4. What is the probability that the coin will land TAILS the same number of times it lands HEADS ? 5. What is the probability that the coin will land on the same side all 4 times? 6. What is the probability that the coin will land TAILS more often than HEADS ? 7. What is the probability that the coin will land TAILS 75 percent of the time? 8. What is the probability that the coin will land HEADS at leastonce? Optional Experiment 9. Do the coin-flipping experiment several times and record the actual results. Combine your results with those of your classmates. Do the actual results come close to the predicted results? Actual Results Conclusions

LESSON 77 Name Date Time Making a Fair Game 238 Copyright © Wright Group/McGraw-Hill Work with your group to figure out how to make the following game fair. Sum Game Materialsone each of number cards 1, 3, 6, and 10 (from the Everything Math Deck, if available) Players1 Directions 1. Mix the cards and place them facedown on the playing surface. 2. Turn over two of the cards. 3. Add the numbers on the two cards. The 1-card (or ace) is worth 1, the 3-card is worth 3, and so on. The sum is your score for the game. 4. You win if you score at least a certain numberof points. Otherwise, you lose. Your group’s job is to figure out the certain numberso the game is fair. In other words, you must find the answer to the following question: What is the least number of points you must score to win half of the time? Answer: You win if you score at least points. Explain how you found the answer.

STUDY LINK 7 8 Reviewing Probability 239 Name Date Time Copyright © Wright Group/McGraw-Hill 1. Each fraction in the left column below shows the probability of a chance event. Write the letter of the description next to the fraction that represents it. 1 3 A. Probability of getting HEADS if you flip a coin 1 4 B. Probability of rolling 3 on a 6-sided die 1 2 C. Probability of choosing a red ball from a bag containing 2 red balls, 3 white balls, and 1 green ball 1 6 D. Probability of drawing a heart card from a deck of playing cards 2. Sidone bought 3 new swimsuits— 1 red suit, 1 blue suit, and 1 white suit. She also bought 2 pairs of beach sandals—1 red pair and 1 white pair. Make a tree diagram in the space at the right to show all possible combinations of swimsuits and sandals. a. How many different combinations of suits and sandals are there? b. If Sidone chooses a swimsuit and a pair of sandals at random, what is the probability that they will be the same color? 3. a. Ten students in Ms. Garcia’s class play the piano. Seven students play the guitar. Two students play both the piano and the guitar. Complete the Venn diagram at the right. b. How many students are in Ms. Garcia’s class? students Explain how you know. Ms. Garcia’s Students Piano Guitar 10 148–155, 263, 264

LESSON 7 8 Name Date Time Pascal’s Triangle 240 Copyright © Wright Group/McGraw-Hill The triangular array of natural numbers shown below is called Pascal’s triangle. This triangle is named after the French mathematician Blaise Pascal. A pattern is used to generate the numbers of the triangle. This pattern can be extended indefinitely. Compare the numbers in each row of the triangle to the numbers in the row above and below it. Then complete Rows 6 and 7. 1 1 1 1 1 1 2 3 1 4 1 3 6 1 5 10 1 4 10 1 6 15 1 5 15 1 7 35 1 1 7 Row 0 Row 1 Row 2 Row 3 Row 4 Row 5 Row 6 Row 7 Study your completed triangle, looking along rows and diagonals for additional patterns. Describe any pattern(s) you find on the lines below. Then share your pattern(s) with a partner.

LESSON 7 8 Name Date Time Probability and Pascal’s Triangle 241 Copyright © Wright Group/McGraw-Hill 1. Suppose you toss 2 coins. a. Complete the table of possible outcomes at the right. b. How many outcomes are possible? c. Find the probability of tossing both HEADS . only one HEAD . both TAILS . 2. Look at Row 2 of Pascal’s triangle on Math Masters,page 240. a. What is the sum of the numbers in Row 2? b. Copy the numbers from Row 2 of the triangle in the spaces below. c. Compare your answers for Problems 1b and 1c (above) with your answers for Problems 2a and 2b. What do you notice? 3. Suppose you toss 3 coins. Use Row 3 of Pascal’s triangle to complete the following. a. How many outcomes are possible? b. Find the probability of getting 3 HEADS .2 HEADS and 1 TAIL .1 HEAD and 2 TAILS .3 TAILS . 4. Which row of Pascal’s triangle would you use to find the possible outcomes and probabilities when 6 coins are tossed? Row 5. How many different ways could you answer 5 true/false questions? ways Coin 1 Coin 2 HH

STUDY LINK 7 9 Unit 8: Family Letter Copyright © Wright Group/McGraw-Hill 242 Name Date Time Rates and Ratios The next unit is devoted to the study of rates and ratios. Fraction and decimal notation will be used to express rates and ratios and to solve problems. Ratios compare quantities that have the same unit. These units cancel each other in the comparison, so the resulting ratio has no units. For example, the fraction 22 0could mean that 2 out of 20 people in a class got an A on a test or that 20,000 out of 200,000 people voted for a certain candidate in an election. Another frequent use of ratios is to indicate relative size. For example, a picture in a dictionary drawn to 11 0scale means that every length in the picture is 11 0the corresponding length in the actual object. Students will use ratios to characterize relative size as they examine map scales and compare geometric figures. Rates, on the other hand, compare quantities that have different units. For example, rate of travel, or speed, may be expressed in miles per hour (55 mph); food costs may be expressed in cents per ounce (17 cents per ounce) or dollars per pound ($2.49 per pound). Easy ratio and rate problems can be solved intuitively by making tables, such as What’s My Rule?tables. Problems requiring more complicated calculations are best solved by writing and solving proportions. Students will learn to solve proportions by cross multiplication. This method is based on the idea that two fractions are equivalent if the product of the denominator of the first fraction and the numerator of the second fraction is equal to the product of the numerator of the first fraction and the denominator of the second fraction. For example, the fractions 4 6and 6 9are equivalent because 6 º64º9. This method is especially useful because proportions can be used to solve any ratio and rate problem. It will be used extensively in algebra and trigonometry. Students will apply these rate and ratio skills as they explore nutrition guidelines. The class will collect nutrition labels and design balanced meals based on recommended daily allowances of fat, protein, and carbohydrate. You might want to participate by planning a balanced dinner together and by examining food labels while shopping with your child. Your child will also collect and tabulate various kinds of information about your family and your home and then compare the data by converting them to ratios. In a final application lesson, your child will learn about the Golden Ratio—a ratio found in many works of art and architecture. 9∗ 4  36 6 ∗ 6  36 4 6 6 9 

243 Copyright © Wright Group/McGraw-Hill Golden Ratio Theratioof the length of the long side to the length of the short side of a Golden Rectangle, approximatelyequal to 1.618 to 1. The Greek letter (phi)sometimes stands for the Golden Ratio. The Golden Ratio is an irrational number equal to 1 2 5 . n-to-1 ratio Aratioof a number to 1. Every ratio a:bcan be converted to an n-to-1 ratio by dividing abyb. For example, a ratio of 3 to 2 is a ratio of 3 / 2 1.5, or a 1.5-to-1 ratio. part-to-part ratio Aratiothat compares a part of a whole to another part of the same whole. For example,There are 8 boys for every 12 girlsis a part-to-part ratio with a whole of 20 students. Compare to part-to-whole ratio. part-to-whole ratio Aratiothat compares a part of a whole to the whole. For example, 8 out of 20 students are boysand12 out of 20 students are girls are part-to-whole ratios. Compare to part-to-part ratio. per-unit rate Aratewith 1 unit of something in the denominator. Per-unit rates tell how many of one thing there are for one unit of another thing. For example, 3 dollars per gallon, 12 miles per hour, and1.6 children per family are per-unit rates. proportion A number sentence equating two fractions. Often the fractions in a proportion represent ratesorratios. rate A comparison by division of two quantities with different units. For example, traveling 100 miles in 2 hours is an average rate of 10 20 hm ri  or 50 miles per hour. Compare to ratio. ratio A comparison by division of two quantities with the same units. Ratios can be fractions, deci- mals, percents, or stated in words. Ratios can also be written with a colon between the two numbers being compared. For example, if a team wins 3 games out of 5 games played, the ratio of wins to total games is 3 5, 3 / 5, 0.6, 60%, 3 to 5, or 3:5 (read “three to five”). Compare to rate. similar figures Figures that have the same shape, but not necessarily the same size. For example, all squares are similar to one another, and the preimage and image of a size-changeare similar. The ratioof lengths of corresponding parts of similar figures is a scaleorsize-change factor. In the example below, the lengths of the sides of the larger polygon are 2 times the lengths of the corresponding sides of the smaller polygon. Compare to congruent. size-change factor Same as scale factor. scale factor (1) The ratioof lengths on an image and corresponding lengths on a preimage in a size-change. Same as size-change factor. (2) The ratio of lengths in a scale drawing or scale model to the corresponding lengths in the object being drawn or modeled. Vocabulary Important terms in Unit 8: Unit 8: Family Letter cont. STUDY LINK 79 Similar polygons

Copyright © Wright Group/McGraw-Hill 244 Building Skills through Games In Unit 8, your child will continue to review concepts from previous units and prepare for topics in upcoming units by playing games such as: Division Top-It(Advanced Version) See Student Reference Book, page 336 Two to four people can play this game using number cards 1–9. Players apply place-value concepts, division facts, and estimation strategies to generate whole-number division problems that will yield the largest quotient. Spoon Scramble SeeStudent Reference Book, page 333 Playing Spoon Scramble helps students practice finding fraction, decimal, and percent parts of a whole. Four players need a deck of 16 Spoon Scramble cards and 3 spoons to play this game. Study Link 8 1 2. a.13 b.$6.50 3. a. b. 375 words c.14 minutes 4. 0.6 hours 5.About 44 6. –1 7.–1.856 Study Link 8 2 1. 13 5 12 a 5; 25 2. 3 4 0 8 6w 4; 40 3. 2 14 00  21 g6; 9 4. 60 2.96   3c; 91.44 Sample estimates are given. 5. 600; 674 6.100; 91 7.40; 35 As You Help Your Child with Homework As your child brings assignments home, you may want to go over the instr\ uctions together, clarifying them as necessary. The answers listed below will guide you through some of the Study Link\ s in this unit. Words 124 5 Minutes 75 150 300 375 Unit 8: Family Letter cont. STUDY LINK 79 Do-Anytime Activities To work with your child on the concepts taught in this unit and in previo\ us units, try these interesting and rewarding activities: 1.Look with your child through newspapers and magazines for photos, and ch\ eck them to see if a size-change factor is mentioned in the caption: that is, 2X for an enlarged photo 2 \ times life-size; or 1 2X for a photo reduced by half. You might find photos of insects, stars, bacteria, and so on. Have your c\ hild explain to you what the size-change factor means. 2. Encourage your child to read nutrition labels and calculate the percent of fat in the item. tofa tt al c ca alo lori re ie s s   10 ? 0  ?% of calories from fat If your child enjoys this activity, extend it by figuring the percent of calories from protein and carbohydrate. 3. Help your child distinguish between part-to-part and part-to-whole ratio\ s. When comparing a favorite sports team’s record, decide which ratio is being used. For example, wins to losses \ (such as 5 to 15) or losses to wins (15 to 5) are part-to-part ratios. Part-to-whole ratios\ are used to compare wins to all games played (5 out of 20) or losses to all games played (15 out of 20).

245 Copyright © Wright Group/McGraw-Hill Study Link 8 3 1. a.$0.13 per worm b.$3.38 2. a. $0.18 per oz b.$2.88 3. 150,000 people 4.625 gallons 5. $840; $15,120 6. 1 2cent 7. 16 hours; Sample answer: 128 oz 1 gal; 12 gal 1,536 oz; 1.6 1 o,5 z 3 p6 er oz min   960 min; 60 m 9 i6 n 0 pm er in hour   16 hr Study Link 8 4 Answers vary. Study Link 8 5 Answers vary. Study Link 8 6 1. 25 2.27 3.24; 40 4. San Miguel Middle School; Sample answer: I wrote a ratio comparing the number of students to the number of teachers for each school. Richards Middle School, 1 14; San Miguel, 1 13. 5. 6. 14.83 7.88.43 8.12.06 Study Link 8 7 1.20 2.57 3.27 4.6 5. 250 6.42 7.12 21 4 8. 2 8 9 9.4 1 21 0 10. 3 2 47 0 Study Link 8 8 Answers vary for 5a and 5b. 5. a. 6 1 2in.; 4 3 4in.b.5 in.; 3 in. c.7 1 4in.; 3 3 4in. d. 9 1 2in.; 4 1 4in.e.11 in.; 8 1 2in. 6. Answers vary. 7. Sample answers: a.6 1 2 b. 11 8. 2.3 9.57.7 10.10.2 Study Link 8 9 1. a. 64 mm b.32 mm 2. a. 45 mm b.180 mm; 1 4 3. a. 45 mm b.15 mm; 3 4. a. 55 mm b.165 mm; 1 3 Study Link 8 10 1. a. 2:1 b.90 c.9 d.2:1 2. a. 15 b. 3 2 3.90 4. 0.007 5.63.498 6.4.892 7.5.920 Study Link 8 11 1.1.2; Answers vary. 2. 1.65; No. Sample answer: The ratio for a standard sheet of paper is about 1.3 to 1. 3. Lucille; Sample answer: Compare ratios of correct problems to total problems. Jeffrey’s ratio is 0.93 to 1; Lucille’s ratio is 0.94 to 1. 4. 12 5.2.8; Answers vary. 6.888 7. 21,228 8.15,456 9.126,542 Study Link 8 12 1. a. 3.14 to 1 b.1.16 to 1 c.2 to 1 d. 1 to 1 e.3 to 5 2. a. 40% b.3:5, or 3 5 3. b. $7.50 c.8 cans 4. a. 24 members b. 3 5 1 n2; 20 free throws 6. Answers vary. Mystery Adventure Humor Shelf Books Books Books 1 4 10 18 2 6 15 27 3 8 20 36 410 25 45 512 30 54 614 35 63 Unit 8: Family Letter cont. STUDY LINK 79 5.Answers vary.