University of Cincinnati



Lesson 1 Activity 1 Worksheet a Table of ContentsPage 2-4 Snack Smarter Project WorksheetPage 5-14 Unit 3 Pre-AssessmentPage 15-18 Making ComparisonsPage 19-22 Writing Comparison StatementsPage 23-26 Ratios and Rates PracticePage 27-30 Teacher-Guided Ratios and Rates StationPage 31-34 Ratio and Rates Extensions Page 35-38 Comparing Ratios, Percents, and FractionsPage 39-42 Ratio Comparison PracticePage 43-46 Finding Equivalent RatiosPage 47-50 Practice with Scaling RatiosPage 51-54 Comparing Ratios, Percents, and Fractions Practice ProblemsPage 55-56 ?Comparing Ratios, Percents, and Fractions Teacher-Guided StationPage 57-60 Comparing Ratios, Percents, and Fractions Extensions52967831982300Name ________________________________________Snack Smarter Project WorksheetDirections: You will be working on this challenge throughout unit 3. This project is due at the end of the unit. You will present your findings with a poster that will be put up in the hall to convince other students to buy your snack!The Challenge: Find a snack or a recipe for a snack that students at Delhi Middle School will choose to buy over the big cookie.FDA Daily Recommended Values4299971698500The snack must:Show that it will cause a percent decrease in the number of students who buy the big cookie (through the survey).Have less than 8 grams of fatHave more than 1.5 grams of proteinHave less than 20 grams of carbsCost the same as or less than the big cookie.Identify and DefineIf you could choose any snack option during lunch, what would it be?Is your lunch option healthy (use the table to the right to make this decision)?What healthy and delicious lunch options could your team suggest for a better snack at lunch?Gather Information/Identify AlternativesDo some research on at least 5 snack alternatives and complete the table. If you have more than 5 snacks, you can add a separate sheet of paper. Name of SnackTotal GramsCaloriesProtein (g)Carbohydrates (g)Fat (g)Select the Best Solution to TryWhich snack option is your group going to go with? Why?Implement Solution/Evaluate or TestConduct the following survey. You need at least 30 student responses.I would rather have your snack than the cookie.I would rather have the cookie than your snack. CommunicateComplete the following information (you MUST show ALL CALCULATIONS here!!!):The name of your snack ______________________The cost per serving to purchase your snack ____________________________ The cost to sell from the cafeteria with a 35% markup ___________________________ Based on your survey results, what percentage of students who took the survey would rather have your snack than the cookie? _____________________________Using your percentage from part d, if there are 625 students at Delhi Middle School, how many total students will purchase your cookie on a given lunch day? _____________________Based on part e, how much will it cost the school to purchase your snack for a week? ________________________What is the percentage of fat, calories, and carbohydrates out of the total grams in your snack? ______________________Use the class survey to determine the percent decrease in students who would buy the cookie ________________Refine/ReflectBased on your survey results, write a reflection about your snack option using complete sentences. Make sure to answer the following questions in your reflection:Are you happy with the survey results?Are you surprised with the survey results?What would you change about your snack option?Do you think that if students were more aware of nutrition, they would change their mind about what snacks to choose?Name ________________________________________Unit 3 Pre-Assessment601756889037147531752. 4846782239823. 34988531754. 55366205. 4015512617356. 45783576207.5683251701808. 4293762901959. 373900-2251410. 456623011. 4566231258512. 4156372695813. 56786429146514. 609427814015. 6089651905016. 421005698517. 382270571518. 34619120008219. 4016091449020. 3712845114301045031034121.22. BonusName ____________Key____________________________Unit 3 Pre-Assessment606552118112773682288542. 2 1/3 teaspoons7 ? cups4479292235203. 5/21301752102874. 2/355753012705.695 km/hr3992882557786. $1.23401032171457.3/3254032772748. 5/48 hr/task48/5 tasks/hour4236722934979. 4 1/6 mph4 ? mph 4 2/3 mphAnna ran the fastest 374650127010. 20%460248520711. 5%5% 4597401143012. $1.60$41.603867154521213. 56786429146514. 30% increase6064251333515. 6064251714516. 40%52070028511517. 5%39878029527518. 25%3144528102619. 4 ? =9/22/93987801143020. 13 1/3333375168910359092512128521.22. Bonus $13.08Name _____________________________________Making ComparisonsSurveys may report people’s preferences in food, cars, or political candidates. Often, the favorites are easy to recognize. Explaining how much more popular one choice is than another can be more difficult. In this investigation, you will explore strategies for comparing numbers in accurate and useful ways. As you work on the problems, notice how the different ways of making comparisons send different messages about the numbers being compared.-403417324900A Delhi Middle School survey was conducted to get an idea of how students like the food choices. The following results were found:19646905461000In a taste test, students who preferred Asian Day outnumbered those who preferred Hamburger Day by a ratio of 360 to 240.In a taste test, 120 more people preferred Asian Day.In a taste test, 60% of students preferred Asian Day.In a taste test, students who preferred Asian Day outnumbered those who preferred Hamburger Day by a ratio of 3 to 2.Describe what you think each statement above means.The board of education is considering eliminating Asian Day because of the cost of making it. Which of the above statements do you think would be the most effective in changing their mind? Why?Is it possible that all four statements are based on the same survey data? Explain your reasoning. In what other ways can you express the claims in the four above statements? Explain.If you were to survey 1,000 students from another school, what numbers of Asian Day and Hamburger Day would you expect? For your project, you will be designing a meal that could be served by the cafeteria that will be popular among students but also have nutritional content. Write down some ideas of what meal you may create:As you work on this problem and the rest of the unit, you will see statements about ratio comparisons. In mathematics, it is acceptable to write ratios in different ways. Each way is useful.110642487630 Ways to Write a Ratio 3 to 2 3:2 32 It can be confusing to see a fraction representing a ratio. A ratio is usually, but not always, a part-to-part comparison. A fraction usually means a part-to-whole comparison. The context can help you decide whether a fraction represents a ratio.Practice: Analyzing Comparison StatementsStudents at Delhi Middle School are asked if they prefer watching television or listening to the radio. Of 150 students, 100 prefer television and 50 prefer radio.How would you compare student preferences for radio or television?Decide if each statements accurately reports results of the Delhi Middle School Survey:At Delhi Middle School, 1/3 of the students prefer radio to television.Students prefer television to radio by a ratio of 2 to 1.The ratio of students who prefer radio to television is 1 to 2.The number of students who prefer television is 50 more than the number of students who prefer radio.The number of students who prefer television is two times the number who prefer radio.50% of the students prefer radio to pare statements in parts (d) and (e) above. Which is more informative? Explain.Consider on the accurate statements in Question B.Which statement would best convince merchants to place ads on radio? Why?Which statement would best convince merchants to place ads on television? Why?Name ______________Key_______________________Making ComparisonsSurveys may report people’s preferences in food, cars, or political candidates. Often, the favorites are easy to recognize. Explaining how much more popular one choice is than another can be more difficult. In this investigation, you will explore strategies for comparing numbers in accurate and useful ways. As you work on the problems, notice how the different ways of making comparisons send different messages about the numbers being compared.201960030551000-403417324900A Delhi Middle School survey was conducted to get an idea of how students like the food choices. The following results were found:In a taste test, students who preferred Asian Day outnumbered those who preferred Hamburger Day by a ratio of 360 to 240.In a taste test, 120 more people preferred Asian Day.In a taste test, 60% of students preferred Asian Day.In a taste test, students who preferred Asian Day outnumbered those who preferred Hamburger Day by a ratio of 3 to 2.A. Describe what you think each statement above means.Statement 1 means that out of the total surveyed, 360 preferred Asian Day and 240 preferred Hamburger Day. For every 360 who preferred Asian Day, there were 240 who preferred Hamburger Day.B. The board of education is considering eliminating Asian Day because of the cost of making it. Which of the above statements do you think would be the most effective in changing their mind? Why?The ratio 3 to 2 might be the most effective because the numbers are smaller and easier to relate to. C.Is it possible that all four statements are based on the same survey data? Explain your reasoning. Yes, it’s possible. 360 to 240 = 3/2, 360-240=120, and 360+240 = 600 and 60% of 600 is 360D. In what other ways can you express the claims in the four above statements? Explain.1.5 times as many people preferred Asian Day over Hamburger Day. 3/5 of people prefer Asian Day.E. If you were to survey 1,000 students from another school, what numbers of Asian Day and Hamburger Day would you expect? 600 would prefer Asian Day and 400 would prefer Hamburger DayF. For your project, you will be designing a meal that could be served by the cafeteria that will be popular among students but also have nutritional content. Write down some ideas of what meal you may create:Answers will varyAs you work on this problem and the rest of the unit, you will see statements about ratio comparisons. In mathematics, it is acceptable to write ratios in different ways. Each way is useful. 1081405187960Ways to Write a Ratio 3 to 2 3:2 32 It can be confusing to see a fraction representing a ratio. A ratio is usually, but not always, a part-to-part comparison. A fraction usually means a part-to-whole comparison. The context can help you decide whether a fraction represents a ratio.Practice: Analyzing Comparison StatementsStudents at Delhi Middle School are asked if they prefer watching television or listening to the radio. Of 150 students, 100 prefer television and 50 prefer radio.A. How would you compare student preferences for radio or television?Some possible combinations involve the use of ratio because you are comparing among the students. You are comparing the quantities of those who prefer television to those who prefer radio. Students could also say that the preferences could be compared by fractions.B. Decide if each statements accurately reports results of the Delhi Middle School Survey:a. At Delhi Middle School, 1/3 of the students prefer radio to television.Yes – the total number of students is 150b. Students prefer television to radio by a ratio of 2 to 1.Yes. 100:50 = 2:1The ratio of students who prefer radio to television is 1 to 2.Yes. 50:100 = 1:2The number of students who prefer television is 50 more than the number of students who prefer radio.Yes 100-50 = 50. The problem discusses the difference.The number of students who prefer television is two times the number who prefer radio.Yes. 100=2x5050% of the students prefer radio to television.No. About 33% of students prefer radio to televisionC. Compare statements in parts (d) and (e) above. Which is more informative? Explain.Statement e is more informative because it gives individuals, a scale factor, whereas the difference is more dependent on the actual numbers. For example, the difference between 100 and 50 is more impressive than the difference between 1,000 and 1,500. A ratio is more informative in comparing these two quantities than the difference.D. Consider on the accurate statements in Question B.Which statement would best convince merchants to place ads on radio? Why?Possible answer: statement 1 because it frames the preference for radio in a positive lightWhich statement would best convince merchants to place ads on television? Why?Possible answer: Statement 5 because the scale factor of 2 sounds impressiveName _____________________________________________Writing Comparison StatementsAt lunch time, there are a lot of factors that go into making a decision about what to eat. What are some things that you (or your parents/guardians) consider when deciding what to have for lunch?You can describe the nutritional content of food by comparing it to other foods. Selected Lunch OptionsFood (1 serving)Grams of ProteinGrams of FatGrams of CarbsJumbo Cookie (50 g)21233Nachos and Cheese (113 g)12.329.565.8Turkey Sandwich (turkey, 2 slices of bread, slice of cheese, and lettuce)17.39.830.8Pretzel Sticks (39 pretzels)1.50.211.5Sweet and Sour Chicken with White Rice121464Use the table to answer the following questions.How many servings of pretzel sticks equal the same amount of grams of fat as the jumbo cookie?Kenning says that the number of grams of protein in the turkey sandwich is greater than that of the sweet and sour chicken by a ratio of about 3 to 2. Is he correct? Explain.Mary says the difference between the grams of protein in the jumbo cookie and the turkey sandwich is 15.3 grams. Is she correct?How many turkey sandwiches does it take to equal the grams of carbs in the sweet and sour chicken with white rice?Jaime says the grams of fat in the turkey sandwich is less than 50% of the fat in the sweet and sour chicken. Is he correct?Len says that the grams of carbs in the pretzels are about 1/6 of the amount of carbs in the nachos and cheese. Is he correct? Explain.On average, you should have about 65 grams of fat per day. Write two statements comparing the grams of fat in the nachos and cheese with the amount of fat you should have in an entire day. Use fractions, ratios, percent, or differences. 5151632444500A general rule-of-thumb is that 30% of your diet should come from protein, 40% from carbs, and 30% from fat. If a student had nachos and cheese with a jumbo cookie for lunch, what percentage of that meal comes from protein? -171450567690Hint: To find a percent, take the part and divide it by the total. Then, multiply that answer by 100. Now you have the percent!00Hint: To find a percent, take the part and divide it by the total. Then, multiply that answer by 100. Now you have the percent!Name ____________________Key_________________________Writing Comparison StatementsAt lunch time, there are a lot of factors that go into making a decision about what to eat. What are some things that you (or your parents/guardians) consider when deciding what to have for lunch?Answers will varyYou can describe the nutritional content of food by comparing it to other foods. Selected Lunch OptionsFood (1 serving)Grams of ProteinGrams of FatGrams of CarbsJumbo Cookie (50 g)21233Nachos and Cheese (113 g)12.329.565.8Turkey Sandwich (turkey, 2 slices of bread, slice of cheese, and lettuce)17.39.830.8Pretzel Sticks (39 pretzels)1.50.211.5Sweet and Sour Chicken with White Rice121464A. Use the table to answer the following questions.How many servings of pretzel sticks equal the same amount of grams of fat as the jumbo cookie?60 servingsKenning says that the number of grams of protein in the turkey sandwich is greater than that of the sweet and sour chicken by a ratio of about 3 to 2. Is he correct? Explain.Yes – 17.3 is close to 18. 18 to 12 can be reduced to 3 to 2Mary says the difference between the grams of protein in the jumbo cookie and the turkey sandwich is 15.3 grams. Is she correct?YesHow many turkey sandwiches does it take to equal the grams of carbs in the sweet and sour chicken with white rice?2.08, which is about 2Jaime says the grams of fat in the turkey sandwich is less than 50% of the fat in the sweet and sour chicken. Is he correct?No – it is more than 50%Len says that the grams of carbs in the pretzels are about 1/6 of the amount of carbs in the nachos and cheese. Is he correct? Explain.Yes. The carbs in the nachos and cheese is close to 66 and the carbs in the pretzels is close to 11. 11/66 = 1/6On average, you should have about 85 grams of fat per day. Write two statements comparing the grams of fat in the nachos and cheese with the amount of fat you should have in an entire day. Use fractions, ratios, percent, or differences. Nachos and cheese have 29.5 grams of fat. Answers will varyPossible answers: 29.5/65 = 0.45 = 45%The grams of fat in nachos and cheese is close to half of what you should have the entire day.The grams of fat in nachos and cheese is only 35.5 less than what you should have the entire day.5151632444500A general rule-of-thumb is that 30% of your diet should come from protein, 40% from carbs, and 30% from fat. If a student had nachos and cheese with a jumbo cookie for lunch, what percentage of that meal comes from protein? Total protein in meal = 14.3 gramsTotal grams = 163 grams14.3/163 = 0.08773006 = 8.8%-171450721360Hint: To find a percent, take the part and divide it by the total. Then, multiply that answer by 100. Now you have the percent!00Hint: To find a percent, take the part and divide it by the total. Then, multiply that answer by 100. Now you have the percent!Name ___________________________________________________Ratios and Rates PracticeIn a comparison taste test of two drinks, 780 students preferred Berry Blast. Only 220 students preferred Melon Splash. Complete each statement.There were ____________ more people who preferred Berry Blast.In the taste test, _____________% of the people preferred Berry Blast.People who preferred Berry Blast outnumbered those who preferred Melon Splash by a ratio of _____ to _____.A town considers whether to put in curbs along the streets. The ratio of people who support putting in curbs to those who oppose it is 2 to 5. What fraction of people oppose putting in curbs?If 210 people in the town are surveyed, how many do you expect to favor putting in curbs?What percent of the people oppose putting in curbs?18164447363A class at Middlebury Middle School collected data on the kinds of movies students prefer. Complete the statement using the table.The ratio of seventh-graders who prefer comedies to eighth-graders who prefer comedies is ______ to ______.The fraction of total students (both seventh- and eighth-graders) who prefer action movies is ______.The fraction of seventh-graders who prefer action movies is ______.The percent of total students who prefer comedies is ______.The percent of eighth-graders who prefer action movies is ______.Grade ______ has the greater percent of students who prefer action movies.A fruit bar is 5 inches long. The bar will be split into two pieces. For each situation, find the lengths of the two pieces.One piece is 3/10 of the whole bar.One piece is 60% of the bar.One piece is 1 inch longer than the other.right222988The figure to the right shows two members of the Grump family. The figures are geometrically similar.How long is the segment in the smaller Grump that corresponds to the 1.4 inch segment in the larger Grump?The mouth of the smaller Grump is 0.6 inches wide. How wide is the mouth of the larger Grump?0.4 in.b. 0.9 in.c. 1 in.d. 1.2 in.Name _________________Key__________________________________Ratios and Rates PracticeIn a comparison taste test of two drinks, 780 students preferred Berry Blast. Only 220 students preferred Melon Splash. Complete each statement.There were ____560________ more people who preferred Berry Blast.In the taste test, _____78%________% of the people preferred Berry Blast.People who preferred Berry Blast outnumbered those who preferred Melon Splash by a ratio of _39____ to ___11__. Or 780 to 220 , 195 to 55A town considers whether to put in curbs along the streets. The ratio of people who support putting in curbs to those who oppose it is 2 to 5. What fraction of people oppose putting in curbs?5/7If 210 people in the town are surveyed, how many do you expect to favor putting in curbs?60What percent of the people oppose putting in curbs?About 71%18164447363A class at Middlebury Middle School collected data on the kinds of movies students prefer. Complete the statement using the table.The ratio of seventh-graders who prefer comedies to eighth-graders who prefer comedies is ___7___ to ___10___.The fraction of total students (both seventh- and eighth-graders) who prefer action movies is _11/28_____.(75+90)/(180+240) = 11/28The fraction of seventh-graders who prefer action movies is _75/180 = 5/12_____.The percent of total students who prefer comedies is _17/28= 0.6071, which is about 61%_____.The percent of eighth-graders who prefer action movies is __90/240 = 0.375 = 37.5%____.Grade ___7 (41.7% - 8th grade is about 37.5%)___ has the greater percent of students who prefer action movies.A fruit bar is 5 inches long. The bar will be split into two pieces. For each situation, find the lengths of the two pieces.One piece is 3/10 of the whole bar.One piece will be 1.5 in. and the other will be 3.5 in. A ratio of 3:7 also means that one piece will be 0.3 of the fruit bar and the other piece wil be 0.7 of the fruit bar. Thus 0.3 x 5 = 1.5 and 0.7 x 5 = 3.5One piece is 60% of the bar.One piece will be 3 in. long and the other will be 2 in. long (60% = 0.6, 0.6 x 5 = 3)One piece is 1 inch longer than the other.One piece will be 3 in. long and the other will be 2 in. longright222988The figure to the right shows two members of the Grump family. The figures are geometrically similar.How long is the segment in the smaller Grump that corresponds to the 1.4 inch segment in the larger Grump?0.93 in. (The scale factor is 1.5. Therefore, 1.4/1.5 = 0.93)The mouth of the smaller Grump is 0.6 inches wide. How wide is the mouth of the larger Grump?21508721168400.4 in.b. 0.9 in.c. 1 in.d. 1.2 in.Name ______________________________________________________________Teacher-Guided Ratios and Rates Station201701425527Students at a middle school are asked to record how they spend their time from midnight on Friday to midnight on Sunday. Carlos records his data in the table to the right. Use the table for Exercises 1-3.How would you compare how Carlos spent his time on various activities over the weekend? Explain.Decide if each statement is an accurate description of how Carlos spent his time that weekend. He spent one sixth of his time watching television.The ratio of hours spent watching television to hours spent doing chores or homework is 3 to 1.Recreation, talking on the phone, and watching television took about 33% of his time.Time spent doing chores or homework was only 20% of the time spent watching television.Sleeping, eating, and “other” activities took up 12 hours more than all other activities combined.Write other accurate statements comparing Carlos’s use of weekend time for various activities. Use each concept at least once.ratiob. differencec. fractiond. percentIn a comparison taste of new ice creams invented at Moo University, 750 freshmen preferred Cranberry Bog ice cream while 1,250 freshman preferred Coconut Orange ice plete each statement.The fraction of freshmen who preferred Cranberry Bog is ________.The percent of freshmen who preferred Coconut Orange is _______%Freshmen who preferred Coconut Orange outnumbered those who preferred Cranberry Bog by a ratio of _______ to ________.39111472196375The table of FDA recommended values for nutrition is shown below. Answer the following questions by using the table.a. The recommended ratio of saturated fat to total fat is _________ to _________ b. What percent of total fat should come from saturated fat?c. How many more mg of potassium is recommended than mg of sodium?d. The recommended ratio of protein to dietary fiber is ________ to ____________Name ________________________Key______________________________________Teacher-Guided Ratios and Rates Station201701425527Students at a middle school are asked to record how they spend their time from midnight on Friday to midnight on Sunday. Carlos records his data in the table to the right. Use the table for Exercises 1-3.How would you compare how Carlos spent his time on various activities over the weekend? Explain.Possible answer: Fractions are a logical way to compare how students spent their time as they compare the time devoted to each activity (part) to each whole time investigated (whole)Decide if each statement is an accurate description of how Carlos spent his time that weekend. He spent one sixth of his time watching television.No, 6/48 = 1/8The ratio of hours spent watching television to hours spent doing chores or homework is 3 to 1.Yes, 6:2 = 3:1Recreation, talking on the phone, and watching television took about 33% of his time.Yes, 8+2+6 = 16. 16/48= 0.333333…… = 33%Time spent doing chores or homework was only 20% of the time spent watching television.No, 2/6 = 0.3333333, 0.333333 = 33% which is not equal to 20%Sleeping, eating, and “other” activities took up 12 hours more than all other activities combined.Yes, 18+2.5+9.5= 30; 48-30=18; 30-18=12Write other accurate statements comparing Carlos’s use of weekend time for various activities. Use each concept at least once.ratiob. differencec. fractiond. percentThe ratio of hours Carlos spent sleeping to hours he spent watching television is 3 to 1. The ratio of hours spent on the phone to doing chores or homework is 1 to 1. The difference between the number of hours Carlos spent sleeping and the number he spent watching television is 12Carlos spent 1/6 of his time on recreation.Carlos spent 50% of his time watching television and sleeping. Carlos spent about 33% of his time on recreation, watching television, and doing chores and homework.In a comparison taste of new ice creams invented at Moo University, 750 freshmen preferred Cranberry Bog ice cream while 1,250 freshman preferred Coconut Orange ice plete each statement.The fraction of freshmen who preferred Cranberry Bog is ____750/2000 = 3/8____.The percent of freshmen who preferred Coconut Orange is __62.5; here students need to recognize that the fraction they need is 5/8, and 5/8 = 0.625_____%Freshmen who preferred Coconut Orange outnumbered those who preferred Cranberry Bog by a ratio of _5______ to _____3___.39111472196375The table of FDA recommended values for nutrition is shown below. Answer the following questions by using the table.a. The recommended ratio of saturated fat to total fat is ___20______ to ____65_____ or 4/13b. What percent of total fat should come from saturated fat?30.8%c. How many more mg of potassium is recommended than mg of sodium?1100d. The recommended ratio of protein to dietary fiber is ___50_____ to _______25_____ or 2:1Name _____________________________________________________360580735133400Ratio and Rates ExtensionsRewrite this ad so that it will be more effective. 2542236197217Use the table to the pare money spent on food eaten at home and food eaten away from home to the total money spent for food. Write statements for each year.Explain how the statements you wrote in part (a) show the money spent for food away from home increasing or decreasing in relation to the total spent for food.right4982Use the table for Exercises 3-8. Which placement has the greatest difference in advertising dollars between 1990 and 2000?Find the percent of all advertising dollars spent on each placement in 1990.Find the percent of all advertising dollars spent on each placement in 2000.Use your results from Exercises 3-5. Write several sentences describing how advertising spending changed from 1990 to 2000.Suppose you were thinking about investing in either a television station or a radio station. Which method of comparing advertising costs (differences or percent) makes television seem like the better investment? Which makes radio seem like the better investment?Suppose you are a reporter writing an article about trends in advertising over time. Which method of comparison would you choose?Name _____________________Key________________________________360580735133400Ratio and Rates ExtensionsRewrite this ad so that it will be more effective. Possible answer: About 67% of dentists recommend sugarless gum to their patients who chew gum. 2 out of 3 dentists recommend sugarless gum to their patients who chew gum. 255409713970Use the table to the pare money spent on food eaten at home and food eaten away from home to the total money spent for food. Write statements for each year.In 1990, about 64% of money spent on food was spent on food eaten at home. 36% was spent on food eaten away from home. (The total amount of money spent on food in 1990 was $472,700,000,000). In 1998, about 53% of money spent on food was for food eaten at home. 47% was spent on food eaten away from home.Explain how the statements you wrote in part (a) show the money spent for food away from home increasing or decreasing in relation to the total spent for food.The amount of money spent on food eaten away from home is increasing in relation to the total amount spent on food. 47% was spent on food eaten away from home in 1998 as compared to 36% in 1990.335216550800Use the table for Exercises 3-8. Which placement has the greatest difference in advertising dollars between 1990 and 2000?Television45720037782500Find the percent of all advertising dollars spent on each placement in 1990.See aboveFind the percent of all advertising dollars spent on each placement in 2000.See above161531317792700Use your results from Exercises 3-5. Write several sentences describing how advertising spending changed from 1990 to 2000.Possible answers: Suppose you were thinking about investing in either a television station or a radio station. Which method of comparing advertising costs (differences or percent) makes television seem like the better investment? Which makes radio seem like the better investment?For television, discussing the difference makes television seem like a better investment because the percent of expenditures remained relatively consistent (22% as compared to 24%), yet the difference in actual dollar amount was 21,770,000,000. The difference in actual dollar amounts is therefore more impressive. The same is also true for radio as the difference between dollar expenditures would be impressive at 8,204,000,000 as opposed to the change in percents, from 7% in 1990 to 8% in 2000.Suppose you are a reporter writing an article about trends in advertising over time. Which method of comparison would you choose?Percents are easily understood and often used to discuss trends over time. In this case, they would indicate the relative consistency of expenditures per medium. The differences would highlight the impressive overall dollar increase in advertising. The differences would also make a better headline. However, the trends in advertising would be more accurately represented by using percents. (Discuss how such big differences can exist in terms of actual expenditures while percents can remain relatively unchanged.)5446899-30799700Name ____________________________________________________________________________Comparing Ratios, Percents, and FractionsThere are four samples of lemonade. They were made by mixing water and frozen lemonade concentrate. To find the mix that tastes the best, we are going to test some mixes.2197102063750036791901587500Mix A Mix B Ranking (1-4): _________Ranking (1-4): _________ ____ cups concentrate ____ cups water____ cups concentrate ____ cups waterServing SizeCaloriesGrams of FatGrams of SugarServing SizeCaloriesGrams of FatGrams of Sugar 36957001397000Mix C Mix D Ranking (1-4): _________Ranking (1-4): _________ ____ cups concentrate ____ cups water____ cups concentrate ____ cups waterServing SizeCaloriesGrams of FatGrams of Sugar-155575-148018500Serving SizeCaloriesGrams of FatGrams of Sugar A. Which mix makes the juice the most “lemony”? Explain.B. Which mix makes the juice the least “lemony”? Explain.C. Which comparison statement is correct? Explain.5/9 of Mix B is concentrate5/14 of Mix B is concentrateD. Assume that each student will get ? cup of juice.1. For each mix, how many batches are needed to make juice for 240 students?2. For each mix, how much concentrate and how much water are needed to make juice for 240 students?E. For each mix, how much concentrate and how much water are needed to make 1 cup of juice?F. Find the calories per cup for each mix. Which one has the least amount of calories? What did you rank it? Find the grams of sugar per cup of each mix. 5446899-30799700Name __________________Key__________________________________________________________Comparing Ratios, Percents, and Fractions31531042229700There are four samples of lemonade. They were made by mixing water and frozen lemonade concentrate. To find the mix that tastes the best, we are going to test some mixes.3689131678800Mix A Mix B Ranking (1-4): _________Ranking (1-4): _________ ____ cups concentrate ____ cups water____ cups concentrate ____ cups waterServing SizeCaloriesGrams of FatGrams of SugarServing SizeCaloriesGrams of FatGrams of SugarRanking (1-4): _________Ranking (1-4): _________ 3382146088003691408939300Mix C Mix D Ranking (1-4): _________Ranking (1-4): _________Serving SizeCaloriesGrams of FatGrams of Sugar ____ cups concentrate ____ cups water____ cups concentrate ____ cups waterServing SizeCaloriesGrams of FatGrams of SugarRanking (1-4): _________Ranking (1-4): _________ A. Which mix makes the juice the most “lemony”? Explain.Mix A will make the most lemony juice. B. Which mix makes the juice the least “lemony”? Explain.Mix C will make the least lemony juice. C. Which comparison statement is correct? Explain.5/9 of Mix B is concentrate5/14 of Mix B is concentrate5/14 of Mix B is concentrate is correct because a part-to-whole comparison is needed to say the fraction part of the mix that is concentrate.D. Assume that each student will get ? cup of juice.1322705212725001. For each mix, how many batches are needed to make juice for 240 students?left272415002. For each mix, how much concentrate and how much water are needed to make juice for 240 students?2870708698519558018770600E. For each mix, how much concentrate and how much water are needed to make 1 cup of juice?F. Find the calories per cup for each mix. Which one has the least amount of calories? What did you rank it? Find the grams of sugar per cup of each mix. Name __________________________________________________________left335280Ratio Comparison PracticeA. Suppose the pizzas are shared equally by everyone at the table. Does a person sitting at a small table get the same amount as a person sitting at a large table? Explain your reasoning.B. Which table relates to 3/8? What do the 3 and the 8 mean? Is 3/8 a part-to-whole comparison or a part-to-part comparison?C. Selena thinks she can decide at which table a person gets the most pizza. She uses the following reasoning:10-4 = 6 and 8-3 = 5 so the large table is better.What does the 6 mean and what does the 5 mean in Selena’s method of reasoning?Do you agree or disagree with Selena’s method?Suppose you put nine pizzas on the large table. What answer does Selena’s method give? Does this answer make sense?What can you now say about Selena’s method?The ratio of large tables to small tables in the dining room is 8 to 5. There are exactly enough seats for the 240 campers. How many tables of each kind are there?What fraction of the campers sit at small tables?What percent of the campers sit at large tables?Name _________Key_________________________________________________left335280Ratio Comparison PracticeA. Suppose the pizzas are shared equally by everyone at the table. Does a person sitting at a small table get the same amount as a person sitting at a large table? Explain your reasoning.No. Because 4 to 10 and 16 to 40 are equivalent ratios; and 3 to 8 and 15 to 40 are equivalent ratios, we can see that sitting at the large table give a person more pizza since 16 to 40 is greater than 15 to 40. If students use unit rates, they may give the following argument: Those at the large table will get 4/10, or 2/5, of a pizza per person. Those at the small table will get 3/8 of a pizza per person. Similarly, at the large table there are 2.5 people per pizza and at the small table there are 2.666…. people per pizza. Each person at the large table will get more pizza than people at the small table.B. Which table relates to 3/8? What do the 3 and the 8 mean? Is 3/8 a part-to-whole comparison or a part-to-part comparison?3/8 relates to the small table and means 3 pizzas for 8 people. Since it makes no sense to add people and pizza, 3/8 is a part-to-part comparison.C. Selena thinks she can decide at which table a person gets the most pizza. She uses the following reasoning:10-4 = 6 and 8-3 = 5 so the large table is better.What does the 6 mean and what does the 5 mean in Selena’s method of reasoning?Six is the difference between the number of seats and the number of pizzas at the large table. Five is the difference between the number of seats and pizzas at the small table.Do you agree or disagree with Selena’s method?Variable answers at this stage. She is wrong.Suppose you put nine pizzas on the large table. What answer does Selena’s method give? Does this answer make sense?The example given here makes this clear since Selena’s method would give 10-9=1 and 8-3=5 and she would choose the small table. Yet, the large table has almost a whole pizza for each person.What can you now say about Selena’s method?Selena is wrong. It may occasionally accidentally produce a correct answer, but in such a problem, you need to make the comparison based on what portion of a pizza each person gets, not on differences.D. The ratio of large tables to small tables in the dining room is 8 to 5. There are exactly enough seats for the 240 campers. How many tables of each kind are there?There are 16 large tables and 10 small tables. The complexity in this problem is that we have two ratios to deal with. A large table seats 10 people and a small table seats 8 people. One way to think about the problem is to ask what one “group” of tables, 8 large and 5 small, would seat. This would seat 80+40 people, or 120 people. So we need two “groups,” which would be 16 large tables and 10 small tables.What fraction of the campers sit at small tables?80/240, or 1/3What percent of the campers sit at large tables?About 67%Name _________________________________________________________Finding Equivalent RatiosIt is often helpful, when forming ratios, to replace the actual numbers being compared with simpler numbers that have the same relationship to each other.People prefer Bolda Cola over Cola Nola by a ratio of 17,129 to 11,426 or 3 to 2.Students prefer television to radio by a ratio of 100 to 50, or 2 to 1.Monthly sales of Reader’s Digest magazine exceed those of National Geographic by 11,044,694 to 6,602,650, or about 3 to 2Suppose all classes at your grade level took the cola taste test. The result was 100 to 80 in favor of Bolda Cola.How do you scale down this ratio to make it easier to understand?What are some other ratios equivalent to this ratio in which the numbers are greater? Finding greater numbers is scaling up the ratio.How is scaling ratios like finding equivalent fractions for 100/8? How is it different?We are going to watch the Learn Zillion video on creating equivalent ratios: ratio is a _______________________________ between two or more quantities that are ___________________________.What is a common mistake made with ratios? What is the ratio of cookie pieces to frosting pieces? Ratios express a _______________________________ of a relationship.What does 6:3 reduce to? What about 4:2? A ratio can have ______________________________________________________________ just like a _______________________________ can have larger equivalent fractions.Name _____________Key___________________________________________Finding Equivalent RatiosIt is often helpful, when forming ratios, to replace the actual numbers being compared with simpler numbers that have the same relationship to each other.People prefer Bolda Cola over Cola Nola by a ratio of 17,129 to 11,426 or 3 to 2.Students prefer television to radio by a ratio of 100 to 50, or 2 to 1.Monthly sales of Reader’s Digest magazine exceed those of National Geographic by 11,044,694 to 6,602,650, or about 3 to 2Suppose all classes at your grade level took the cola taste test. The result was 100 to 80 in favor of Bolda Cola.How do you scale down this ratio to make it easier to understand?Divide both numbers by 10 to get 10 to 8; divide both numbers by 20 to get 5 to 4What are some other ratios equivalent to this ratio in which the numbers are greater? Finding greater numbers is scaling up the ratio.Sample answers: multiply both by 2 to get 200 to 160; and multiply both by 10 to get 1,000 to 800How is scaling ratios like finding equivalent fractions for 100/8? How is it different?They are alike in that you multiply (or divide) both numbers by the same value; scaling ratios is different in that ratios may not be written in fraction form and do not necessarily represent part-to-whole relationships.We are going to watch the Learn Zillion video on creating equivalent ratios: ratio is a comparison between two or more quantities that are related.What is a common mistake made with ratios? Since the ratio of boys to girls is 2 to 3, there must be just 2 boys and 3 girls.What is the ratio of cookie pieces to frosting pieces? 2 to 1Ratios express a constant pattern of a relationship.What does 6:3 reduce to? What about 4:2? 2:1; 2:1A ratio can have larger equivalent ratios just like a fraction can have larger equivalent fractions.5146628-20955000Name __________________________________________________________Practice with Scaling RatiosMark wants to use a mashed potato recipe as his school lunch option. He has three recipes to choose from:Healthy Mashed Potatoes (1 serving)Garlic Mashed Potatoes (1 serving)Perfect Mashed Potatoes (1 serving)8 garlic cloves2 pounds potatoes1/3 cup light sour cream1 tablespoon fresh oregano1/3 teaspoon salt? teaspoon black pepper2 pounds baking potatoes8 tablespoons butter? cup sour cream2 teaspoons minced garlic2 tablespoons whole milk1 ? teaspoon salt? teaspoon pepper1 ? pounds potatoes? teaspoon salt4 teaspoons heavy cream2 tablespoons butter1 tablespoon milk? teaspoon salt? teaspoon pepperFor the Perfect Mashed Potatoes recipe, how much butter and heavy cream will Mark need if he wants to make 2 servings? 3 servings? 4 servings?Copy and complete the table below:Number of Servings of Perfect Mashed Potatoes1234510Pounds of PotatoesTeaspoons of SaltWhat patterns do you see in your table?Mark puts 32 tablespoons of butter in the Perfect Mashed Potatoes recipe. How much heavy cream should go in to the recipe? Explain.Mark has a total of 135 pounds of potatoes in the Perfect Mashed Potatoes recipe for the school. How much milk is needed for the mix?What is the ratio of butter to potatoes in the perfect mashed potatoes recipe?Scale this ratio up to show the ratio of butter to potatoes that will feed 21 students.To feed 18 students the Healthy Mashed Potatoes recipe, Mark needs 36 pounds of potatoes and 144 garlic cloves. Show how to scale down this ratio to feed 3 students.Mark wants to compare the amount of whole milk to butter in the Garlic Mashed Potatoes Recipe. He makes this claim:“There is 2/6 as much milk as butter in the Garlic Mashed Potatoes Recipe.”Darla says that Mark is wrong. She makes this claim:“There is ? as much milk as butter in the Garlic Mashed Potatoes Recipe.”Who is correct? Explain.Mark narrowed his mashed potato choices down to the Healthy Mashed Potatoes recipe and the Perfect Mashed Potatoes Recipe. He did a taste test with these two recipes. The ratio of students who preferred the Healthy recipe to those who preferred the Perfect recipe is 5 to 4. What fraction of the total students preferred the Healthy recipe?5146628-20955000Name __________________Key________________________________________Practice with Scaling RatiosMark wants to use a mashed potato recipe as his school lunch option. He has three recipes to choose from:Healthy Mashed Potatoes (1 serving)Garlic Mashed Potatoes (1 serving)Perfect Mashed Potatoes (1 serving)8 garlic cloves2 pounds potatoes1/3 cup light sour cream1 tablespoon fresh oregano1/3 teaspoon salt? teaspoon black pepper2 pounds baking potatoes8 tablespoons butter? cup sour cream2 teaspoons minced garlic2 tablespoons whole milk1 ? teaspoon salt? teaspoon pepper1 ? pounds potatoes? teaspoon salt4 teaspoons heavy cream2 tablespoons butter1 tablespoon milk? teaspoon salt? teaspoon pepperFor the Perfect Mashed Potatoes recipe, how much butter and heavy cream will Mark need if he wants to make 2 servings? 3 servings? 4 servings?Ingredient1 Serving2 Servings3 Servings4 ServingsButter2 tbsp.4 tbsp6 tbsp8 tbspHeavy Cream4 tsp.8 tsp.12 tsp.16 tsp.Copy and complete the table below:Number of Servings of Perfect Mashed Potatoes1234510Pounds of Potatoes1 ? 34.567.515Teaspoons of Salt? 11.522.55What patterns do you see in your table?The pounds of potatoes is always three times the teaspoons of salt. The teaspoons of salt is always 1/3 the pounds of potatoes. The pounds of potatoes increase at a rate of 1.5 pounds per additional serving. The teaspoons of salt increase at a rate of ? tsp. per servings. To find the number of pounds of potatoes for any given number of servings, multiply the number of servings by 1.5.Mark puts 32 tablespoons of butter in the Perfect Mashed Potatoes recipe. How much heavy cream should go in to the recipe? Explain.64 tsp heavy cream. 32 tbsp is 16 times as much butter than in the recipe, so you have to take 4tsp x 16 to get 64 tsp heavy cream.Mark has a total of 135 pounds of potatoes in the Perfect Mashed Potatoes recipe for the school. How much milk is needed for the mix?What is the ratio of butter to potatoes in the perfect mashed potatoes recipe?2 tbsp butter: 1.5 pounds of potatoesScale this ratio up to show the ratio of butter to potatoes that will feed 21 students.42 tbsp butter: 31.5 pounds of potatoesTo feed 18 students the Healthy Mashed Potatoes recipe, Mark needs 36 pounds of potatoes and 144 garlic cloves. Show how to scale down this ratio to feed 3 students.6 pounds of potatoes and 24 cloves of garlicMark wants to compare the amount of whole milk to butter in the Garlic Mashed Potatoes Recipe. He makes this claim:“There is 2/6 as much milk as butter in the Garlic Mashed Potatoes Recipe.”Darla says that Mark is wrong. She makes this claim:“There is ? as much milk as butter in the Garlic Mashed Potatoes Recipe.”Who is correct? Explain.Darla is correct. There is 4 times as much butter as milk in the recipe.Mark narrowed his mashed potato choices down to the Healthy Mashed Potatoes recipe and the Perfect Mashed Potatoes Recipe. He did a taste test with these two recipes. The ratio of students who preferred the Healthy recipe to those who preferred the Perfect recipe is 5 to 4. What fraction of the total students preferred the Healthy recipe? 5/9Name ______________________________________________________Comparing Ratios, Percents, and Fractions Practice Problems355524222891200Compare these four mixes for apple juiceWhich mix would make the most “appley” juice?Suppose you make a single batch of each mix. What fraction of each batch is concentrate?Rewrite your answers to part (b) as percents.Suppose you make only 1 cup of Mix W. How much water and how much concentrate do you need?Examine these statements about the apple juice mixes in Exercise 1. Decide whether each is accurate. Give reasons for your answers.Mix Y has the most water, so it will taste least “appley.”Mix Z is the most “appley” because the difference between the concentrate and water is 2 cups. It is 3 cups for each of the others.Mix Y is the most “appley” because it has only 1 ? cups of water for each cup of concentrate. The others have more water per cup.Mix X and Mix Y taste the same because you just add 3 cups of concentrate and 3 cups of water to turn Mix X into Mix Y.At camp, Miriam uses a pottery wheel to make three bowls in 2 hours. Duane makes five bowls in 3 hours.Who makes bowls faster, Miriam or Duane?At the same pace, how long will it take Miriam to make a set of 12 bowls?At the same pace, how long will it take Duane to make a set of 12 bowls?Guests at a pizza party are seated at 3 tables. The small table has 5 seats and 2 pizzas. The medium table has 7 seats and 3 pizzas. The large table has 12 seats and 5 pizzas. The pizzas at each table are shared equally. At which table does a guest get the most pizza?Suppose a news story about the Super Bowl claims “Men outnumbered women in the stadium by a ratio of 9 to 5.” Does this mean that there were 14 people in the stadium – 9 men and 5 women? If not, what does the statement mean?Which of the following is an interpretation of the statement “Men outnumbered women by a ratio of 9 to 5?”There were four more men than women.The number of men was 1.8 times the number of women.The number of men divided by the number of women was equal to the quotient of 5 ÷9. In the stadium, five out of nine fans were women.Name ______________________Key________________________________Comparing Ratios, Percents, and Fractions Practice Problems355524222891200Compare these four mixes for apple juiceWhich mix would make the most “appley” juice?Mix Y is the most appley given it has the highest concentrate to juice ratio.Suppose you make a single batch of each mix. What fraction of each batch is concentrate?Mix W = 5/13, Mix X = 3/9 = 1/3, Mix Y = 6/15 = 2/5, Mix Z = 3/8Rewrite your answers to part (b) as percents.Mix W = 38.5%, Mix X = 33.3%, Mix Y = 40%, and Mix Z = 37.5%Suppose you make only 1 cup of Mix W. How much water and how much concentrate do you need?Mix W: 8/13 cup water and 5/13 cup concentrateExamine these statements about the apple juice mixes in Exercise 1. Decide whether each is accurate. Give reasons for your answers.Mix Y has the most water, so it will taste least “appley.”Not accurate since both water and concentrate contribute to the least appley taste. A mix with 9 cups of water that had 1 cup of concentrate would taste much less appley. Mix Z is the most “appley” because the difference between the concentrate and water is 2 cups. It is 3 cups for each of the others.Not accurate. Mix Y is the most appley. Also, being the most appley is not dependent on the difference between the two ingredients, but the fraction or percent of concentrate of the total cups of liquid.Mix Y is the most “appley” because it has only 1 ? cups of water for each cup of concentrate. The others have more water per cup.Accurate. Mix Y is the most appley because it has the greatest ratio of concentrate to water.Mix X and Mix Y taste the same because you just add 3 cups of concentrate and 3 cups of water to turn Mix X into Mix Y.Not accurate. The taste is determined by the ratio of concentrate to water. Since Mix Y has more concentrate per water it will have the most appley taste. At camp, Miriam uses a pottery wheel to make three bowls in 2 hours. Duane makes five bowls in 3 hours.Who makes bowls faster, Miriam or Duane?Duane. He can make about 1.7 (5/3) bowls per hour and Miriam can make only 1.5 bowls per hour.At the same pace, how long will it take Miriam to make a set of 12 bowls?8 hours because 2/3 = 8/12At the same pace, how long will it take Duane to make a set of 12 bowls?It will take Duane a little over 7 hours, or about 7.2 hours to make 12 bowls. Possible strategy: 5/3 = 1 2/3 and 12/1 1/3 = 7.2Guests at a pizza party are seated at 3 tables. The small table has 5 seats and 2 pizzas. The medium table has 7 seats and 3 pizzas. The large table has 12 seats and 5 pizzas. The pizzas at each table are shared equally. At which table does a guest get the most pizza?The medium table; at the medium table, each person gets about 3/7, or 43% of a pizza. In other words, there are about 2.3 people per pizza. At the small table, each person gets only 2/5, or 40%, of a pizza. There are 2.5 people per pizza. At the large table, each person gets about 5/12, or 42% of a pizza. There are 2.4 people per pizza. Suppose a news story about the Super Bowl claims “Men outnumbered women in the stadium by a ratio of 9 to 5.” Does this mean that there were 14 people in the stadium – 9 men and 5 women? If not, what does the statement mean?No, but if there had been only 14 people, then 9 would have been male and 5 would have been female. It means for every 9 men in the entire stadium, there were 5 females. So if there were 9,000 males, there were 5.000 females.Which of the following is an interpretation of the statement “Men outnumbered women by a ratio of 9 to 5?”There were four more men than women.56170357785The number of men was 1.8 times the number of women.The number of men divided by the number of women was equal to the quotient of 5 ÷9. In the stadium, five out of nine fans were women.Name ______________________________________________________________Comparing Ratios, Percents, and Fractions Teacher-Guided StationFor each business day, news reports tell the number of stocks that gained (went up in price) and the number that declined (went down in price). In each of the following pairs of reports, determine which is better news for investors[Gains outnumber declines by a ratio of 5 to 3] or [Gains outnumber declines by a ratio of 7 to 5][Gains outnumber declines by a ratio of 9 to 5] or [Gains outnumber declines by a ratio of 6 to 3][Declines outnumber gains by a ratio of 10 to 7] or [Declines outnumber gains by a ratio of 6 to 4]If possible, change each comparison to a fraction comparison. If it is not possible, explain why.The nut mix has 30% peanuts.The ratio of almonds to other nuts in the mix is 1 to 7.38442907620Use the table to the right to answer parts (a) – (e). What percent of the 55-64 age group walk for exercise?What percent of the 12-17 age group walk for exercise?Write a ratio statement to compare the number of 12- to 17-year-olds who walk to the number of 55- to 64-year-olds who walk. Use approximate numbers to simplify the ratio.Write a ratio statement to compare the percent of 12- to 17-year-olds who walk for exercise to the percent of 55- to 64-year-olds who walk for exercise.Which data – actual numbers of walkers or percents – would you use in comparing the popularity of exercise walking among various groups? Explain. Name ______________Key________________________________________________Comparing Ratios, Percents, and Fractions Teacher-Guided Station1. For each business day, news reports tell the number of stocks that gained (went up in price) and the number that declined (went down in price). In each of the following pairs of reports, determine which is better news for investors[Gains outnumber declines by a ratio of 5 to 3] or [Gains outnumber declines by a ratio of 7 to 5]The ratio of 5 to 3 is better than 7 to 5 for investors. In the ratio of 5 to 3, 5 out of every 8 people gain whereas the ratio 7 to 5, 7 out of every 12 people gain. Another way to look at it is the ratio 5:3 = 1.6667 and the ratio 7:5 = 1.4[Gains outnumber declines by a ratio of 9 to 5] or [Gains outnumber declines by a ratio of 6 to 3]The ratio of 6:3 is better than 9:5[Declines outnumber gains by a ratio of 10 to 7] or [Declines outnumber gains by a ratio of 6 to 4]The ratio of 10 to 7 is better for investors. 7/17 = 41% whereas 4/10 = 40%If possible, change each comparison to a fraction comparison. If it is not possible, explain why.The nut mix has 30% peanuts.3/10 peanutsThe ratio of almonds to other nuts in the mix is 1 to 7.1/8 almonds38442907620Use the table to the right to answer parts (a) – (e). What percent of the 55-64 age group walk for exercise?About 38.4%What percent of the 12-17 age group walk for exercise?About 16.3%Write a ratio statement to compare the number of 12- to 17-year-olds who walk to the number of 55- to 64-year-olds who walk. Use approximate numbers to simplify the ratio.The ratio of 12- to 17-year olds who walk for exercise to 55- to 64-year olds who walk for exercise is 3,781 to 8,694 or about 4 to 9Write a ratio statement to compare the percent of 12- to 17-year-olds who walk for exercise to the percent of 55- to 64-year-olds who walk for exercise.The ratio of the the percentage of 12- to 17-year olds who walk for exercise to the percent of 55- to 64-year olds who walk for exercise is 8 to 19Which data – actual numbers of walkers or percents – would you use in comparing the popularity of exercise walking among various groups? Explain. Percents, because the number sampled in each category is not the same number, therefore percents seem more appropriate to use so that the two categories can be compared, based on numbers out of 100.Name ________________________________________________Comparing Ratios, Percents, and Fractions Extensions778476441857Mammals vary in the length of their pregnancies, or gestations. Gestation is the time from conception to birth. Use the table to answer the questions that follow.Plan a way to compare life span and gestation time for animals and use it with the dataWhich animal has the greatest ratio of life span to gestation time? Which has the least ratio?Plot the data on a coordinate graph (on a separate sheet of graph paper) using (gestation, life span) as data points. Describe any interesting patterns that you see. Decide whether there is any relation between the two variables. Explain how you reached your conclusionWhat pattern would you expect to see in a graph if each statement were true?Longer gestation time implies longer life spanLonger gestation time implies shorter life span2741930-3397252. Use the table below.In which sport do boys most outnumber girls?In which sport do girls most outnumber boys?The participation in these team sports is about the same for students at Key Middle School.Suppose 250 boys at Key play sports. How many would you expect to play each of the three sports?Suppose 240 girls at Key play sports. How many would you expect to play each of the three sports?Name ____________________Key____________________________Comparing Ratios, Percents, and Fractions Extensions7784764418571. Mammals vary in the length of their pregnancies, or gestations. Gestation is the time from conception to birth. Use the table to answer the questions that follow.a. Plan a way to compare life span and gestation time for animals and use it with the dataRatios are a possible method of comparison. First change life, which is measured by years, to be measured by days. This can be done by multiplying the number of years for life span by 365 (days). Then, change the ratios into decimals in order to compare (Figure 3).b. Which animal has the greatest ratio of life span to gestation time? Which has the least ratio?The greatest life span to gestation time ratio is the chipmunk, which has a ratio of 2,190 to 31, or 70.6. The least life span to gestation time ratio is the giraffe, which has a ratio of 3,650: 425, or 8.6.right61921500c. Plot the data on a coordinate graph (on a separate sheet of graph paper) using (gestation, life span) as data points. Describe any interesting patterns that you see. Decide whether there is any relation between the two variables. Explain how you reached your conclusionMost of the coordinates follow the pattern that as gestation increases, life span increases. This is true except for two of the mammals, the moose and giraffe. From the pattern, there does appear to be a relationship between the gestation and the life span. d. What pattern would you expect to see in a graph if each statement were true?Longer gestation time implies longer life spanA positive slope, going up from the left to the right, to illustrate that as x (gestation) goes up/increases, y (life span) goes up/increases.Longer gestation time implies shorter life spanA negative slope, going down from left to right, so as x, or gestation, goes up/increases, y (life span) goes down/decreases. 1618083988542. Use the table below.a. In which sport do boys most outnumber girls?Football (The ratio of boys to girls is 6:1, the greatest ratio of all the sports.)b. In which sport do girls most outnumber boys?Soccerc. The participation in these team sports is about the same for students at Key Middle School.i. Suppose 250 boys at Key play sports. How many would you expect to play each of the three sports?Basketball = 89, football = 67, soccer = 94ii. Suppose 240 girls at Key play sports. How many would you expect to play each of the three sports?Basketball = 45, football = 15, soccer = 180 ................
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