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215-222 SB MS1 TE U04 A17.indd Page 215 07/03/14 11:12 AM user-g-w-728215-222 SB MS1 SE U04 A17.indd Page 215 05/03/14 9:42 AM user-g-w-728/103/SB00001 DEL/work/indd/TE/M01 Middile School/Math 01/Application files/TE M1 ./103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .Understanding RatiosACTIVITY 17All About PetsLesson 17-1 Understanding RatiosACTIVITY17DirectedActivity Standards FocusIn this activity, students learn that aratio is a comparison of two quantities,and can be written as a fraction, usingthe word “to”, or using a colon. Theyalso learn the terminology associatedwith ratios, and apply ratios in real-lifesituations to find missing values in atable and represent the table as a graphin the coordinate plane determining ifthe relationship is proportional.My NotesLearning Targets:Understand the concept of a ratio and use ratio language.Represent ratios with concrete models, fractions, and decimals.Give examples of ratios as multiplicative comparisons of twoquantities describing the same attribute. SUGGESTED LEARNING STRATEGIES: Interactive Word Wall,Visualization, Create Representations, Look for a PatternA ratio is a comparison of two quantities. Ratios can represent acomparison of part-to-part, part-to-whole, or whole-to-part. Ratios canbe written as fractions, or using the word “to” or a colon.Example AUse the tags below. Find each of these ratios:a. stars to bonesb. stars to total number of tagsc. total number of tags to bonesMATH TERMSEach part of a ratio is called a term.Terms can be: Numbers, such as 4 and 8: 48 ,4 to 8, 4:8 Variables, such as x and y: xy ,x to y, x:y The product of a number and avariable, such as 3x and 9y:3 x , 3x to 9y, 3x:9y9yWrite each ratio three different ways. State whether the ratio is a partto-part, part-to-whole, or whole-to-part.Lesson 17-1PLANPacing: 1 class periodChunking the LessonExample AExample BCheck Your UnderstandingLesson PracticeTEACHBell-Ringer ActivitySolution:a. stars to bonesnumber of stars 4; 4 to 8, 4:8number of bones 8b. stars to total number of tagsnumber of stars 4part-to-whole:; 4 to 12; 4:12number of tags 12c. total number of tags to bonesnumber of tagswhole-to-part: 12 ; 12 to 8; 12:8number of bones 8 2014 College Board. All rights reserved. 2014 College Board. All rights reserved.part-to-part:MATH TIPLike fractions, ratios cansometimes be rewritten in lowestterms.Try These AUse ratios to compare the pet toys shown. Write each ratio threedifferent ways. State whether the ratio is a part-to-part, part-to-whole,or whole-to-part.a. balls of yarn to mice4 1 , 1 to 2, or 1:28 24 1 , 1 to 3, or 1:312 312 3 , 3 to 2, or 3:28 2Example A Note taking, SharedReading Students explore ratios as acomparison of part-to-part, part-towhole, and whole-to-part. As studentscompare the numbers of stars, bones,and tags by writing various ratios, makesure they write the ratio correctly byidentifying each quantity as a part or asa whole. It is important for students tohave an opportunity to share how theyexpressed the ratios before moving on tocalculating with ratios in Lesson 17-2.This should provide the teacher with animportant formative assessment.4 , 4:5, 4 to 5; part-to-part5b. white balls of yarn to total number of toysc.3 , 3:9, 3 to 9 or 1 , 1:3, 1 to 3; part-to-whole93gray mice to white mice 41 , 4:1, 4 to 1; part-to-partCommon Core State Standards for Activity 176.RP.A.1Activity 17 Understanding RatiosAsk students to count the number ofgirls in the class and the number ofboys, and to write a fraction with thenumber of girls as the numerator andthe number of boys as the denominator.Have them show how the fraction wouldchange if two girls moved away. Discusswith students how they rewrote theirfractions to represent this new situation.215Understand the concept of a ratio and use ratio language to describe a ratio relationshipbetween two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate Creceived nearly three votes.”6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoningabout tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.6.RP.A.3a Make tables of equivalent ratios relating quantities with whole-number measurements, findmissing values in the tables, and plot the pairs of values on the coordinate plane. Use tables tocompare ratios.Students may mention that the ratios inthe example have not been simplified.Take time to read the Math Tip signalbox so that students understand thatthey often are simplified.Developing Math LanguageEncourage students to mark the text andtake notes explaining the newvocabulary. Make sure studentsunderstand that ratios compare twoquantities, and that each part of a ratiois called a term.Activity 17 Understanding Ratios215
215-222 SB MS1 TE U04 A17.indd Page 216 8/7/13 3:04 PM dksharma/103/SB00001 DEL/work/indd/TE/Math 01/Application files/TE M1 Unit 04215-222 SB MS1 SE U04 A17.indd Page 216 7/26/13 5:25 AM gg-57/103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .ACTIVITY 17 ContinuedcontinuedMy NotesA ratio is also a multiplicative comparison of two quantities.The ratio of circles to the total number of shapes below is 2 .5This means 2 of all the shapes are circles and that for every 2 circles5added, a total of 5 shapes will be added.MATH TIPLike fractions, ratios can be writtenas decimals. The ratio 3 is the4quotient of 3 4 or 0.75.Suppose a set of shapes with the pattern above includes 8 circles. Youknow that 2 4 8, so multiply the number of shapes in the repeatingpart of the set (2 circles 3 squares 5 shapes) by 4 to find the totalnumber of shapes when there are 8 circles: 5 4 20 total shapes.Example BMake sense of problems. In January, for every 3 cats adopted, 4 dogswere adopted. A total of 16 dogs were adopted. How many cats wereadopted?Step 1:Write a ratio comparing the number of cats to the number ofdogs adopted.number of cats 3number of dogs 4The number of cats adopted is 3 times the number of dogs4adopted.Step 2:Multiply the ratio times the number needed to create anequivalent ratio showing 16 dogs.3 4 12 cats4 4 16 dogsTEACHER to TEACHERIf students need more review forfinding unknown quantities in ratios,there is a Mini-Lesson: Using Ratiosin the eBook Teacher Resources.CONNECT TO APSolution: 12 cats were adopted.Emphasize the importance of ratiosin algebra and future math courses.For example, the ratio of the verticalchange to the horizontal change ofthe graph of a linear function givesthe slope of the line, and this ratio isconstant for all pairs of points on theline. It is the rate of change for thelinear function. Nonlinear functionsdo not have this property, but incalculus, the ratio of the “rise” to the“run” is still used to describe the rateof change quickly and efficiently.Check:Does the ratio of 12 cats to 16 dogs equal 3 ?412 12 4 316 16 4 4Try These BAt the dog park on Monday, 2 dogs out of every 5 were terriers. A totalof 20 dogs were at the park.a. How many terriers were there? Explain how you got your answer.8 terriers; the ratio of terriers to the total number of dogs is2 4 8 terriers .5 420 dogs b. The ratio of Irish terriers to the total number of terriers was 1:4.How many of the terriers were Irish terriers? Explain how you gotyour answer.2 Irish terriers; the ratio of Irish terriers to the total number ofterriers is 1 8 2 Irish terriers.14 216 SpringBoard Mathematics Course 1, Unit 4 RatiosCommon Core State Standards for Activity 17 (continued)6.EE.C.9216Use variables to represent two quantities in a real-world problem that change in relationship toone another; write an equation to express one quantity, thought of as the dependent variable,in terms of the other quantity, thought of as the independent variable. Analyze the relationshipbetween the dependent and independent variables using graphs and tables, and relate theseto the equation. For example, in a problem involving motion at constant speed, list and graphordered pairs of distances and times, and write the equation d 65t to represent the relationshipbetween distance and time.SpringBoard Mathematics Course 1, Unit 4 Ratios 2014 College Board. All rights reserved.Example B Activating PriorKnowledge, Think-Pair-Share,Debriefing In this example, studentswill use the idea that a ratio is also amultiplicative comparison between twoquantities. They will need to multiplyboth terms in the ratio by a factor thatwill give an equivalent ratio. Havestudents read the steps together andidentify the equivalent fractions asratios. Make sure that debriefing theexample includes checking the solutionby using the inverse process of dividingboth terms of the ratio by 4 to get theoriginal reduced ratio of cats to dogs.It is important to validate the purpose ofeach step in finding the number of catsadopted when 16 dogs were adopted.Lesson 17-1Understanding RatiosACTIVITY 17 2014 College Board. All rights reserved.Paragraphs Have students read anddiscuss the text above Example B.Students may need to extend the patternto understand what is meant by the text.
215-222 SB MS1 TE U04 A17.indd Page 217 24/08/13 10:23 AM user-g-w-728215-222 SB MS1 SE U04 A17.indd Page 217 09/03/13 11:07 PM s-059/103/SB00001 DEL/work/indd/TE/Math 01/Application files/TE M1 Unit 04/103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .ACTIVITY 17 ContinuedLesson 17-1Understanding RatiosACTIVITY 17continuedStudents should understand that whenthey find a ratio equivalent to anotherratio, they are using the IdentityProperty of Multiplication. InExample B, since they are multiplyinga ratio (a real number) by a form of 1,the product is an equivalent ratio (alsoequal to the same real number).My NotesCheck Your Understanding1. For a given ratio, how many equivalent ratios can be written?Explain your reasoning.2. How can you check to see if the ratio 1:2 is equivalent to anotherratio?3. Find as many whole-number ratios equal to 50:100 as you can,using division.Check Your UnderstandingDebrief students’ answers to these itemsto ensure they understand how to writeratios equivalent to a given ratio.LESSON 17-1 PRACTICEAnswers4. Use ratios to compare the dog bowls shown. Write each ratio threedifferent ways. State whether the ratio is a part-to-part, part-towhole, or whole-to-part.1. Infinitely many because you canmultiply both terms in the ratio byany number.2. Multiply both terms in 1:2 by a factorthat will give the terms in the secondratio.3. Five; 50:100, 25:50, 10:20, 5:10, 1:2.a. white bowls to total number of bowlsb. black bowls to gray bowlsc. all bowls to bowls that are not grayASSESS 2014 College Board. All rights reserved.5. At the veterinarian’s office, 4 animals out of every 5 seen were cats.A total of 35 animals were seen.a. How many cats were seen?b. The ratio of male cats to all cats seen was 6:7. How many of thecats seen were males? 2014 College Board. All rights reserved.TEACHER to TEACHERUse the lesson practice to assessstudents’ understanding of how to writeratios and how to use a ratio as amultiplicative comparison of twoquantities.6. There are twelve rabbits in a cage. The ratio of white rabbits to allrabbits is 3:4. How many white rabbits are in the cage?See the Activity Practice for additionalproblems for this lesson. You may assignthe problems here or use them as aculmination for the activity.7. Make sense of problems. Each veterinarian has seen 40 animalstoday. Two out of every 5 animals Vet A has seen have been dogs.Three out of every 8 animals Vet B has seen have been dogs. Whichvet saw more dogs today? Explain your reasoning.LESSON 17-1 PRACTICE8. Reason abstractly. The ratio of red collars to black collars sold atone store is 9 to 10. In one month 30 black collars are sold. Is 57 areasonable number for the total number of red and black collars soldthat month? Explain your reasoning.9. There are 15 black mice in a cage. The ratio of all mice to black miceis 5:1. How many mice are in the cage?Activity 17 Understanding Ratios2174. a. 3 1 , 1:2, 1 to 2; part-to-whole6 2b. 2 , 2:1, 2 to 1; part-to-part1c. 6 , 6:5, 6 to 5; whole-to-part55. a. 28 cats; 4 285 35b. 24 male cats: 6 247 286. 9 white rabbits7. Vet A saw 16 dogs: 2 16 , Vet B5 40saw 15 dogs: 3 15 , 16 15. Vet A8 40saw more dogs.8. Yes. In the ratios 9 ? , 30 is10 303 10, so ? is 3 9, or 27.27 30 579. 75 miceADAPTCheck students’ answers to the LessonPractice to ensure they understand howto use a ratio as a multiplicativecomparison. Review this concept withstudents and provide additional practiceas needed.Activity 17 Understanding Ratios217
215-222 SB MS1 TE U04 A17.indd Page 218 07/03/14 11:12 AM user-g-w-728/103/SB00001 DEL/work/indd/TE/M01 Middile School/Math 01/Application files/TE M1 .215-222 SB MS1 SE U04 A17.indd Page 218 05/03/14 9:42 AM user-g-w-728ACTIVITY 17 ContinuedLesson 17-2Lesson 17-2Ratios in Proportional RelationshipsACTIVITY 17continuedPLANMy NotesPacing: 1 class periodChunking the LessonLearning Targets:Make tables of equivalent ratios relating quantities.Use tables to compare ratios.Plot the pairs of values on the coordinate plane and describe therelationship. Example AExample BCheck Your UnderstandingLesson PracticeSUGGESTED LEARNING STRATEGIES: Interactive Word Wall,Visualization, Create Representations, Identify a SubtaskTEACHMATH TERMSIntroduction Shared Reading,Note Taking, Developing MathLanguage Have students read theintroductory paragraph and mark thetext. Encourage them to mark the textand add notes in their own words aboutthe definition and usage of equivalentratios, proportional relationships, andratio table. They will use these conceptsas they do the examples and items, sohave them revisit and update their notesto enhance their understanding.Equivalent ratios are found bymultiplying or dividing both termsof a ratio by the same number.Example AReason quantitatively. A recipe for a homemade dog treat calls fora mixture of 8 ounces of oats to 12 ounces of finely chopped liver.Complete the ratio table.Oats (oz)Liver (oz)8 48 2246312 4 12 28128 2168 102412012 212 1080a. How many ounces of liver are needed with 16 oz of oats?Solution: 24 oz of liver are needed with 16 oz of oats.b. How many ounces of oats are needed with 120 oz of liver?Solution: 80 oz of oats are needed with 120 oz of liver.c. Use the table to name four ratios equivalent to 8 .12Solution: The ratios 2 , 4 , 16 , and 80 are equivalent to 8 .3 6 2412012Try These Aa. In one recipe for dog biscuits, the ratio of cups of water to cups offlour used is 3:9. Complete the ratio table.3 3Water (c)Flour (c)139 3393 2 3 4 3 6 3 91827612183654819 2 9 4 9 6 9 9b. How many cups of water are needed with 81 cups of flour? 27c. How many cups of flour are needed with 12 cups of water? 36d. Use the table to name five ratios equivalent to 3:9.Sample answer: 1:3, 6:18, 12:36, 18:54, and 27:81.218SpringBoard Mathematics Course 1, Unit 4 RatiosSpringBoard Mathematics Course 1, Unit 4 Ratios 2014 College Board. All rights reserved.Example A Create Representations,Think-Pair-Share Encourage studentsto study the table to make sense of theinformation given in the problem and tosee how division and multiplicationwere used to fill in the table anddetermine the ratios needed to answerthe questions posed. Point out the hintsat the top of the tables if students needhelp to begin. Have them discuss theexample questions with their groupmembers. Point out that they can usethe pattern in the table to help themfind the number of ounces of oats for agiven number of ounces of liver. Askstudents to describe patterns that theynotice in the table and encourage themto extend the table using these patterns.Then ask them to apply what they havelearned to Try These A problems.Encourage precision and accuracy inmathematical language.Equivalent ratios are ratios thatname the same number, just asequivalent fractions do.Relationships that have equivalent ratios are called proportionalrelationships. All the columns in a ratio table show equivalent ratios. 2014 College Board. All rights reserved.Bell-Ringer ActivityGive students 2 minutes to write all thefractions they can that are equivalent to 3 .4Have them compare their list with apartner.218/103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .
215-222 SB MS1 TE U04 A17.indd Page 219 24/08/13 10:24 AM user-g-w-728/103/SB00001 DEL/work/indd/TE/Math 01/Application files/TE M1 Unit 04/103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .215-222 SB MS1 SE U04 A17.indd Page 219 09/03/13 11:07 PM s-059ACTIVITY 17 ContinuedLesson 17-2Ratios in Proportional RelationshipsACTIVITY 17continuedMy NotesA relationship is proportional if the graph of the relationship is a set ofpoints through which a straight line can be drawn and the straight linepasses through the point (0, 0).Example BAt the animal food store, 20 dog biscuits cost 6. Is the relationshipbetween the number of biscuits and the cost proportional?Step 1:Number of Biscuits, x10204060Total Cost ( ), y3612189630x20406080Number of Biscuitsa. Not proportional; the linedoes not pass through (0, 0).yTry These BGraph each relationship in the My Notes section to the right. Determineif the relationship is proportional or not proportional. Explain yourreasoninga.b.Number of Hours, x24689Total Cost ( ), y1525354550Number of Hours, x24689Total Cost ( ), y612182427Cost ( )Solution: A line passes through all the points and through (0, 0). Thismeans that the relationship is proportional.50403020100b. Proportional; the line passesthrough (0, 0) and all thepoints.y50403020100Equivalent fractions in the ratio tablewill translate into a constant ratiobetween points of the line, and thatconstant ratio will be known as theslope of the line in future lessons andmathematics courses. Modeling slopeas the rate of change is an importantconnection to more advancedmathematics classes like calculus.As noted in the AP Calculus CourseDescription, “students should be ableto work with functions represented ina variety of ways: graphical, numerical,analytical and verbal.”x0 2 4 6 8 10Number of HoursActivity 17 Understanding RatiosNoticing whether and how studentslabel the graph and create the scale inthe Try These B items provides aformative assessment regardingstudent knowledge of these skills.Note that some students may reversethe independent and dependentvariables when they graph the datafrom the table. If necessary, discussproper labeling and where thedependent and independent variablesshould be graphed. Have studentsexplain their reasoning for describingthe relationships as proportional ornot proportional. Make sure theyconsider whether (0, 0) is a point ofthe graph before they decide.CONNECT TO APx0 2 4 6 8 10Number of HoursCost ( ) 2014 College Board. All rights reserved.0 2014 College Board. All rights reserved.TEACHER to TEACHERGraph the relationship between the number of biscuits x andthe cost y.Cost of Dog BiscuitsPlot the ordered pairsy(x, y) from the table:18(10, 3), (20, 6), (40, 12),15and (60, 18).12Cost ( )Step 2:Make a ratio table.Example B Look for a Pattern, CreateRepresentations, Think-Pair-ShareAsk students to discuss the pattern inthe table with their partners and howthe pattern translates into a graph thatappears to be points that lie in line.Point out that if a line does pass throughall of the points and through (0, 0), thenthe relationship is proportional. Somestudents may need to insert additionalcolumns in the table and then graph thepoints to help them see the pattern.219Developing Math LanguageThis lesson contains the idea of aproportional relationship. Encouragestudents to return to where they firstmarked this term in the text and reviseor add to the explanation they wrote atthe beginning of the lesson.Activity 17 Understanding Ratios219
215-222 SB MS1 TE U04 A17.indd Page 220 27/03/14 9:15 AM user-g-w-728/103/SB00001 DEL/work/indd/TE/M01 Middile School/Math 01/Application files/TE M1 .215-222 SB MS1 SE U04 A17.indd Page 220 24/08/13 1:45 AM user-s068a 000 /103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .ACTIVITY 17 ContinuedLesson 17-2Ratios in Proportional RelationshipsACTIVITY 17My NotesCheck Your UnderstandingAnswers1. How can you use a ratio table to find the value of x in the ratio x:20if the ratio is equivalent to 5:2? Explain your reasoning.1. Since 2 10 20, multiply 5 10to find x: x 5 10, or 50.2. Graph the ordered pairs, (x, y).If a line can be drawn connecting thepoints and the line goes through(0, 0), the values have a proportionalrelationship. If the x- and y-values inthe table simplify to the same ratio,then the values are proportional.2. Name two ways to determine if the x- and y-values in a table have aproportional relationship.LESSON 17-2 PRACTICE3. Reason quantitatively. The recipe for a homemade dog treat callsfor a mixture of 2 eggs for every 8 cups of flour.a. Complete the ratio table.ASSESSNumber of EggsUse the lesson practice to assess students’understanding of how to write and grapha ratio table. In Item 3, have partnersdiscuss how they found the values for theratio table. This will ensure that studentsunderstand how to write equivalentratios. Then debrief the answers to parts band c as a class. The whole groupdebriefing should focus on how the ratiosin the table are interpreted as a real-lifeuse of the ratios. Circulate as studentsbegin calculations to be sure students aregraphing the ratio table data in Item 4bcorrectly.Cups of Flour12Cups ofFlour48 24 40 64b. 10 eggsc. 24 eggsd. 1 , 6 , 10 , 164 24 40 64e. 1:44. a.Number of1Days, xNumber of Days, xTotal Cost ( ), yTotal Cost( ), y541210 20 40yd. 30 b. SpringBoardMathematics Course 1, Unit 4 Ratios220Cost ( )40Check students’ answers to the LessonPractice to ensure they understand howto write and graph a ratio table. Reviewthese concepts and provide additionalpractice as needed.6448208ADAPT302010x00 26 10 14 18Number of daysc. Yes; a line can be drawn connecting thepoints, and the line goes through (0, 0).22040b. Graph the relationship between the number of days x and thecost y.c. Is the relationship between the number of days and the costproportional? Justify your answer.d. Use your graph to determine how much Julie should charge for 6days of dog sitting.e. Is 4:20 equivalent to 10:50? Explain using the graph.5. Are 2 and 5 equivalent ratios? Justify your answer.636. Are 2 and 6 equivalent ratios? Justify your answer.7217. Are 2 and 3 equivalent ratios? Justify your answer.466 10 16284. Model with mathematics. For every 4 days of dog sitting Juliecharges 20.a. Complete the table to find the amount Julie shouldcharge for 1, 2, and 8 days of dog sitting.LESSON 17-2 PRACTICENumberof Eggs6b. How many eggs are needed with 40 cups of flour?c. How many cups of flour are needed with 6 eggs?2d. Use the table to name four ratios equivalent to 8 .e. Which ratio is equivalent to 2:8 in lowest terms?See the Activity Practice for additionalproblems for this lesson. You may assignthe problems here or use them as aculmination for the activity.3. a.21SpringBoard Mathematics Course 1, Unit 4 Ratiose. Yes; (10, 50) is a point on the line, so10:50 is equivalent to 4:20.5. No, 3 2 6, but 2 2 4, not 5.Therefore 2 and 5 are not equivalent36ratios.6. Yes, 7 3 21, and 2 3 6. Therefore2 and 6 are equivalent ratios.7217. Yes, 2 1 and 3 1 , so they are6 24 2equivalent ratios. Also, both ratios,when graphed, are on a line that goesthrough (0, 0). 2014 College Board. All rights reserved.Debrief student answers to these itemsto ensure that students understand howa write a ratio table and then graph thetable.continued 2014 College Board. All rights reserved.Check Your Understanding
215-222 SB MS1 TE U04 A17.indd Page 221 24/08/13 10:25 AM user-g-w-728/103/SB00001 DEL/work/indd/TE/Math 01/Application files/TE M1 Unit 04215-222 SB MS1 SE U04 A17.indd Page 221 24/08/13 1:46 AM user-s068a 000 /103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .ACTIVITY 17 ContinuedUnderstanding RatiosAll About PetsACTIVITY 17 PRACTICEWrite your answers on notebook paper.Show your work.Lesson 17-11. Write a ratio in three different ways to representthe number of boys to the number of girls inthe class.GirlsBoys12152. Write a ratio for each situation.a. 310 heartbeats per 5 minutesb. 68 for 8 hours of workc. Work 40 hours in 5 days3. A recent study shows that out of 100 pieces of apopular multicolored snack, there will usuallybe the following number of pieces of eachcolor. 2014 College Board. All rights reserved. 2014 College Board. All rights reserved.Brown Yellow Red131413Blue Orange Green242016a. The numbers for two colors form a ratiothat is equal to 7 . What are the colors?12What is their ratio?b. If there were 500 pieces, about how manywould be red?4. Katie is making lemonade from a powder mix.The ratio of scoops of powder mix to water is4 scoops to 1 gallon.a. How much water should Katie mix if sheuses 12 scoops of mix?b. How much powder mix should Katie use ifshe plans to use 5 gallons of water?ACTIVITY 17continued6. Which of the following expressions is not aratio?2A. 3B. 2:3C. 2 to 3D. 2 37. Which of the following compares the numberof stars to the number of circles?A. 68C. 3:4B. 4:3D. 8 to 148. How does a ratio comparing the number ofsquares to the total number of shapes compareto a ratio comparing the number of arrows tothe total number of shapes?9. There are three types of animals in the picturesin Mica’s album: horses, cows, and sheep. Theratio of horses to total number of animals inthe pictures is 2:8. The ratio of cows to totalnumber of animals in the pictures is 1:4.a. What can you conclude about the number ofhorses and the number of cows in thepictures?b. There are 40 animals pictured in Mica’salbum. How many are either horses or cows?ACTIVITY PRACTICE1. 15:12, 15 to 12, 15122. a. 310:5 (or 310 or 310 to 5)5b. 68:8 (or 68 or 68 to 8)8c. 40:5 (or 40 or 40 to 5)53. a. yellow and blue; 14:24, whichsimplifies to 7:12b. about 65; 13 ? , 5 13 65100 5004. a. 3 gallonsb. 20 scoops5. Yes. The ratio of red to all blocks is 3to 5. 3 ? . 5 12 60, so 3 125 60 36. So there are more than enoughred blocks.6. D7. B8. Both ratios are 6:12, so they areequivalent ratios.9. a. There is the same number ofhorses as there are cows becausethe ratios are equivalent.b. 20, 10 10 2010. a. Sample answer: circles to allshapes; 3:4b. Sample answer: circles torectangles; 3:1c. Sample answer: all shapes torectangles; 4:110. Write a ratio in lowest terms for each type ofrelationship for the following shapes.a. part-to-wholeb. part-to-partc. whole-to-part5. There are a total of 60 plastic blocks. Three outof every 5 blocks are red. Is it reasonable forBriana to think there are enough red blocks tomake a design that uses 32 red blocks? Explainyour reasoning.Activity 17 Understanding Ratios221Activity 17 Understanding Ratios221
215-222 SB MS1 TE U04 A17.indd Page 222 25/03/14 2:12 PM user-g-w-728/103/SB00001 DEL/work/indd/TE/M01 Middile School/Math 01/Application files/TE M1 .215-222 SB MS1 SE U04 A17.indd Page 222 7/26/13 5:24 AM gg-57/103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .ACTIVITY 17 ContinuedUnderstanding RatiosAll About PetsACTIVITY 174539036631651133013223112. C13. D14. a. Yes. The graph is a line thatpasses through (0, 0), so therelationship is proportional.b. 150 milesc. x 515. Check students’ graphs. Notproportional; The graph is a line butit does not pass through (0, 0), sothe relationship is not proportional.ADDITIONAL PRACTICEIf students need more practice on theconcepts in this activity, see the eBookTeacher Resources for additionalpractice problems.continuedLesson 17-211. Complete the ratio table to show ratiosequivalent to 9:33.45314. The following is a graph of the number ofhours driven versus the number of milestraveled. Use the graph to answer parts a–c.y6333030013212. Which of the following ratios is not equivalentto 9:33?18B.A. 5466198C. 1D. 6222513. The ratios 4:5 and x:80 have a proportionalrelationship. What is the value of x?A. 79B. 100C. 81D. 64250Number of Miles11.200150100501234567xHoursa. Is the relationship between the number ofhours driven and the number of milestraveled proportional? Explain yourreasoning.b. After 3 hours of driving, how many mileswould be traveled?c. Find the value of x.2 x100 250222 SpringBoard Mathematics Course 1, Unit 4 Ratios222SpringBoard Mathematics Course 1, Unit 4 RatiosNumber of Pens, y248Total Cost ( ), x1012 161220 2014 College Board. All rights reserved.15. Graph the following relationship. Determine ifthe relationship is proportional or notproportional. Explain your reasoning 2014 College Board. All rights reserved.MATHEMATICAL PRACTICESConstruct Viable Arguments
215-222 SB MS1 SE U04 A17.indd Page 215 05/03/14 9:42 AM user-g-w-728/103/SB00001 DEL/work/indd/SE/M01 Middile School/Math 01/Application files/SE M1 .Understanding RatiosACTIVITY 17All About PetsLesson 17-1 Understanding RatiosMy NotesLearning Targets:Understand the concept of a ratio and use ratio language.Represent ratios with concrete models, fractions, and decimals.Give examples of ratios as multiplicative comparisons of twoquantities describing the same attribute. SUGGESTED LEARNING STRATEGIES: Interactive Word Wall,Visualization, Create Representations, Look for a PatternA ratio is a comparison of two quantities. Ratios can represent acomparison of part-to-part, part-to-whole, or whole-to-part. Ratios canbe written as fractions, or u
Step 1: Write a ratio comparing the number of cats to the number of dogs adopted. numberofcats numberofdogs 3 4 The number of cats adopted is 3 4 times the number of dogs adopted. Step 2: Multiply the ratio times the number needed to create an equivalent ratio showing 16 dogs.
