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Find the unit rate:Great gas mileage!115 miles5 gallons56 action-packed pages filled with guidednotes, worksheets, math poetry, activities,and assessments! A complete unit formastering ratios, rates, and proportions intwo weeks or y-Schneiderman Barry Schneiderman, 2013
Instructions for the teacherHere it is at last – the real deal! Everything you need to introduce students to ratio, rate, unit rate,and proportion concepts and ensure they understand and retain them! This product addresses sixth,seventh, and eighth grade common core standards, but can also be used for advanced fifth gradestudents. Follow these instructions and use the various materials step-by-step, and your studentswill not only learn how to solve ratio, rate, and proportion problems, but also discover why we usethem and their incredible value and versatility in solving day-to-day real-world problems.This product is broken up into six different sections:1. Ratios – Includes a warm-up activity, note-taking page, illustrated poetry, and worksheet.2. Rates – Includes a warm-up activity, note-taking page, illustrated poetry, and worksheet.3. Proportions – Includes a two warm-up activities, two note-taking pages, illustrated poetry, andtwo worksheets.4. Proportion Word Problems - Includes a warm-up activity, note-taking page, and worksheet.5. Tricky Rate / Proportion Word Problem Challenge – An exciting competition that serves as areview for the unit assessment.6. Rate / Ratio / Proportion Unit Assessment (which can also be used as a pre-assessment)As indicated above, each of the first four of these sections, which eventually ready the students forthe final two sections, contains four different worksheets/activities. The recommendedimplementation process of each of these is described below:a. The Warm-up activity. This activity is done at the beginning of the class and serves at leastthree purposes:- It gets the students’ creative juices flowing, and stimulates their mathematical thinking, therebyreadying them for the lesson to come.- It generates enthusiasm for the topic and for the guided note-taking via a discussion of thestudents’ potential solutions to the problems .- It serves as an informal pre-assessment, as you walk around the room and observe what thestudents know and don’t know about this particular topic, pitfalls you will need to overcome, etc.You can either project the warm-up on to a screen and have the students work out solutions onpaper, or distribute the warm-up as a worksheet, to be put in the students’ math notebook uponcompletion. In either case, keep the following in mind as you do the warm-up activity:- Warm-up time should not be a time for you to teach the students, but rather a time to see whatthe students know and how they are thinking.- Therefore, you should be using this as an opportunity to see what solutions the students offer,and not yet present any solutions yourself. In some cases, you may not even tell the students thecorrect answers (keys with correct answers are provided), but just allow them to explain theirpotential methods of getting to the answers.- When you feel the creative juices are flowing and the students’ curiosity is sufficiently piqued,dive into the guided note-taking activity. You may come back to the warm-up to work theproblems using appropriate methods if you choose to after the ore/Barry-Schneiderman Barry Schneiderman, 2013
Instructions for the teacher (continued)b. The Notes page. This pictorially illustrated, guided note-taking activity immediately follows thewarm-up activity and should be used as follows:- Distribute copies of the notes page. These pages not only contain lots of information, but also havemany strategically placed blanks and/or work areas that need to be filled in by the students.- Project a copy of the notes page. Work through it with the students. Have them fill in the blanksand/or work the problems with your guidance as you go (a detailed key is provided for each notespage), discussing the concepts as appropriate. The notes page should go into the students’ notebooksfor reference as they do the worksheets and study for the unit assessment.- When you feel the students understand the content of the notes page, go directly to the poetry to helpfurther cement the concepts. You may also go back to the warm-up activity and address it usingmethods learned via the notes page if appropriate.c. The Poetry sheet. I have found this illustrated poetry is a key piece to cementing the concepts forthe students. For instance, they may seem like they know exactly what makes a rate a rate, butsometimes they do not truly remember the reasons until they recite the poetry.- Read through the poetry with the students, having them recite it also or repeat it back to you.Address the concepts one more time via the illustrations as you go.- Give the students a copy of the poetry to put in their notebooks.- Review the poetry or use some key verses from it as often as necessary as you go through the lessonsand review for the unit assessment.- Some students may memorize the poetry, some may not. If they do so, it will help them prepare forthe assessment. If not, simply reciting the poetry will help ensure they have the concepts correctlysorted out as they work through the unit.- After completing the poetry, dive directly into the worksheet so the students can implement andpractice what they have learnedd. The Worksheet. The use here is self-explanatory. The students use the worksheet to practicewhat they have learned via the warm-up, note taking, and poetry. Students may work on theworksheet either alone or with partners. Detailed keys are provided for you to review the worksheetsolutions with the students.After spending the required amount of time on the warm-ups, notes, poetry, and worksheets for eachsection (an exact timeline is not provided as timing will vary by class, ability, and level of priorknowledge), move to the Tricky Rate / Proportion Word Problem Challenge . I usually givethe students 1 – 1.5 class periods to complete this, usually with partners, and usually for some sort ofprize for the winners. I also usually do a couple of “tricky” examples with the students before we start.This activity, which serves as a partial review for the assessment, helps the students realize the level ofcomplexity of problems they can now solve using the concepts they have learned. It also helps toremind the students they must truly read word problems to successfully tackle them.All that remains at this point is to do the Unit Assessment. Again, detailed keys are provided.Good luck in your implementation ofRatios, Rates, and Proportions arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio Warm-upThere are 4 girls and 6 boys in Mr. Tolentino’s classGirls1.Fill in the blanks below:Number of GirlsNumber of BoysNumber of BoysNumber of GirlsNumber of GirlsNumber of StudentsNumber of BoysNumber of StudentsBoys 2. If you had to explain to someone what part of the classwas boys and what part was girls, which of the comparisonsabove would you use? y-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio Warm-up - KEYThere are 4 girls and 6 boys in Mr. Tolentino’s classGirlsBoys1.Fill in the blanks below:Number of GirlsNumber of BoysNumber of BoysNumber of GirlsNumber of GirlsNumber of StudentsNumber of BoysNumber of Students 4664410610 233225352. If you had to explain to someone what part of the classwas boys and what part was girls, which of the comparisonsabove would you use? Why? Answers will vary. Thisshould be used to springboard into a discussion ofwhat ratios are, the difference between part-to-partand part-to-whole ratios, etc., and should lead directlyinto the notes on the next ry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio NotesRATIO A ratio can be expressed in three ways; in form,using a , or using the word “ ”.Example – Girls and Boys in Mr. Tolentino’s Class:The ratio of girlsto boysis:Fraction FormUsing a ColonUsing “To”Ratios are easiest to understand and use when they are inform, so we always ratios.Ratios vs. FractionsIs the ratio in fraction form above actually a fraction?Why or why not?We could turn the part-to-part ratio of girls to boys into a part-towhole ratio (fraction) byWords:part wholeFraction: Simplified Fraction: Ratios with different cannot be converted in to fractions.Give four examples of ratios that cannot be converted to e/Barry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio Notes - KEYRATIO The amount of one quantity compared to theamount of another quantity.A ratio can be expressed in three ways; in fraction form,using a colon , or using the word “to”.Example – Girls and Boys in Mr. Tolentino’s Class:The ratio of girlsto boysFraction Form𝟒𝟔 𝟐𝟐 is:Using a Colon𝟐𝟑Using “To”4:6 or 2:34 to 6 or 2 to 3Ratios are easiest to understand and use when they are insimplest form, so we always simplify ratios.Ratios vs. FractionsIs the ratio in fraction form above actually a fraction? NOWhy or why not? Because it compares the PART of theclass that is girls to the PART of the class that is boys.(It is a PART-TO-PART ratio, NOT a fraction)We could turn the part-to-part ratio of boys to girls into a part-towhole ratio (fraction) by Putting the whole class in the denominator!Words:Part WholegirlsFraction: girls boys410Simplified Fraction: 25Ratios with different units cannot be converted in to fractions. Givefour examples of ratios that cannot be converted to fractions:Examples will vary. Discuss ratios vs. fractions at this chneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio PoetryA ratio just compares,One quantity to another.Like dogs to cats, mice to rats,Or your sisters to your brothers!Ratios can be writtenThree different ways – it’s true:2 dogsIn fraction form 3 cats , with a colon, 3 mice : 2 ratsOr just using the word, “to”. 4 sisters to 3 brothersAll ratios can look like fractions,If written with a fraction bar,But it’s only part-to-whole ratios,That really truly are.2 dogs3 catsNot afraction!Fraction!2 dogs5 arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio Worksheet1. Write each comparison below as a ratio in the three differentforms indicated (make sure you convert it to simplest form!). Thenanswer “yes” or “no” in the last two columns of the table.Comparison:FractionFormColon“To”Is afraction?Can beconvertedto afraction?1 ball to 6 players8 boys to 20 classmembers6 A’s to 14 B’s in a class60 miles on 3 gallons12 completions in 20pass attempts40 gummy bears for 5to6 chipmunks to 7squirrels27 students to /Barry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio Worksheet (continued)2. In an orchard, there are 150 orange trees and 250 apple trees.a.In simplest fraction form, what is the ratio of orange trees toapple trees?b.In simplest fraction form, what is the ratio of apple trees toorange trees?c.In simplest fraction form, what is the ratio of orange trees tototal trees in the orchard?d.In simplest fraction form, what is the ratio of apple trees tototal trees in the orchard?e.Which of the answers to a, b, c, and d above are fractions?f.Explain why the answers you listed in question e are fractions:g.Challenge question: Write each of the answers listed in questione as decimals and percents. SHOW YOUR WORK!3. Use words to write two different ratios that can’t be convertedto fractions:4. The ratio of boys to girls in a class is 4 to 5. There are 20 boys in theclass. How many girls are in the arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio Worksheet - KEY1. Write each comparison below as a ratio in the three differentforms indicated (make sure you convert it to simplest form!). Thenanswer “yes” or “no” in the last two columns of the table.Comparison:FractionFormColon“To”Is afraction?Can beconvertedto afraction?1 ball to 6 players𝟏𝟔1:61 to 6NONO𝟓𝟑5:35 to 3NONO8 boys to 20 classmembers𝟖𝟐𝟎 𝟐𝟓8:20or 2:58 to 202 to 5YESYES6 A’s to 14 B’s in a class𝟔𝟏𝟒 376:14or 3:76 to 143 to 7NOYES60 miles on 3 gallons𝟔𝟎𝟑 𝟐𝟎𝟏60:3or 20:160 to 320 to 1NONO12 completions in 20pass attempts𝟏𝟐𝟐𝟎 𝟑𝟓12:20or 3:512 to 203 to 5YESYES40 gummy bears for 5𝟒𝟎𝟓 𝟖𝟏40:5or 8:140 to 58 to 1NONO𝟏𝟏4:4or 1:14 to 41 to 1NOYESto𝟒𝟒 6 chipmunks to 7squirrels𝟔𝟕6:76 to 7NOYES27 students to 4teachers𝟐𝟕𝟒27:427 to arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Ratio Worksheet (continued) - KEY2. In an orchard, there are 150 orange trees and 250 apple trees.a.In simplest fraction form, what is the ratio of orange trees toapple trees?b.150250In simplest fraction form, what is the ratio of apple trees toorange trees?c.3 52501505 3In simplest fraction form, what is the ratio of orange trees tototal trees in the orchard?d.3 8In simplest fraction form, what is the ratio of apple trees tototal trees in the orchard?e.1504002504005 8Which of the answers to a, b, c, and d above are fractions?c and df.Explain why the answers you listed in question e are fractions:The answers to c and d are fractions because they are PART-TOWHOLE ratios. The answers to a and b are PART-TO-PART ratios.g.Challenge question: Write each of the answers listed in questione as decimals and percents. SHOW YOUR WORK!C: 3 8 0. 375 37.5%D: 5 8 0. 625 62.5%3. Use words to write two different ratios that can’t be convertedto fractions:Answers will vary. Use as discussion point during which you ensure thatanswers have numerators and denominators with units that cannot bereadily combined.4. The ratio of boys to girls in a class is 4 to 5. There are 20 boys in theclass. How many girls are in the class? Answer is 25 girls. Method isnot important at this point. Use this as a checkpoint to see ifstudents are thinking about ratios and ready for tore/Barry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate Warm-up1. Satvinder goes to the car dealership to look for a car with hisfamily. On the window of a the first car they test drive, he sees asign that reads:Great gas mileage!115 miles5 gallonsa. Is the mileage on the sign a ratio?b. Is the mileage on the sign a fraction?Why or why not?c. Can it be made into a fraction?Why or why not?d. Would the information on the sign be easy for acustomer to understand?Why or why not?e. What could be done with the information on the sign tomake it easier to understand for the e/Barry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate Warm-up - KEY1. Satvinder goes to the car dealership to look for a car with hisfamily. On the window of a the first car they test drive, he sees asign that reads:Great gas mileage!115 miles5 gallonsa. Is the mileage on the sign a ratio? YES! It comparesone quantity to another.b. Is the mileage on the sign a fraction? NO!Why or why not? Because it is definitely a part-to-partratio! The denominator does not represent the “whole”.c. Can it be made into a fraction? NO!Why or why not? Because miles and gallons cannot beadded together to form a part-to-whole ratio.d. Would the information on the sign be easy for acustomer to understand? NOWhy or why not? Because it does not tell you how manymiles the car gets for EACH gallon.e. What could be done with the information on the sign tomake it easier to understand for the customer?Answers may vary, but the ideal answer reflects that thestudent has thought about the fact that it would be easier forthe customer to understand the mileage PER GALLON, therebyleading into the notes and discussion of the value of unit arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate NotesRATIO RATE ExamplesRatios that are not ratesRatios that are ratesRates and Unit RatesRates are often most useful if they are written asUNIT RATE A rate can be converted to a unit rate byExampleRate:Great gas mileage!115 miles115 miles5 gallons5 gallonsConversion: Unit Rate:miles gallonUsing Unit Rates to Make ComparisonsUnit rates can also be used to easily compare different amounts of the same item:ExampleUse unit rates to determine which of these is the best deal? 0.76 1.08Rate: eggsConversion: Unit Rate:Rate: eggeggsConversion: Unit Rate: eggOption is the better rry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate Notes - KEYRATIO The amount of one quantity compared to the amount of another quantity.RATE A ratio with units that are different enough that it cannot be written as a fraction.ExamplesRatios that are not ratesRatios that are ratesBoys to girlsA’s to B’sCats to dogsDesks to StudentsMinutes to MilesHot Dogs per guestRates and Unit RatesRates are often most useful if they are written as unit ratesUNIT RATE A rate with a denominator of ONE.A rate can be converted to a unit rate by dividing the numerator anddenominator by the denominator.ExampleRate:Great gas mileage!115 miles115 miles5 gallons5 gallonsConversion:Unit Rate:5 23 miles 51 gallonUsing Unit Rates to Make ComparisonsUnit rates can also be used to easily compare different amounts of the same item:ExampleUse unit rates to determine which of these is the best deal? 0.76 1.08Rate: 1.08Conversion: 12 eggs1212 Unit Rate:Rate: 0.09 0.761 egg8 eggsConversion:Unit Rate:8 0.095 8 1 eggOption A is the better rry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate PoetryWhen you need to find a rate,First do some ratio action,Cause a rate is just a ratio,That can’t be made into a fraction.Miles to gallons is a ratio,But it’s called a rate too,Cause you can’t add miles to gallons,No matter what you do.45 miles3 gallonsCan’t be madeinto a fraction!A unit rate is easy.And you can get it done.Cause a unit rate is just a rate,Where denominator equals one.To find a unit rate,45 milesWrite in fraction form 3 gallons , and later Just divide the top and bottom,By the denominator. 45 miles 3 3 gallons315 miles1 arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate Worksheet1. Complete the first three columns of the table with “yes” or “no”.Convert to a unit rate in the fourth column if possible (otherwise write“not possible”). Then answer the last column with “yes” or no”.Comparison:Is aratio?Is arate?Is aunitrate?Convert to a unit ratehere if possible (showwork)Can beconvertedto afraction?6 players to 1 ball8 boys to 20 classmembers6 A’s to 14 B’s in a class60 miles on 3 gallons12 completions in 20pass attempts40 gummy bears for 5to6 chipmunks to 7squirrels43 miles per ry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate Worksheet (continued)2. Use unit rates to answer the questions below. Use the first question asan example for how to show your work:a.You earn 12 per lawn you mow. If you mow 8 lawns, how much money doyou earn? 121 𝑙𝑎𝑤𝑛 8 lawns 96Units cancel!We are left with dollars!b.You drive 42 miles per hour? How far do you drive in 3 hours?c.There are 12 inches per foot. How many inches are there in 14 feet?d.There are 2.54 centimeters per inch. How many centimeters are there on a12-inch ruler?3. Use unit rates to determine which sale is the best deal (show all work):a.Oranges!5 for 4Rate:Unit Rate: oranges orangeis the best deal! 1.50 1.80b. 4.60is the best rry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate Worksheet - KEY1. Complete the first three columns of the table with “yes” or “no”.Convert to a unit rate in the fourth column if possible (otherwise write“not possible”). Then answer the last column with “yes” or no”.Comparison:Is aratio?Is arate?6 players to 1 ballYESYES YES 6 players to 1 ball NOYESYES NO𝑇𝑉𝑠𝐻𝑜𝑢𝑠𝑒8 boys to 20 classmembersYESNONOnot possibleYES6 A’s to 14 B’s in a classYESNONOnot possibleYES60 miles on 3 gallonsYESYES NO12 completions in 20pass attemptsYESNO40 gummy bears for 5YESYES NO𝑏𝑒𝑎𝑟𝑠YESNONOnot possibleYES6 chipmunks to 7squirrelsYESNONOnot possibleYES43 miles per hourYESYES YES43 miles per hourNOtoIs aunitrate?NOConvert to a unit ratehere if possible (showwork)42 𝑚𝑖𝑙𝑒𝑠𝑔𝑎𝑙𝑙𝑜𝑛𝑠 60 3 2233 not possible 405 55Can beconvertedto afraction?21201NONOYES ry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Rate Worksheet (continued) - KEY2. Use unit rates to answer the questions below. Use the first question asan example for how to show your work:a.You earn 12 per lawn you mow. If you mow 8 lawns, how much money doyou earn? 121 𝑙𝑎𝑤𝑛b. 8 lawns 96Units cancel!We are left with dollars!You drive 42 miles per hour? How far do you drive in 3 hours?42 𝑚𝑖𝑙𝑒𝑠1 ℎ𝑜𝑢𝑟c. 3 hours 126 milesThere are 12 inches per foot. How many inches are there in 14 feet?12 𝑖𝑛𝑐ℎ𝑒𝑠1 𝑓𝑜𝑜𝑡d. 14 feet 168 inchesThere are 2.54 centimeters per inch. How many centimeters are there on a2.54 𝑐𝑚12-inch ruler?1 𝑖𝑛 12 in 30.48 cm3. Use unit rates to determine which sale is the best deal (show all work):a.Oranges!5 for 4Rate:Unit Rate: 455 oranges 5 0.801 orangeRate:Unit Rate: 910 oranges 1010 Unit Rate: 0.90 0.82 per orange1 orange5 for 4 is the best deal! 1.80b. 1.50Rate: 1.503 lollipopsUnit Rate: 33 0.501 lollipop 1.804 l.p.4 for 180 is the best deal! 44 4.60 0.45 4.601 l.p.10 l.p. 1010 0.461 ry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Proportion Warm-up1. Which of these pairs of ratios are equivalent?Insert an “ ” sign between the equivalent pairs. Insert a “ ”sign between the pairs that are not arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Proportion Warm-up - KEY1. Which of these pairs of ratios are equivalent?Insert an “ “ sign between the equivalent pairs. Insert a “ ”sign between the pairs that are not equivalent.a.23 46b.912 2736c.915 1620d.3.56 5.259e.2255 1640Remember, this is a “warm-up”. You are not explaining how to dothese problems yet, just determining if the students are thinkingcreatively. You should see what solutions the students comeup with, allow for some discussion about how and why they cameup with their answers, not give the correct answers yet, go throughthe Proportion Notes, then come back to the warm-up and useestablished methods if appropriate and if time allows at that arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Proportion NotesRATIO RATE UNIT RATE PROPORTION Proportion Examples25 820400 𝑐𝑎𝑙𝑜𝑟𝑖𝑒𝑠1 𝑏𝑢𝑟𝑔𝑒𝑟 1200 𝑐𝑎𝑙𝑜𝑟𝑖𝑒𝑠3 𝑏𝑢𝑟𝑔𝑒𝑟𝑠1620 4455Proportions are almost always written in form.Checking for Proportions:You can determine if two ratios form a proportion using two methods:Method 1 – Simplify Both1640 2050 So1640Method 2 – Cross Products1640 205040 20 ? 50 16 2050is a So16402050is aChecking for Proportions – Practice Problems:Determine whether each of the pairs of ratios forms a proportion:a.26824b.61091221c. 3035501.8d. Barry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Proportion Notes - KEYRATIO The amt. of one quantity compared the amt. of another quantity.RATE A ratio with units that are different enough that it can’t be written as a fraction.UNIT RATE A rate with a 1 in the denominator.PROPORTION Two ratios which are equal to each other.Proportion Examples25 820400 𝑐𝑎𝑙𝑜𝑟𝑖𝑒𝑠1 𝑏𝑢𝑟𝑔𝑒𝑟 1200 𝑐𝑎𝑙𝑜𝑟𝑖𝑒𝑠3 𝑏𝑢𝑟𝑔𝑒𝑟𝑠1620 4455Proportions are almost always written in fraction form.Checking for Proportions:You can determine if two ratios form a proportion using two methods:Method 1 – Simplify Both𝟖𝟖1640 2050 𝟏𝟎𝟏𝟎So1640 Method 2 – Cross Products𝟐𝟓 1640𝟐𝟓20502050 40 20 ? 50 16800 800is a proportion!So1640 2050is a proportion!Checking for Proportions – Practice Problems:Determine whether each of the pairs of ratios forms a proportion:a.268 24b.𝟐𝟔 𝟐 ��𝟗𝟏𝟐 610 𝟐912𝟑 𝟐 𝟓𝟑𝟑 𝟑𝟒21c. 30 𝟐𝟏𝟑𝟎𝟑𝟓𝟓𝟎𝟑3550𝟕 𝟑 𝟏𝟎𝟓𝟓 𝟕𝟏𝟎1.8d. 7.5 1.251.2 7.5 ? 1.8 59 Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Proportion Worksheet1. Determine whether each pair of ratios forms a proportion. You maysimplify both ratios or use the cross-product method. Then insert an“ “ or “ ” sign between the pair of ratios.a.412e.2551552b.711497712 𝑝𝑒𝑛𝑠24 𝑝𝑒𝑛𝑠f. 4 𝑝𝑒𝑛𝑐𝑖𝑙𝑠1512c.g.2 𝑝𝑒𝑛𝑐𝑖𝑙𝑠281621282639Time for some decimal and fraction 1421106492234d.1025h.9 𝑑𝑜𝑔𝑠21 𝑐𝑎𝑡𝑠l.2575 1.402 𝑑𝑜𝑛𝑢𝑡𝑠6 𝑑𝑜𝑔𝑠14 𝑐𝑎𝑡𝑠 4.204 ayteachers.com/Store/Barry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Proportion Worksheet - KEY1. Determine whether each pair of ratios forms a proportion. You maysimplify both ratios or use the cross-product method. Then insert an“ “ or “ ” sign between the pair of ratios.a.412𝟒𝟏𝟐𝟓𝟏𝟓e.515 𝟒𝟏𝟕𝟏𝟏 𝟒 𝟑𝟓𝟒𝟗𝟕𝟕𝟏 𝟓 𝟑2552 711b.4977 𝟏𝟕240𝟕12 𝑝𝑒𝑛𝑠24 𝑝𝑒𝑛𝑠g.2 𝑝𝑒𝑛𝑐𝑖𝑙𝑠𝟒𝟐 𝟐 33621282639 𝟑𝟐𝟏𝟐𝟖 𝟕 𝟒𝟏𝟐𝟏𝟐𝟔𝟑𝟗 𝟏𝟑 𝟑 𝟒 𝟏𝟐𝟒𝟐i.2.4 5 ? 3 41212 j.𝟏𝟓𝟒 131153𝟏𝟏𝟓𝟏𝟒m.8.85 11.886.7511.88 5 ? 8.8 6.7559.4 59.4341103 ? 𝟏𝟎𝟑k. �492234𝟐𝟓𝟕𝟓 𝟐𝟓 𝟑h.𝟗𝟐𝟏𝟏𝟑𝟐𝟔𝟏𝟒 𝟓𝟐 14l.6 𝟏𝟎 ?𝟏𝟐 𝟓 𝟓𝟑1 𝟔10 25 25 75𝟏𝟎𝟐𝟓𝟕Time for some decimal and fraction action!2.43 45d.15 16 ? 12 28 𝟕 𝟏𝟏f. 4 𝑝𝑒𝑛𝑐𝑖𝑙𝑠 5 5 ? 2 225 42816 𝟕 𝟏 𝟏𝟏𝟏𝟐𝟒1512c.𝟓𝟐𝟐𝟓𝟏9 𝑑𝑜𝑔𝑠21 𝑐𝑎𝑡𝑠𝟑 6 𝑑𝑜𝑔𝑠14 𝑐𝑎𝑡𝑠𝟑 𝟑 𝟕𝟐𝟑 𝟐 𝟕 1.402 𝑑𝑜𝑛𝑢𝑡𝑠 4.204 𝑑𝑜𝑛𝑢𝑡𝑠4.2 2 ? 1.4 48.4 5.6𝟏𝟓6353𝟒𝟎 𝟔 ? 𝟗𝟏𝟔 rs.com/Store/Barry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Solving Proportions Warm-up1.Find the value of x for each problem below:a.53 𝑥6b.212 2.5𝑥c.𝑥15 y-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Solving Proportions Warm-up - KEY1. Find the value of x for each problem below:a.53𝑥 6x 10b.2122.5 𝑥x 15c.𝑥158 20x 6As on the previous day’s warm-up questions, you are not explaininghow to do these problems yet, just determining if the students arethinking creatively. You should see what solutions the studentscome up with, allow for some discussion about how and why theycame up with their answers, not give the correct answers yet, gothrough the Solving Proportion Notes, then come back to thewarm-up and use established methods if appropriate and if timeallows at that arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Solving Proportion NotesProportions can also be used to solve all kinds of problems.Examples – Solve for x in each proportion below:Side to Side Method53 Up and Down Method𝑥6212x Cross Product Method7𝑥𝑥15x Remember, the arrow always pointsthe variable! Let’s dosomeAlgebra!82015 8 20x Solving Proportions – Practice Problems:Solve using side to side method:a.26 𝑥24b.𝑛36 512c.2127 7𝑔248 𝑚12c.ℎ35 315𝑛15 810c.46Solve using up and down method:a.2𝑦 312b.Solve using cross products:a.69 10𝑥b. rry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Solving Proportion Notes - KEYProportions can also be used to solve all kinds of problems.Examples – Solve for x in each proportion below:Side to Side Method 253 6 2𝑥6 Up and Down Method127𝑥 2Cross Product Method 6𝑥15 Let’s dosomeAlgebra!82015 8 20x120 20x20206 xProblems:x 10x 42towardRemember, the arrow always pointsthe variable!Solving Proportions – PracticeSolve using side to side method:a.26 𝑥24b. 4𝑛36 512c. 3x 8 4 2n 153 412 𝑦 3b.y 824821277𝑔 3Solve using up and down method:a. 3 3 4 g 9𝑚 312ℎ35 5c.m 36 315 5h 7Solve using cross products:a.69 10𝑥b.𝑛15 810c.46 6𝑔8 15 10n6 6 4g120 10n36 4g10104412 n9 Schneiderman Barry Schneiderman, 20139 10 6x90 6x6615 x
Name:Date:Proportion PoetryClass:2 𝑑𝑜𝑔𝑠3 catsA ratio compares,One thing to another,A proportion is two ratios,Set equal to each other.24 363 4 124 362 6 12But you can make them simple,By just cross-multiplying.Proportion!Checking for proportions,2Can be mystifying.Variables in proportions,Make you want to solve ‘em.Cause you can use three methods,To solve each and every problem! 253 𝑥6 6212 2X 10X 15 2.5𝑥 6𝑥15 820Let’s dosomeAlgebra!120 20x20 206 Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Proportion Worksheet (Round 2)1. Solve for the variable in each of the proportions below (whole numbers):a.75 𝑥15b.e.4𝑑 1015f.8𝑔4936𝑛 69c.g.𝑦7𝑏15 27912090d.4𝑧h.18241624 6ℎ2. Solve for the variable in each of the proportions (fractions and decimals):a.2115e.2.25𝑑 𝑥534b.f.6𝑔248 27𝑛 213c.g.46𝑏12 𝑥152560d.h.8.8𝑑412𝑔 arry-Schneiderman Barry Schneiderman, 2013
Name:Date:Class:Proportion Worksheet (Round 2 - continued)3. Review of Ratios, Rates, and ProportionsA car company is trying ou
paper, or distribute the warm-up as a worksheet, to be put in the students’ math notebook upon completion. In either case, keep the following in mind as you do the warm-up activity: - Warm-up time should not be a time for you to teach the students, but rather a time
