Grade 7, Unit 2 Practice Problems - RUSD Math

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Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMLesson 1Problem 1Which one of these shapes is not like the others? Explain what makes itdifferent by representing each width and height pair with a ratio.SolutionC is different from A and B. For both A and B, the width:height ratio is 5:4.However, for C, the width is 10 units and the height is 6 units, so thewidth:height ratio is 5:3.Problem 2In one version of a trail mix, there are 3 cups of peanuts mixed with 2 cupsof raisins. In another version of trail mix, there are 4.5 cups of peanutsmixed with 3 cups of raisins. Are the ratios equivalent for the two mixes?Explain your reasoning.SolutionYes, since 3 times 1.5 is 4 and 2 times 1.5 is 3.Problem 3(from Unit 1, Lesson 12)For each object, choose an appropriate scale for a drawing that fits on aregular sheet of paper. Not all of the scales on the list will be used.ObjectsScalesA. A person1. 1 in : 1 ftB. A football field (120 yards by53 13 yards)2. 1 cm : 1 mC. The state of Washington(about 240 miles by 360 practice problems.html3. 1: 10004. 1 ft: 1 milePage 1 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMD. The floor plan of a house5. 1: 100,000E. A rectangular farm (6 miles by2 mile)6. 1 mm: 1 km7. 1: 10,000,000SolutionAnswers vary. Sample responses:1. 1 in :1 ft2. 1: 10003. 1: 10,000,0004. 1cm: 1 m5. 1: 100,000Problem 4(from Unit 1, Lesson 11)Which scale is equivalent to 1 cm to 1 km?A.B.C.D.E.1 to 100010,000 to 11 to 100,000100,000 to 11 to 1,000,000SolutionCProblem 5(from Grade 7, Unit 2, Lesson 5)1. Find 3 different ratios that are equivalent to 7 : 3.2. Explain why these ratios are equivalent.Solution1. Answers vary. Sample response: 14 : 6 , 21 : 9 , 28 : 122. Answers vary. Sample response: 7 and 3 are each multiplied by 2, 3,and 4, respectively.Lesson 2Problem 1When Han makes chocolate milk, he mixes 2 cups of milk with 3tablespoons of chocolate syrup. Here is a table that shows how to makebatches of different practice problems.htmlPage 2 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMUse the information in the table to complete the statements. Some termsare used more than once.1. The table shows a proportional relationship betweenand .2. The scale factor shown is .3. The constant of proportionality for this relationship is .4. The units for the constant of proportionality are per.Bank of Terms: tablespoons of chocolate syrup, 4, cups of milk, cup of milk,32Solution1. cups of milk, tablespoons of chocolate syrup2. 43.324. tablespoons of chocolate syrup, cup of milkProblem 2A certain shade of pink is created by adding 3 cups of red paint to 7 cups ofwhite paint.1. How many cups of red paint should be added to 1 cup of white paint?cups of white paintcups of red paint1732. What is the constant of proportionality?Solution1.372.37cups of red paintProblem 3(from Unit 1, Lesson 12)A map of a rectangular park has a length of 4 inches and a width of 6inches. It uses a scale of 1 inch for every 30 miles.1. What is the actual area of the park? Show how you know.2. The map needs to be reproduced at a different scale so that it has anarea of 6 square inches and can fit in a brochure. At what scale shouldthe map be reproduced so that it fits on the brochure? Show yourreasoning.Solution1. 21,600 square miles. Sample reasoning: The area on the map is 24square inches. 1 square inch represents 900 square miles, since30 30 90. The actual area is 24 900, which equals 21,600 squaremiles. ce problems.html Page 3 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AM2. 1 inch to 60 miles. Sample explanations:If 21,600 square miles need to be represented by 6 squareinches, each square inches needs to represent 3,600 squaremiles: 21, 600 6 3, 600. This means each 1-inch side of thesquare needs to be 60 miles.The area of this new map is 14 of the first map, since 6 is 14 of 24.This means each 1 inch square has to represent 4 times as mucharea than the first. 900 4 3, 600. If each 1 inch squarerepresents 3,600 square miles, every 1 inch represents 60 miles. Problem 4(from Unit 1, Lesson 6)Noah drew a scaled copy of Polygon P and labeled it Polygon Q.If the area of Polygon P is 5 square units, what scale factor did Noah applyto Polygon P to create Polygon Q? Explain or show how you know.SolutionThe area of polygon Q is 45 square units, so the area has scaled by a factorof 9, since 5 9 45. Since the area of a scaled copy varies from theoriginal area by the square of the scale factor, the scale factor is 3. Problem 5(from Grade 7, Unit 2, Lesson 5)Select all the ratios that are equivalent to each other.A.B.C.D.E.4:78 : 1516 : 282:320 : 35SolutionA, C, and ELesson 3Problem 1Noah is running a portion of a marathon at a constant speed of 6 miles perhour.Complete the table to predict howlong it would take him to rundifferent distances at that speed,and how far he would run indifferent time s/2/practice problems.htmlPage 4 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMtimein hoursmiles traveled at6 miles per hour1121 131 1294 12Solutiontime in hoursmiles traveled at 6 miles per hour161231138141 121 129344 12Problem 2One kilometer is 1000 meters.1. Complete the tables. What is the interpretation of the constant ofproportionality in each 505122010.3The constant of proportionalitytells us that:The constant of proportionalitytells us that:2. What is the relationship between the two constants of 2500.25120.01210.0010.001 kilometers per /practice problems.htmlPage 5 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMkilometersmeters11,00055,0002020,0000.33001000 meters per kilometer2. 0.001 and 1000 are reciprocals of each other. This is easier to see if10.001 is written as 1000.Problem 3Jada and Lin are comparing inches and feet. Jada says that the constant of1proportionality is 12, Lin says it is 12. Do you agree with either one ofthem? Why or why not?SolutionJada is saying that there are 12 inches for every 1 foot. Lin is saying that1there are 12foot for every 1 inch.Problem 4(from Unit 1, Lesson 12)The area of the Mojave desert is 25,000 square miles. A scale drawing ofthe Mojave desert has an area of 10 square inches. What is the scale of themap?Solution1 inch to 50 milesProblem 5(from Unit 1, Lesson 11)Which of these scales is equivalent to the scale 1 cm to 5 km? Select all thatapply.A.B.C.D.E.3 cm to 15 km1 mm to 150 km5 cm to 1 km5 mm to 2.5 km1 mm to 500 mSolutionA, D, EProblem 6(from Unit 2, Lesson 1)Which one of these pictures is not like the others? Explain what makes itdifferent using /practice problems.htmlPage 6 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMSolutionM is different from L and N. The width:height ratios for the outsides of thepictures are all equivalent to 5:4. However, the width:height ratios of theinsides of L and N both have a 3:4 ratio of width:height, while the insideof M has a width of 4 units and a height of 8 units, making its ratio 1:2.Alternatively, the ratio of height to thickness at the widest part for L and Nare both 4:1. But M has a height of 8 units and a thickness of 3 units,making that ratio 8:3.Lesson 4Problem 1A certain ceiling is made up of tiles. Every square meter of ceiling requires10.75 tiles. Fill in the table with the missing values.square meters of ceilingnumber of tiles110100aSolutionsquare meters of ceilingnumber of tiles110.7510107.59.3100a10.75 a Problem 2On a flight from New York to London, an airplane travels at a constantspeed. An equation relating the distance traveled in miles, d, to the number1of hours flying, t , is t 500d . How long will it take the airplane to travel 800miles?Solution1.6 hours since1500 800 1.6Problem 3Each table represents a proportional relationship. For each, find theconstant of proportionality, and write an equation that represents eachers/2/practice problems.htmlPage 7 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMsPdC2826.2831239.42520515.710401031.4Constant of proportionality:Constant of proportionality:Equation: P Equation: C Solution1. Constant of proportionality: 4. Equation: P 4s2. Constant of proportionality: 3.14 Equation: C 3.14dProblem 4(from Unit 1, Lesson 11)A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200.Are these two ways of reporting the scale the same? Explain yourreasoning.SolutionYes. Sample response: There are 12 inches in a foot and 5280 feet in 1 mile,so that’s 63,360 inches in a mile and 1,267,200 inches in 20 miles.Problem 5(from Unit 1, Lesson 3)Here is a polygon on a grid.1. Draw a scaled copy of the polygon using a scale factor 3. Label thecopy A.2. Draw a scaled copy of the polygon with a scale factor12. Label it B.3. Is Polygon A a scaled copy of Polygon B? If so, what is the scale factorthat takes B to chers/2/practice problems.htmlPage 8 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AM3. Yes, A is a scaled copy of B with a scale factor of 6.Lesson 5Problem 1The table represents the relationship between a length measured in metersand the same length measured in kilometers.1. Complete the table.2. Write an equation forconverting the number ofmeters to kilometers. Use xfor number of meters and yfor number of .001x0.001x2. y 0.001x or equivalentProblem 2Concrete building blocks weigh 28 pounds each. Using b for the number ofconcrete blocks and w for the weight, write two equations that relate thetwo variables. One equation should begin with w and the other shouldbegin with b .Solutionw 28b and b 1w28Problem 3A store sells rope by the meter. The equation p 0.8L represents the pricep (in dollars) of a piece of nylon rope that is L meters ractice problems.htmlPage 9 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AM1. How much does the nylon rope cost per meter?2. How long is a piece of nylon rope that costs 1.00?Solution1. 0.80 or dollar or dollar.2. 1.25 meters or54meters or 1 14 meters.Problem 4(from Unit 2, Lesson 4)The table represents a proportional relationship. Find the constant ofproportionality and write an equation to represent the relationship.ay2233110103124Constant of proportionality:Equation: y SolutionConstant of proportionality:13Equation: y 1a3Problem 5(from Unit 1, Lesson 8)On a map of Chicago, 1 cm represents 100 m. Select all statements thatexpress the same scale.A. 5 cm on the map represents 50 m in Chicago.B. 1 mm on the map represents 10 m in Chicago.C. 1 km in Chicago is represented by 10 cm the map.D. 100 cm in Chicago is represented by 1 m on the map.SolutionB, CLesson 6Problem 1A car is traveling down a highway at a constant speed, described by theequation d 65t, where d represents the distance, in miles, that the cartravels at this speed in t hours.1. What does the 65 tell us in this situation?2. How many miles does the car travel in 1.5 hours?3. How long does it take the car to travel 26 miles at this speed?Solution1. The car travels 65 miles in 1 hour. Or, the car is traveling 65 miles ctice problems.htmlPage 10 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMhour. Or, 65 miles per hour is the constant of proportionality.2. The car travels 97.5 miles in 1.5 hours.253. It takes the carmiles.of an hour, or 0.4 hours, or 24 minutes to travel 26Problem 2Elena has some bottles of water that each holds 17 fluid ounces.1. Write an equation that relates the number of bottles of water (b) tothe total volume of water (w ) in fluid ounces.2. How much water is in 51 bottles?3. How many bottles does it take to hold 51 fluid ounces of water?Solution1. w 17b or b 1w172. 867 fluid ounces, because 17 51 8673. 3 bottles, because 51 17 3Problem 3(from Unit 2, Lesson 5)There are about 1.61 kilometers in 1 mile. Let x represent a distancemeasured in kilometers and y represent the same distance measured inmiles. Write two equations that relate a distance measured in kilometersand the same distance measured in miles.Solutionx 1.61y and y 11.61x or y 0.62xProblem 4(from Unit 2, Lesson 2)In Canadian coins, 16 quarters is equal in value to 2 toonies.number of quartersnumber of toonies116220241. Fill in the table.2. What does the value next to 1 mean in this situation?Solution1.number of quartersnumber of rg/7/teachers/2/practice problems.htmlPage 11 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AM2.18means that one-eighth of a toonie is worth the same as 1 quarter.Problem 5(from Unit 2, Lesson 2)Each table represents a proportional relationship. For each table:1. Fill in the missing parts of the table.2. Draw a circle around the constant of onProblem 6(from Unit 1, Lesson 4)Describe some things you could notice in two polygons that would help youdecide that they were not scaled copies.SolutionIf they were not the same shape (for example, if one was a triangle and onewas a square), they could not be scaled copies. I could find an anglemeasure in one that was not an angle measure of the other. I could findthat a different scale factor would have to be used on one part of the pairthan on another.Lesson 7Problem 1Decide whether each table could represent a proportional relationship. Ifthe relationship could be proportional, what would the constant ofproportionality be?1. How loud a sound isdepending on how far awayyou aredistance tolistener (ft)soundlevel (dB)5851079207340672. The cost of fountain drinks atHot Dog Hut.volume(fluid ounces)cost( )16 1.4920 1.5930 ers/2/practice problems.htmlPage 12 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AM1. Not proportional since the ratio of distance to listener to sound level isnot always the same.2. Not proportional since the ratio of volume to cost is not always thesame.Problem 2A taxi service charges 1.00 for the first1additional 10mile after that.Fill in the table with the missinginformation then determine if thisrelationship between distancetraveled and price of the trip is aproportional relationship.110mile then 0.10 for eachdistance traveled (mi)price (dollars)91023 10110Solutiondistance traveled (mi)price (dollars)9101.8022.903 1014.001010.90This is not a proportional relationship since the ratio of price to distancetraveled is not always the same.Problem 3A rabbit and turtle are in a race. Is the relationship between distancetraveled and time proportional for either one? If so, write an equation thatrepresents the relationship.Turtle’s run:Rabbit’s run:distance (meters)time (minutes)distance (meters)time .751,52432.5SolutionThe distance might be proportional to the time for the turtle. The equationwould be d 54 t, where d represents the distance traveled in metersand t is the time in minutes. Problem 4(from Unit 2, Lesson 2)For each table, answer: What is the constant of /teachers/2/practice problems.html2.3.4.Page 13 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 22551373121440100.437 12Solution1. 7 (or17)11202. 120 (or3.125)(or 25)4. 2 12 (or25)Problem 5(from Unit 1, Lesson 4)Kiran and Mai are standing at one corner of a rectangular field of grasslooking at the diagonally opposite corner. Kiran says that if the the fieldwere twice as long and twice as wide, then it would be twice the distance tothe far corner. Mai says that it would be more than twice as far, since thediagonal is even longer than the side lengths. Do you agree with either ofthem?SolutionKiran is correct. If we scale the length and width of a rectangle by a factor of2, then the diagonal will also scale by a factor of 2.Lesson 8Problem 1The relationship between a distance in yards (y) and the same distance inmiles (m ) is described by the equation y 1760m.1. Find measurements in yards and miles for distances by filling in thetable.distance measured in milesdistance measured in yards153,52017,6002. Is there a proportional relationship between a measurement in yardsand a measurement in miles for the same distance? Explain why orwhy chers/2/practice problems.htmlPage 14 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMdistance measured in milesdistance measured in yards11,76058,80023,5201017,6002. There is a proportional relationship. The constant of proportionality is1760 yards per mile.Problem 2Decide whether or not each equation represents a proportionalrelationship.1. The remaining length (L ) of 120-inch rope after x inches have been cutoff: 120 x L2. The total cost (t ) after 8% sales tax is added to an item's price (p):1.08p t3. The number of marbles each sister gets (x) when m marbles areshared equally among four sisters: x m44. The volume (V ) of a rectangular prism whose height is 12 cm and baseis a square with side lengths s cm: V 12s2Solution1. no2. yes3. yes4. noProblem 31. Use the equation y 5x2to fill in the table.Is y proportional to x and y? Explain why or whynot.xy2362. Use the equation y 3.2x 5 to fill in the table.Is y proportional to x and y? Explain why or rg/7/teachers/2/practice problems.htmlPage 15 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMxy253152615Yes, there is a proportional relationship between x and y sincein each row.yx 522.xy18.2211.4417.8No, there is no proportional relationship between x and y. In the firstyyrow x 8.2 but in the second row x 5.7.Problem 4(from Unit 2, Lesson 6)To transmit information on the internet, large files are broken into packetsof smaller sizes. Each packet has 1,500 bytes of information. An equationrelating packets to bytes of information is given by b 1,500p where prepresents the number of packets and b represents the number of bytes ofinformation.1. How many packets would be needed to transmit 30,000 bytes ofinformation?2. How much information could be transmitted in 30,000 packets?3. Each byte contains 8 bits of information. Write an equation torepresent the relationship between the number of packets and thenumber of bits.Solution1. 20 packets2. 45,000,000 bytes3. x 12,000pLesson 9Problem 1For each situation, explain whether you think the relationship isproportional or not. Explain your reasoning.1. The weight of a stack of standard 8.5x11copier paper vs. number of sheets of paper.2. The weight of a stack of different-sizedbooks vs. the number of books in the practice problems.htmlPage 16 of 28

Grade 7, Unit 2 Practice Problems - Open Up Resources9/13/17, 10)32 AMSolution1. There is a proportional relationship between weight and number ofsheets of paper. Each piece of paper has the same weight. To find theweight of a stack, multiply the number of sheets of paper by theweight of a single sh

Grade 7, Unit 2 Practice Problems - Open Up Resources 9/13/17, 1032 AM ce_problems.html Page 1 of 28

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