7.2D STUDENT ACTIVITY #1 - rgccisd

GRADE 7 MATHEMATICS(7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justifysolutions. The student is expected to: (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price,recipes, and student-teacher ratio.PURPLE PAINT WORKMATScaleFactorRedBlueRatioProcessTotal1 2 3 4 10 CTEKSING TOWARD TAKS 2009 6 Weeks 4 - Lesson 1 Page5

GRADE 7 MATHEMATICS(7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justifysolutions. The student is expected to: (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price,recipes, and student-teacher ratio.7.2D STUDENT ACTIVITY #2Materials: 20 red and 30 blue cm cubes per pair, Purple Paint Workmat I on white paper per pair,1 poster size sheet of 1" grid paper per group of 4, peel-and-stick dots, meterstick, markersPart I Procedure: Work with a partner.Questions for Purple Paint Workmat I:•What is the ratio of the number of red cubes to the number of blue cubes in the first columnlabeled “1”?•Does the ratio compare two wholes, two parts, or a part and a whole? Explain your answer.•What is the relationship between the number of cubes in the first column and the number ofcubes in the second column?•Describe any patterns you see on the mat.•Describe what you would show in the 10 column?What would you write in the ratio and process boxes in the 10 column?•Examine the process row in Purple Paint Workmat I and describe your observations.•Look at the column with the heading “c”. How would you describe column “c”?What would you write in the process row with the heading “c”?•Complete the Total row on Purple Paint Workmat I. What is the ratio of the number of red cubesto the total number of cubes?•What is the relation of the scale factor to the part-whole ratios for each column?•Explain the meaning of a scale factor.TEKSING TOWARD TAKS 2009 6 Weeks 4 - Lesson 1 Page6

GRADE 7 MATHEMATICS(7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justifysolutions. The student is expected to: (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price,recipes, and student-teacher ratio.PART II Procedure:•Work with a group of 4.•Use the large sheet of inch grid paper, peel-and-stick dots, meterstick and markers to make ascatterplot to represent the data in the Purple Paint Record table.•Label your scatterplot.•Display your scatterplot on the wall in the classroom.Answer the following questions about your graph:•Does your graph represent a proportional relationship? Explain your answer.•Write an equation which describes the relationship between the number of blue cubes and thenumber of red cubes.•What is the constant of proportionality for this relationship?•Explain the meaning of the constant of proportionality.•If the paint mixer had started with a gallon of paint which already had 2 drops of blue coloring,then he added 2 drops of red and 3 drops of blue and continued to add drops in this way howwould the graph be different?•Would this new graph represent a proportional relationship? Explain your answer.TEKSING TOWARD TAKS 2009 6 Weeks 4 - Lesson 1 Page8

GRADE 7 MATHEMATICS(7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justifysolutions. The student is expected to: (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price,recipes, and student-teacher ratio.7.2D OPEN ENDED #1Problem #1: A recipe calls for 2 1 3cups of flour to make 3 dozen cookies.•Write a ratio that compares the amount of flour to the number of cookies in three different ways.•Write a proportion that can be used to find how much flour Mrs. Smith will need to make 9 dozencookies.•Use the proportion to solve the problem. Show your work.Problem #2: For a field trip the school policy is to have 2 adults for every 9 students.•Write a ratio that compares the number of adults to the number of students.If 72 students have signed up to go on this week’s field trip, how many adults must go on the fieldtrip?•Write a proportion that can be used to find how many adults must go on the field trip.•Use the proportion to solve the problem. Show your work.1. What mathematical concepts and vocabulary do I need to know to be able to work these problems?2. Will the Grade 7 Mathematics Formula Chart be helpful on these problems? Why or why not?3. Will a picture or diagram be helpful on these problems? If so, how?4. What problem-solving strategy or strategies will I use to help solve this problem?5. Extension (7.2B): How much flour did Mrs. Smith use for each dozen cookies?TEKSING TOWARD TAKS 2009 6 Weeks 4 - Lesson 1 Page9

GRADE 7 MATHEMATICS(7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justifysolutions. The student is expected to: (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price,recipes, and student-teacher ratio.NAME___________________ DATE___________ SCORE ___/57.2D Homework #11. Party balloons cost $15 for four balloons. How much will Mary spend on balloons if she buys a dozen balloons? Show yourwork.2. Johnny is the local paperboy for our neighborhood. He can deliver 15 papers in 10 minutes. How long will it take him todeliver 300 papers? Show your work.3. The ratio of girls to boys in Mrs. Green’s seventh grade homeroom is 7:6. If there are 12 boys in her homeroom, how manytotal students are in her homeroom? Show your work.4. Reams of typing paper were on sale for 3 for $10.00 at the local office supply store. If Mrs. Lange spent $100.00 on paper,how many reams did she buy?5. A bag contains 12 red, 10 blue, 6 yellow and 8 green marbles. What is the ratio of the red to green marbles in the bag?TEKSING TOWARD TAKS 2009 6 Weeks 4 - Lesson 1 Page10

GRADE 7 MATHEMATICS(7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justifysolutions. The student is expected to: (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price,recipes, and student-teacher ratio.NAME___________________ DATE___________ SCORE ___/57.2D Homework #21. A bag contains 10 red, 10 blue, 4 yellow and 6 green marbles.•What is the ratio of the blue to green marbles in the bag? Explain how you found your answer and show your work.•What is the ratio of yellow to blue marbles in the bag? Explain how you found your answer and show your work.2. Walking around his neighborhood, Barry can walk 12 blocks in 8 minutes. At this rate, how many blocks can he walk in 30minutes? Show your work.3. The ratio of the length of the shorter base of a trapezoid to the length of the longer base of the trapezoid is 5:8. If the length ofthe longer base is 20 units, what is the length of the shorter base? Show your work.4. A recipe for 2 dozen cookies calls for 3.5 cups of flour. Mrs. Brown plans to make 5 dozen cookies. How many cups of flourdoes she need? Show your work.5. The student-teacher ratio for the seventh grade at Brown Middle School is 80 to 1. Brown Middle School has six seventhgrade math teachers. How many seventh grade students does Brown Middle School have? Show your work.TEKSING TOWARD TAKS 2009 6 Weeks 4 - Lesson 1 Page11