gallons minute square yards 1 hour

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1 Domain: Ratios & Proportional Relationships Focus: Unit Rate Lesson: #1 Standard: 7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Directions: Fill in the boxes with the correct number. 1 2 Example A: Jose can sweep of a square yard in of an hour. What is his speed in terms of 2 3 square yards per hour? square yards 1 hour Example B: A garden hose fills 4 9 of a gallon bucket in 2 3 per minute? minutes. What is the flow rate in gallons gallons minute Directions: Find the correct answer to each question and explain your answer. 1. The white rabbit travels 2 5 miles in 4 days. The brown rabbit travels 3 miles in 6 days. Which 7 rabbit travels at the faster pace? Explain how you know. 2. It takes Kristi 15 minutes to run laps. It takes Marie, her friend, minutes to run 1 2 Explain which girl runs the fastest lap and how you can tell. of a lap. 3

2 Domain: Ratios & Proportional Relationships Focus: Unit Rate Lesson: #2 Standard: 7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Directions: Find the unit rate. Round answers to the nearest tenth. Example A: A 1 2 gallon of paint costs $6.50. How much will one gallon of paint cost? Example B: Which is the better buy, 2 1 cookies for $0.33 or 18 cookies for $5.16? 2 1. Which is the better buy? Item 1, which costs $0.95 for 6 2 ounces or Item 2, which 5 costs $3.25 for ounces? 2. Which is the better buy? 5 pounds of popcorn for $8.50 or 3 1 pounds of popcorn for 3 $6.75? 4

3 Domain: Ratios & Proportional Relationships Focus: Unit Rate Lesson: #3 Standard: 7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Directions: Use unit rate to find the answers to the following problems. (Round all calculations to the nearest tenth.) Example A: Alexis runs yards every seconds. How long will it take her to run 50 yards? Student Page Example B: Nathan can drive 110 miles with of gas? gallons of gas. How many miles can he drive with 12 gallons 1. It takes Lily 4 5 of an hour to read 100 pages of her book. How many pages can she read in hours? 2. Logan wants to buy pounds of grapes. Store A has them priced at $4.00 for pounds. Store B has them priced at $3.00 for pounds. What is the least he will have to pay for his grapes? 5

4 Domain: Ratios & Proportional Relationships Focus: Unit Rate Lesson: #4 Standard: 7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Directions: Perform the indicated conversion. (Round all computations to the nearest tenth.) Example A: 6 kilometers per hour = meters per second Example B: 20 yards per hour = feet per minute meters per hour = centimeters per second yards per mile = inches per foot 6

5 Domain: Ratios & Proportional Relationships Focus: Unit Rate Evaluation: #1 Directions: Find the answer to each of the following problems while working independently. Circle your answer. (Round all calculations to the nearest tenth.) 1. Which is the better buy, Item A, selling at pounds for $9.52 or Item B, selling at 11 5 $1.98? pounds for 2. Riley reads her library book minutes every 4 7 book each hour? of an hour. How many minutes does she read her 3. During an eating contest, Claire can eat of a hamburger in 2 3 can she eat in 1 minute? of a minute. How many hamburgers 4. Dylan can drive miles on gas? gallons of gas. How many miles can he travel with 15 gallons of Use the following table for question 5: kilometers per hour = meters per second 7

6 Common Core Standards Plus Mathematics Grade 7 Performance Lesson #1 Domain: Ratios and Proportional Relationships Student Page 1 of 2 Vocabulary: Unit rate: The value of one measurement relative to one unit. Ratio: The comparison of two numbers or quantities using division. Complex Fraction: A fraction that has one or more fractions in the numerator and/or the denominator. Numerator: The top number in a fraction. Denominator: The bottom number in a fraction. Unit price: The price for one item. Measurement conversion: Converting between larger or smaller units within the same scale or between customary and metric measurement scales. MEASUREMENT CONVERSIONS LENGTH CAPACITY 1 foot (ft) = 12 inches (in.) 1 cup (c) = 8 fluid ounces 1 yard (yd) = 3 feet 1 pint (pt) = 2 cups 1 yard = 36 inches 1 quart (qt) = 2 pints 1 mile = 1,760 yards 1 quart = 4 cups 1 mile = 5,280 feet 1 gallon (gal) = 4 quarts 1 km = 1,000 m 1 m = 100 cm WEIGHT 1 pound (lb) = 16 ounces (oz) 1 ton (T) = 2,000 pounds CONVERSION BETWEEN CUSTOMARY AND METRIC MEASUREMENT 1 yard = m 1 quart = L 1 foot = m 1 ounce = g 1 inch = 2.54 cm 1 pound = 0.45 kg Part I: Directions: Write a problem for each of the scenarios listed below. Create an answer key that shows how to solve the problems and defend your answers. 1. A problem that involves a complex fraction. 2. A problem that involves a fraction and a decimal. 3. A problem that involves money. 4. A problem that involves a complex fraction and decimals. 5. A problem that uses customary to metric conversion. 6. A problem that uses metric to customary conversion. 9

7 2 of 2 Common Core Standards Plus Mathematics Grade 7 Performance Lesson #1 Domain: Ratios and Proportional Relationships Part II: Directions: Trade your problems with another student. Each of you will solve each other s problems. Then you will work together to check your solutions against your answer keys. Part III: Directions: In groups of 4 or 6, discuss the process of writing problems and creating answer keys. Then discuss the process of solving and checking solutions. Finally, each of you will share how you defended your solution, and the whole class will discuss and critique the reasoning. 10

8 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #5 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Directions: Determine if each table shows a proportional relationship. Student Page Example A: x y Ratio y x Do the numbers represent a proportional relationship?. How can you tell? Example B: x y Ratio y x 1. x y Ratio y x Do the numbers represent a proportional relationship?. How can you tell? 2. Complete the table using proportional relationships. number of books cost $2.50 $12.50 $

9 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #6 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Directions: Determine if each table shows a proportional relationship and identify the constant of proportionality. Example A: x y Ratio y x What is the constant of proportionality? Example B: Zoe is able to save $30 of every $72 she earns at her job. Complete the table. earns $12 $72 $108 saves $10 $60 What is the constant of proportionality? 1. x y Ratio y x What is the constant of proportionality? 2. A grocery store was trying to sell a new soft drink. To promote the drink, they were giving away 2 drinks for every 7 drinks that were purchased. Complete a table to show the proportional relationship between the free drinks and the purchased drinks. 12

10 1 of 2 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #7 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Example A: i) How are the graphs alike? ii) How are the graphs different? iii) Which graph is proportional? iv) What makes it proportional? Example B: The graph below represents the price of oranges at one store. What is the constant of proportionality? Price (cents) Pounds Constant of proportionality: 13

11 2 of 2 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #7 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 1. Connor wants to buy some new shirts for school. He went to 4 stores and found the following information. Create a graph to determine if the number of shirts and cost are in a proportional relationship. Is the graph proportional? Explain your answer. number shirts cost store 1 1 $1.50 store 2 4 $7 store 3 2 $3.50 store 4 6 $ Bella is mixing milk and cocoa to make hot chocolate. Create a graph to determine if the amount of cocoa is proportional for each serving size. Is this graph proportional? Explain your answer. serving size cups of milk tablespoons of cocoa

12 1 of 2 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #8 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Example A: The graph below represents the number of oranges in a box. Use the graph to complete the table and to find the constant of proportionality. boxes 3 Number of oranges Oranges Boxes Is the relationship proportional? Explain your answer. If it is proportional, what is the constant of proportionality? Example B: The graph below represents the price of books. Use the graph to complete the table and to find the constant of proportionality. number of books price ($) Is the relationship proportional? Explain your answer. If it is proportional, what is the constant of probability? 15

13 2 of 2 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #8 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 1. At a grocery store, 4 avocadoes cost $3.00. Use the graph to complete the table and to find the constant of proportionality. avocadoes 1 4 _ 8 cost $3.00 $ Cost ($) Avocadoes Is the relationship proportional? Explain your answer. If it is proportional, what is the constant of proportionality? 1 2. Owen is hiking 1 miles per 1 hour. Represent the relationship using a table and a graph. 2 2 What is the constant of proportionality? hours 1 3 miles miles hours 16

14 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Evaluation: #2 1. Khloe s car can travel 75 miles on 3 gallons of gas. Complete the table, then graph the data points and determine if there is a proportional relationship. Find the constant of proportionality. miles gallons 3 5 A) Is the data proportional? B) The constant of proportionality is: 2. Use the graph to complete the table and then determine if the relationship is proportional. Find the constant of proportionality. A) Is the data proportional? B) The constant of proportionality is:

15 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #9 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Example A: Which equation(s) show a proportional relationship? A) y 25x B) y 4x 1 C) y 10x D) y 3 4 x Example B: Write a proportional equation to represent the data in the table. cases price 1 $ $ $ $ Write a proportional equation to represent the data shown in the graph. The equation is: 2. During his first day at work, Julian sold 5 pairs of shoes. On the second day, he sold 14 pairs of shoes. At the end of the third day at work, he had sold 21 pairs. Use the table to help determine the corresponding equation. day shoes The equation is: After working 5 hours at her job, Claire has earned $ A) What is the constant of proportionality? B) What is the equation of proportionality? 4. Write an equation to represent the data in the table. dollars $14 $22.75 $47.25 cupcakes

16 1 of 2 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #10 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Example A: Benjamin is mixing trail mix using chocolate chips and peanuts. Use the graph below to write the equation representing his trail mix mixture. (x) peanuts (y) chocolate chips The equation is: Example B: Evelyn is needs to graph the relationship between the money she saved and the money she earned. She knows the equation of her data is y 3x. Complete the graph of her data below. saved (x) 0 $1 $2 earned (y) 1. The graph below shows the cost of boxes of cereal. Represent the relationship using a table and an equation. boxes of cereal cost ($) The equation is: 20

17 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Lesson: #10 Standard: 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 2. Use the table below to find the constant of proportionality and write the corresponding equation. Student Page 2 of 2 miles hours The equation is: Luke is making lemonade. His recipe takes 5 cups of lemon mix and 2 cups of water. Complete the table and the graph. Write an equation to show the relationship. (x) cups of lemon mix (y) cups of water The equation is: 4. A proportional relationship, when graphed, has 5 data points on it. To get from one point to the next, move 1 unit to the right, and then move up 2 3 of a unit. What is the proportional equation? The equation is: 21

18 Domain: Ratios & Proportional Relationships Focus: Multistep Ratio Problems Lesson: #11 Standard(s): 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Example A: Audrey has a recipe that requires 3 4 teaspoon of vanilla flavoring for every 3 1 cups of flour. If 2 Audrey decreases the amount of flour in her recipe to 2 cups, how many teaspoons of vanilla are needed? Example B: A garden hose can fill a swimming pool at a rate of 15 gallons/minute. If the pool holds 18,000 gallons, how many hours will it take to fill the pool? 1. Several of the 7 th grade students went on an afterschool skating trip. Of the students, 60 students had skateboarded before. The ratio of the number of students who previously roller-skated to the number of students who previously skateboarded was 3:4. How many students went on the trip? 2. Jack is riding his bicycle. When the pedals on the bicycle turn 3 times, the rear wheel turns 9 times. If the wheel s circumference is 50 inches, how far has the bike traveled when the pedals turn 5 times? 3. One side of a square figure measures 3 1 inches. If the length of each side of the figure is doubled, what is 2 the ratio of the area of the old square to the new square? 4. Landon bought 3 oranges for $4.50. How many can he buy for $31.50? 22

19 Domain: Ratios & Proportional Relationships Focus: Multistep Ratio Problems Lesson: #12 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: A 10 x 12 photograph is reduced so the length is 6 inches. What is the area of the new photograph? Student Page Example B: Arianna enlarged the size of a triangle to a width of 11.6 inches. What is the new height if it was originally 5.8 inches wide and 0.4 inches tall? 1. The 7 th grade class will be going on a trip with their parents. The ratio of students to women to men is 5:4:3. If there are 240 people going, how many men are going? How many women are going? How many students are going? 2. A house drawing uses a scale of 1-inch equals to 12 feet. A room on the drawing is inches by inches. If carpeting costs $4.00 per square foot, how much will it cost to carpet the room? 3. The cities of Seattle and Houston are separated by 9 inches on a map. If 1.5 inches represents 450 miles, how long will it take a plane traveling at 300 mph to make the trip? 4. During a storm, snow falls at the rate of inches in 1 6 up to reach six feet? of an hour. How long will it take the snow building 23

20 Domain: Ratios & Proportional Relationships Focus: Proportional Relationships Evaluation: #3 1. Henry found the following costs for different sizes of juice containers at the grocery store. Use the graph to determine if the cost and weight are proportional. Explain you answer. Find the constant of proportionality. weight (lbs) cost (dollars) A) Are the cost and weight proportional? B) Explain your answer. C) What is the constant of proportionality? D) What is the proportional equation? 2. To get purple paint, Stella mixes red paint and blue paint in the ratio of three to four. If she used gallons of blue paint, how much red paint does she need? 3. A drawing of a room has a scale of 1 inch = 6 feet. If a room on the drawing measures much will carpeting cost for the room be if it sells for $4.50 a square foot? in. 3 in. how

21 Domain: Ratios & Proportional Relationships Focus: Multistep Ratio Problems Lesson: #13 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: Molly s family of 4 uses 315 gallons of water each week. How much water will Molly use in 23 days? Example B: A car is traveling at a rate of 55 mph for a distance of amount of time at 45 mph, how far will it travel? miles. If the car is driven the same 1. On a sunny day, Lucy s shadow is 8 feet, 6 inches long. A nearby tree casts a shadow that is 18 feet, 10 inches long. If Lucy is 5 feet, 4 inches tall, how many feet tall is the tree next to her? 2. The angles of a triangle are in the ratio of 2:3:4. What are the measures of the angles? 3. Ian is shopping for a new cell phone plan. If he talks 500 minutes per month, which is the least expensive plan for him to purchase? Plan A 6 cents per minute No monthly charge Plan B $6.00 monthly charge 4 cents/minute Plan C 300 anytime minutes $10 per month (15 cents each additional minute) 4. Rectangle A has a length of 15 inches and an area of 52.5 square inches. If Rectangle B is similar to Rectangle A and has a length of 60 inches, what is the perimeter of Rectangle B? 25

22 Domain: Ratios & Proportional Relationships Focus: Multistep Ratio Problems Lesson: #14 Standard(s): 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: Cole lives in a family that has 4 members. If each person in the family eats $9.68 of food each day, how much will the family spend on food in 4 5 of a year? Example B: 8 bags of candy have a total of 560 calories. How many calories will be in 2 dozen bags? 1. Caroline runs 4 miles in 40 minutes. How many hours will it take her to run 1 mile? 2. In a school district, the ratio of men to women is 5:12. If there are 2,028 women working in the district, how many men are in the district? 3. Blake can read 36 pages in 55 minutes. How many pages can he read in hours? 4. A watch is losing 2.5 minutes for every 10 hours that go by. How many minutes will it lose in one week? 26

23 Domain: Ratios & Proportional Relationships Focus: Simple Interest Lesson: #15 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: Nathan was paid $15,000. If he puts all the money in his bank account at a rate of 7% annually for 2 years, how much interest will he earn? Example B: Cooper borrowed $60,888 from his bank for 21 months at 6.08%. How much money will he need to pay back? 1. Luis borrows $820 at 6% for 50 months. How much money will he need to pay back? 2. Melanie puts $300 a month into her savings account at 12% interest. How much money will be in her account after 10 years? 3. Adam has $16,100 in his bank account that gives its customers 4.22% interest. After 20 months how much money will he have in his account? 4. Josh borrowed $ for a bicycle. His dad loaned him the money at 4.31% for 12 months. His Dad said Josh could pay him back by mowing the lawn. If Josh gets $15 every time he mows the lawn, how many times will he have to mow the lawn to pay his Dad back? 27

24 Domain: Ratios & Proportional Relationships Focus: Simple Interest Lesson: #16 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: Morgan loaned a friend $5,555 for 42 months. Her friend paid her the principal amount plus $ in interest. What was the loan rate? Example B: Wyatt borrowed $48,560 for a new car. The interest rate was 8.35%. The amount of interest on the loan was $18, How many years was the loan? 1. Jasmine put $6,000 into her savings account for 18 months. If she earned $ in interest, what was the interest rate? 2. Jocelyn had a loan at 14.4% for 46 months on which she owed $2, in interest. How much did she borrow? 3. Andrea s loan was for 4 years at 2.75% interest. The amount of her interest was $82, What was the original amount of her loan? 4. Chase put $46,248 into his bank account. The interest rate was 2.81%. Several months later he checked his account balance and he had $47, in his account. How much time had passed? 28

25 Domain: Ratios & Proportional Relationships Evaluation: #4 Focus: Simple Interest 1. The angles of a triangle are in the ratio of 3:4:5. What are the measures of the angles? 2. A watch loses 1.75 minutes every hours. How many hours will it lose in one month? 3. If the interest is $ in 42 months at 8.25%, find the principal. 4. Dominic put $6,650 into his bank account. The bank will pay him 9.1% interest. After 30 months, how much money will he have in his account? 29

26 Domain: Ratios & Proportional Relationships Focus: Sales Tax & Gratuities Lesson: #17 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: Ian buys a new pair of basketball shoes for $ The sales tax is 7.35%. How much is the tax? How much will he have to pay for the shoes? Example B: Mackenzie eats dinner at a restaurant that has a sign stating there is a 6% gratuity on all meals. In addition, the sales tax is 8.25%. If the bill without the gratuity and tax included is $45.12, how much will Mackenzie need to pay? 1. The original price of a pair of pants is $ If the tax rate is 5.55%, how much will the pants cost? 2. Katherine s restaurant bill before tax is $ The sales tax rate is 8.35%. If Katherine wants to leave the waiter a 20% tip based on the pre-tax amount, how much will the total bill be? 3. A motel requires a 15% gratuity added to the cost of the room. If the pre-tax room rate was $ and the tax rate was 7.55%, how much is the total room cost? 4. Carson buys a skateboard for $ The sales tax rate is 7.25%. How much will he pay for the skateboard? 31

27 Domain: Ratios & Proportional Relationships Focus: Sales Tax & Gratuities Lesson: #18 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: Sydney decides to buy a $350 watch. The tax was $ What was the tax rate? Example B: After 12.4% sales tax, a pair of jeans was $ How much were they before the tax? 1. It costs Payton $46.75 to have her dog groomed. The groomer charges a gratuity of 9% for the grooming of all dogs. Payton wants to also leave the groomer a 15% tip. If the sales tax is %, what is the total she will need to pay the pet salon? 2. At a restaurant, Parker only has $25 to spend on dinner. In addition to the dinner, he must pay 8.4% sales tax and he wants to leave a 20% tip for the waitress. How much money will he be able to spend on food? 3. Maya bought a hammer that costs $8.95. The sales tax was $0.54. What was the tax rate? 4. Diego bought a school textbook that cost $ This amount includes a tax of 6.60%. What was the cost of the book before the tax? 32

28 Domain: Ratios & Proportional Relationships Focus: Discount Lesson: #19 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: A shirt is marked down 35%. If the original price was $18.99, what is the sale price of the sweater before sales tax? Example B: A video game store has a 45% sale on all video games. If the regular price of the game you want to purchase is $35.99, how much is the discount? 1. Cole wants to buy a surfboard for $ The store has marked the price down 24.5%. How much will Cole have to pay for the surfboard if the tax rate is 7%? 2 A leather jacket is marked down 35%. If the original price is $198.99, how much will Jeremiah have to pay before sales tax? 3. A new suit is regularly priced at $ A store has it on sale marked 6 3 % off. If the tax rate is 6.75%, 4 how much will Owen have to pay for the suit? 4. A DVD that normally sells for $14.99 is marked, 9.99% off. What is the discount? What is the pre-tax sale price? 33

29 Domain: Ratios & Proportional Relationships Focus: Discount Lesson: #20 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Example A: Riley sold her bicycle to Bryan for 15% off. Bryan sold it again to Mariah at 20% below the price he paid for the bicycle. If the original price of the bicycle was $89.09, how much did Mariah pay for the bicycle? Example B: A sweater is on sale for 40% off. The sale price is $45. What was the original price? What was the amount of the discount? 1. Leah bought her new computer at 14 1 % discount. She paid $855 for the computer. How much money did 2 she save? 2. Claire buys a notebook for $1.75, a mechanical pencil for $3.99, and a ruler for $0.74. Each item is on sale for 35% off. If Claire must pay a sales tax of 8.5%, how much will she be paying for school supplies? 3. Shirts are on sale at a store with an offer of buy one and get 33% discount on the other. If the regular price of one shirt is $29.99, how much will he pay for 2 shirts? 4. A hardware store buys 24 hammers for $ and gets a discount of 8% on each hammer. What was the original price of each hammer? 34

30 Domain: Ratios & Proportional Relationships Focus: Tax, Gratuity, & Discount Evaluation: #5 1. Max and three friends went out to dinner together. The total of their restaurant bill was $ The sales tax rate is 7 1 %. If Max wants to leave the waitress a 15% tip based on 2 the pre-tax amount, how much will the total bill be? 2. Paige buys a horse for $528. The sales tax rate is 12.5%. What was the original price of the horse? 3. A purebred puppy is on sale for 15 1 % off the regular price. If the regular price were $350, 2 how much would you have to pay if the sales tax rate is 6 3 4? 4. A department store buys 12 waffle irons for $ and gets a discount of 18% on each waffle iron. What was the original price of each waffle iron? 35

31 Domain: Ratios & Proportional Relationships Focus: Markup Lesson: #21 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Example A: The cost of a shirt is $ If the store has a 35 1 % markup and a 7.35% tax, 4 what is the selling price? Example B: A jacket that normally sells for $74.99 is marked up 12%. If the store charges a 8.25% tax, how much is the selling price? 1. The price of a radio was increased by 16%. If the original price was $135, how much was the price increased? 2. The original price of a pair of shoes was marked up 125%. If the original pair of shoes cost $89.99, what was the pre-tax price? 3. The cost of a computer game is $9.99. If the markup is 45% and the sales tax is %, what is the selling price? 4. The markup at a restaurant for a steak meal is 225%. If the meal cost the restaurant $8.95 to make, how much will Jaden be charged if the sales tax is 8% and Jayden wants to leave a pre-tax tip of 20%? 37

32 Domain: Ratios & Proportional Relationships Focus: Markup Lesson: #22 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Example A: The markup on a camera is 75%. If the amount of the markup is $130.05, what is the pretax total price? Example B: The wholesale price of a CD player is $49. If the retail price is $71.05, what is the percent of markup? 1. Rachel bought a sweater that had been marked up $22. If she paid $55 for it, what was the percent of markup? If the sales tax amount was 7%, what was the pre-tax price for the sweater? 2. Paige paid $75.75 for a new suitcase. If it was marked up 150%, what was the original price? What was the amount of change? 3. A computer external drive cost a store $65 wholesale. They decide to sell it for $ What is the percent of markup? 4. A giant jar of peanut butter was marked up $0.29. If the percent of markup was 5%, what was the original price? What was the retail price? 38

33 Domain: Ratios & Proportional Relationships Focus: Commission & Fees Lesson: #23 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Example A: Eric is selling televisions and makes a 12% commission on all sales. What would his commission be on $4260 worth of televisions? Example B: A salesperson made $ selling $6940 worth of camera equipment. What was the commission rate? 1. A real estate agent earned a commission of $7845 for selling a house. If his rate of commission is 3.5%, what was the selling price of the house? 2. A car dealer sold an automobile for $35,100. If the commission was 2.2% of the selling price, what was the amount of the dealer s commission? 3. Carlos makes $8.50 an hour plus a 10.25% commission on all the watches he sells. How much does he earn for 8 hours of work during which he sold $452 worth of watches? 4. Layla sells office supplies and earns a base salary of $375 per week, plus a % commission on all her sales. How much would her pay be during a week she sells $799 worth of office supplies and her employer deducts 15% from her check to pay taxes? 39

34 Domain: Ratios & Proportional Relationships Focus: Commission & Fees Lesson: #24 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Example A: Charlotte earns a step commission on sales based on the following rates: 6% on amounts up to $ % on amounts between $1000 and $ % on amounts over $2000 What will be her total commission on sales of $1550 and $2430? Example B: Caleb is offered two sales positions. Job 1 pays $650 per month plus 3.5% commission on all sales over $2500 while Job 2 pays a straight commission of 10.5%. Based on monthly sales of $12,625, which job will pay Caleb the most? 1. Nathan set a sales goal to earn $2000 during the month of August. He receives a base salary of $650 per month as well as 8.5% commission for all sales in that month. How much merchandise will he have to sell to meet his goal? 2. Justin s commission is broken down into different levels: 6% on amounts up to $ % on amounts between $1000 and $ % on amounts over $2000 What will his commission be on sales of $1428? 3. Alexa works at a cell phone store. She is paid $7.25 per hour for an 35 1 hour week, plus 2 a commission of 6.5% on her sales. If all her sales for one week were $ , how much did she earn during that week? 4. In Problem 3, what would Alexa s sales for the week have to be for her to earn $600 in one week? 40

35 Domain: Ratios & Proportional Relationships Focus: Markup & Commission Evaluation: #6 1. A watch was marked up 65%. If the wholesale price of the watch was $87.99 and the sales tax was %, what was the selling price? 2. A leather jacket cost a store $ The store decided to sell the jacket for $ What was the percent of markup? 3. A real estate agent earned a commission of $6444 for selling a house. If his rate of commission is 4.2%, what was the selling price of the house? 4. Riley makes $7.25 an hours plus a 12 1 % commission on all merchandise she sells over $500. How much 4 does she earn for 8 hours of work during which she sold $985 worth of merchandise? 5. Aubrey is offered two sales positions. Position 1 pays $1500 per month plus 4.25% commission on all sales over $3000. Position 2 pays a straight commission of 14%. Based on a monthly sales of $14,775, which job will pay Aubrey the most? 6. A salesperson set a goal to earn $2500 during the month of December. She receives a base salary of $700 per month plus a 12% commission for all sales during that month. How much merchandise will she have to sell to meet her goal? 41

36 Domain: Ratios & Proportional Relationships Focus: Percent Increase/Decrease Lesson: #25 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Example A: Gasoline prices are projected to increase by 125% by If a gallon of gasoline currently costs $4.15, what is the projected cost of gallon of gas in 2014? Student Page Example B: Christian had to travel 87 miles from home to work. After he moved, he only had to travel 38 miles to work. What was the percent of change? 1. The price of a watch was increased by 60% to $125. What was the original price? 2. The population of a city was 56,000 in By 2010, the population had grown to 128,156. What was the percent of increase? 3. After a raise, Jesse s salary increased from $5.25 an hour to $6.50 an hour. The raise was what percent? 4. Khloe runs a beauty supply store. She has made some changes and expects her expenses to drop by 35% next month. If her expenses were $10,224 this month, what is Khloe s expense projection for next month? 43

37 Domain: Ratios & Proportional Relationships Focus: Percent Increase/Decrease Lesson: #26 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Example A: Victoria bought a painting for $ She later sold it to a friend for $65. What was the percent of decrease? Example B: Thirty is what percent less than 48? 1. What is the percent of decrease of a television that is marked down from $1236 to $924? 2. The enrollment at a local college was 14,250 students. If the enrollment went down %, what was the new enrollment? 3. The selling price of a home was dropped from $250,000 to $195,000. By what percent did the price drop? 4. A textbook has gone up in price from $56 to $ What is the percent of increase? 44

38 Domain: Ratios & Proportional Relationships Focus: Percent Error Lesson: #27 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Directions: Find the percent error of the following real-life scenarios. Student Page Example: Janelle told her mom that a birthday party at the bowling alley only costs $250 for 10 kids. The total price of the party was $276. What was Janelle s percent error? 1. Joe planned on 9 soccer players for the fall season. He received 10 players on his roster. What was Joe s percent error? 2. Conner estimated that he would need $15 to complete his science project. His total at the hobby shop was $ What was his percent error? 3. Paul is making cookies for his first period class. He had all of the ingredients at home except for the sugar. He borrowed 2 cups from his friend down the street on his way home without knowing how much he would actually need. When he got home and read the recipe, he found out that he needed 2 ⅓ cups of sugar. What was Paul s percent error? 4. Esmeralda wants to buy a new bike. She estimated that she would need $125. After researching, she discovered that the model that she wants to buy is actually $157. What was her percent error? 5. Mallory bought 6 feet of ribbon to make bows for all of her soccer teammates. She had 11 inches of ribbon left over. What was her percent error? 45

39 Domain: Ratios & Proportional Relationships Focus: Percent Increase, Decrease, & Error Lesson: #28 Standard: 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Directions: Find the percent of change in the following real-life scenarios. Example: Last month Judy s electric bill was $154. This month her electric bill is $176. By what percent did Judy s electric bill increase? 1. Sarah received 6 new students during first semester. She received an additional 15 students second semester. By what percent did her enrollment increase from first semester to second semester? 2. Tyler estimated that he needs 50 flyers to hang around campus. After putting up flyers everywhere he could think of, he had 13 left over. By what percent did he overestimate? 3. A school district needs to cut teachers pay from $4,200 per month to $3,800 per month. By what percent will the teachers expect to have their salary decreased? 4. A local skate shop wants to mark-up their wallet inventory. The average wallet costs $28. By what percent will they mark-up their price if they were to charge $32 for a wallet? 5. Jonathon estimated that he needed 2 gallons of paint for a kitchen remodel. Half way through the project he realized that it was not going to be enough paint and purchased a third gallon. After he finished painting the kitchen he had a quarter of a can of paint left over. What was Jonathon s percent error? 46

40 Domain: Ratios and Proportional Relationships Focus: Markdown, Markup, Commission & Percent of Change Evaluation: #7 Directions: Find the markdown, markup, commission or percent of change for the following real-life scenarios. 1. A pair of shoes is on sale for $ Their original price was $55. By what percent have the shoes been marked down? 2. The wholesale price of a watch is $15. A store sells the watch for $ How much did the store markup the watch? 3. A real estate agent sold a house for $245,000 and earned a commission of $7,350. What percent is the real estate agent s commission in comparison with the selling price of the house? 4. A team of teachers decided to reduce the amount of problems on the final exam from 50 problems to 35 problems. By what percent did they reduce the problems? 5. Riley wants to buy a new jacket. She estimated that she would need $40. When she arrived at the store, the jacket was on sale for $ What was her percent error? 47

41 Common Core Standards Plus Mathematics Grade 7 Performance Lesson #2 Domain: Ratios and Proportional Relationships Student Page 1 of 4 Vocabulary: Proportional relationship: A relationship in which the ratio of y/x is constant. Equivalent: Having the same value; the same size. Constant of proportionality: The mathematical term for the unit rate. Ordered pairs: Corresponding numbers in a table that are used to locate a point on a coordinate plane. Coordinate plane: A grid formed by the intersection of a horizontal number line (x- axis) and a vertical number line (y- axis). x- axis: The horizontal number line at the starting position (0, ) on the coordinate plane. y- axis: The vertical number line at the starting position (,0) on the coordinate plane. Percent: Rate per one hundred. Interest: The amount of money paid or earned for the use of money. Principal: The amount of money in an account. Rate: The percentage at which money is loaned or borrowed. Time: The length of time money is borrowed; always measured in years. Sales tax: The amount of money added to a total purchase based on the total sales and determined by the government. Gratuity: An additional amount given to a person who provides service; a tip. Discount: The amount by which the regular price of an item is reduced. Sales price: The amount that an item costs to purchase. Markup: The amount added to the price of goods by retailers to cover their costs. Commission: A fee paid to sales people for selling merchandise. Percent error: The percent a projection differs from the actual value. 49

42 2 of 4 Common Core Standards Plus Mathematics Grade 7 Performance Lesson #2 Domain: Ratios and Proportional Relationships Directions: Use a sales advertisement to solve the following problems. 1. You have $100 to spend on items that are on sale in the advertisement. The sales tax is 7.5% on all non- food items. What would you buy? List the items you would buy, their prices, and the total price. Calculate the tax on the total purchase to ensure that you are able to pay for the total with $100 or less. 2. You have a special coupon that gives you an additional 30% off one item in the sales advertisement. Which item would you buy? What is the cost of the item in the advertisement, and what is the cost after you apply the coupon? How much money will you save on the item? 50

43 Common Core Standards Plus Mathematics Grade 7 Performance Lesson #2 Domain: Ratios and Proportional Relationships Student Page 3 of 4 3. Choose four items that are on sale. Graph their prices from quantities of one to five for each of the five items. What do you notice about your graph? If the store sold exactly five of each of the items you chose, and the store made a profit of 17% on the items, what would the profit be on the total? 4. Choose one item in the advertisement. Assume that one salesperson sold 50 of that item. The salesperson makes a commission of 4% of the total. What is the salesperson s commission? If the salesperson made 6% commission, how many fewer of the item would he/she need to sell to make the same total commission? 51

44 4 of 4 Common Core Standards Plus Mathematics Grade 7 Performance Lesson #2 Domain: Ratios and Proportional Relationships 5. Find two items in the advertisement that have different prices that are within $5 of each other. Graph the sale of quantities of one to seven of the items. What do you notice about the lines? What conclusions can you draw from the graphs? 52