Mathematical Practices: #1 Make sense of problems and persevere in solving them #4 Model with mathematics #6 Attend to precision

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1 Grade: 7 th - Course 2 Detail Lesson Plan Lesson: Replacement Lesson How can I make it smaller or bigger? Scaling Quantities CC Standards: 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commission, fees, percent increase and percent decrease, percent error. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a a = 1.05a means that increase by 5% is the same as multiply by Objective: Students use multiplication to scale a quantity. Students connect finding percents to a number with multiplying by an equivalent fraction or decimal. Mathematical Practices: #1 Make sense of problems and persevere in solving them #4 Model with mathematics #6 Attend to precision Calculator usage: No Teacher Input: Bellwork Teacher selected Core Problems 7-19 through 7-20 Extra Practice Homework See extra practice problems below. Teacher selected Closing Today we used multiplication to scale a quantity. What does scaling mean? To reduce or enlarge a quantity. We also rewrote expressions in different forms. This helped us see how the quantities were related. What were the four different forms we used to rewrite expressions? 1) Fraction 2) Decimal 3) Percents 4) Words

2 In Chapter 5, you learned to find the percent of a number by making a diagram to relate the part to the whole and find the desired portion. This calculation is fairly straightforward if the percent is a multiple of 10, like 40%, or can be thought of as a fraction, like However, it can be more challenging if the percent is something like 6.3% or 84.5%. Today you will connect what you have learned previously about the relationship between distant, rate, and time to the idea of scale factors. Remember, scaling is the process of enlarging or reducing a quantity. You will learn how to use a scale factor to find the corresponding lengths of similar figures. This idea will add a powerful new tool to your collection of problem-solving strategies that will help you to calculate percents Dan is training for a bicycle race. He can ride his bike 25 miles per hour. One day, when he had been riding for of an hour, he had to stop and fix a flat tire. How many miles had he ridden when he stopped? Answer: miles Matt thought about problem 7-16 and drew the diagram at the right. Look at Matt s drawing and decide how he is thinking about this problem. a. Write an equation that uses the scale factor to find x. Then find the value of x. b. What connection is Matt making between finding a distance using the rate and time (as you did in problem 7-16) and using a scale factor with similar figures? How are the situations alike? How are they different?

3 7-18. In the two previous problems, is used in two ways: first, as time in the rate problem hrs, and second, as the scale factor in the similar triangle problem used to find three-fifths of 25 miles. Both of these situations resulted in an equivalent calculation: How else could this be written? a. Using the portions web shown at the right, work with your team to find three other ways to write the equation. Fraction (given): 25 = 15 Words: Decimal: Percent: b. Use the idea of scaling to find the following values. Write an expression using either a fraction or a decimal, and then find the result. Example: 12% of 60 miles Write expression: Answer: 7.2 miles or 7 90% of 25 miles Write expression: Answer: 8% of $75 Write expression: Answer: 25% of 144 Write expression: Answer:

4 7-19. Josea went out to dinner at an Indian restaurant. The total bill was $38. She wanted to leave a 15% tip. a. How could you represent this multiplier as a fraction? b. How could you represent it as a decimal? c. Does it make a difference which representation, fraction or decimal, you use to solve the problem? d. Which do you think will be easier to use, fraction or decimal? e. How much should Josea leave for the tip? Show your calculations. f. If Josea changes her mind and wants to leave a 20% tip instead, how much will this be? While shopping for a computer game, Isaiah found one that was on sale for 35% off. He was wondering if he could use as a multiplier to scale down the price to find out how much he would have to pay for the game. a. If Isaiah uses as a scale factor (multiplier), will he find the price that he will pay for the game? Why or why not? b. There is scale factor (multiplier) other than 35% that can be used to find the sale price. What is it? Complete the diagram to show how this scale factor is related to 35%. Label the parts of your diagram discount and sale price along with the relevant percents. c. How much will Isaiah have to pay for the game if the original price is $40? Show your strategy.

5 Name: Period: 7 th Grade Working with Percents and Number Conversions Directions: Convert each percent to a fraction and a decimal. Write your fraction in simplest form. 1) 7.5% Decimal Fraction: 2) 12% Decimal Fraction: 3) 3.75% Decimal Fraction: 4) 20% Decimal Fraction: Directions: Use a method of your choice to solve each percent problem below. 5) Samantha wants to leave a 15% tip for her waitress on her lunch bill of $ How much tip will she leave? Answer: $ 6) The sales tax rate is 7.5% in Mississippi. Find the amount of tax on a curling iron that sells for $120. Answer: $ 7) Find the amount saved for a $150 pair of boots that are advertised at 25% off. Answer: $ 8) A store owner paid $15 for a book. She marked up the price of the book by 40% to determine its selling price. What is the selling price of the book? Answer: $ 9) A customer buys a different book that has an original selling price of $38. The book is discounted 25%. What is the amount that the customer will pay for the book? Answer: $ 10) Heather bought a top for $26 and a matching pair of shoes for $38. If the sales tax rate is 6% what is the total cost of both items? Answer: $

6 Answer Key In Chapter 5, you learned to find the percent of a number by making a diagram to relate the part to the whole and find the desired portion. This calculation is fairly straightforward if the percent is a multiple of 10, like 40%, or can be thought of as a fraction, like However, it can be more challenging if the percent is something like 6.3% or 84.5%. Today you will connect what you have learned previously about the relationship between distant, rate, and time to the idea of scale factors. Remember, scaling is the process of enlarging or reducing a quantity. You will learn how to use a scale factor to find the corresponding lengths of similar figures. This idea will add a powerful new tool to your collection of problem-solving strategies that will help you to calculate percents Dan is training for a bicycle race. He can ride his bike 25 miles per hour. One day, when he had been riding for of an hour, he had to stop and fix a flat tire. How many miles had he ridden when he stopped? miles Matt thought about problem 7-16 and drew the diagram at the right. Look at Matt s drawing and decide how he is thinking about this problem. a. Write an equation that uses the scale factor to find x. Then find the value of x. 25 = 15 miles b. What connection is Matt making between finding a distance using the rate and time (as you did in problem 7-16) and using a scale factor with similar figures? How are the situations alike? In both problems you are reducing the length from 25 miles to 15 miles. In both cases you multiply to find your answer. 25 = 15 miles How are they different? In problem 7-16, is described as part of an hour. In 7-17, is described as the scale factor.

7 7-18. In the two previous problems, is used in two ways: first, as time in the rate problem hrs, and second, as the scale factor in the similar triangle problem used to find three-fifths of 25 miles. Both of these situations resulted in an equivalent calculation: How else could this be written? a. Using the portions web shown at the right, work with your team to find three other ways to write the equation. Fraction (given): 25 = 15 Words: three-fifths of twenty-five is fifteen Decimal: 25.6 = 15 Percent: 60% of 25 is 15 b. Use the idea of scaling to find the following values. Write an expression using either a fraction or a decimal, and then find the result. Example: 12% of 60 miles Write expression: Answer: 7.2 miles or Answer: 7 90% of 25 miles Write expression: Answer: 22.5 miles 8% of $75 Write expression: Answer: $6 25% of 144 Write expression: Answer: 36

8 7-19. Josea went out to dinner at an Indian restaurant. The total bill was $38. She wanted to leave a 15% tip. a. How could you represent this multiplier as a fraction? b. How could you represent it as a decimal?.15 c. Does it make a difference which representation, fraction or decimal, you use to solve the problem? It doesn t matter which one you use. The fraction and decimal both represent 15%. d. Which do you think will be easier to use, fraction or decimal? Answers will vary, but most prefer using a decimal over a fraction as a multiplier. e. How much should Josea leave for the tip? Show your calculations. $38 x.15 = $5.70 f. If Josea changes her mind and wants to leave a 20% tip instead, how much will this be? $38 x.20 = $7.60

9 7-20. While shopping for a computer game, Isaiah found one that was on sale for 35% off. He was wondering if he could use as a multiplier to scale down the price to find out how much he would have to pay for the game. a. If Isaiah uses as a scale factor (multiplier), will he find the price that he will pay for the game? Why or why not? will give him the amount that will be subtracted for the sale, not the price he will have to pay; he could use the information to find the sale price if he subtracts the amount from the original price of the game. b. There is scale factor (multiplier) other than 35% that can be used to find the sale price. What is it? Draw a diagram to show how this scale factor is related to 35%. Label the parts of your diagram discount and sale price along with the relevant percents. Answer: c. How much will Isaiah have to pay for the game if the original price is $40? Show your strategy. ($40) (.65) = $26

10 Name: Period: 7 th Grade Working with Percents and Number Conversions Directions: Convert each percent to a fraction and a decimal. Write your fraction in simplest form. 1) 7.5% Decimal.075 Fraction: 2) 12% Decimal.12 Fraction: 3) 3.75% Decimal.0375 Fraction: 4) 20% Decimal.20 Fraction: Directions: Use a method of your choice to solve each percent problem below. Show your work. 5) Samantha wants to leave a 15% tip for her waitress on her lunch bill of $ How much tip will she leave? Answer: $1.875, rounded $1.88 6) The sales tax rate is 7.5% in Mississippi. Find the amount of tax on a curling iron that sells for $120. Answer: $9 7) Find the amount saved for a $150 pair of boots that are advertised at 25% off. Answer: $ ) A store owner paid $15 for a book. She marked up the price of the book by 40% to determine its selling price. What is the selling price of the book? Answer: $21 9) A customer buys a different book that has an original selling price of $38. The book is discounted 25%. What is the amount that the customer will pay for the book? Answer: $ ) Heather bought a top for $26 and a matching pair of shoes for $38. If the sales tax rate is 6% what is the total cost of both items? Answer: $67.84