Course 2, Lesson 7.1.2

HW: 7-21 to 7-26

Learning Target: Scholars will use multiplication to scale a quantity. Scholars will connect finding percent’s of a number with multiplying by an equivalent fraction or decimal.

In Chapter 5, you learned how 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 = 25%. 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 distance, rate, and time to the idea of scale factors. 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.

7-16. Dane 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? The diagram below may be useful.

7-17.Matt thought about problem 7-16 and drew the diagram at right. Look at Matt’s drawing and decide how he is thinking about this problem.

  1. Write an equation that uses the scale factor to findx.
  2. 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 and how are they different?

7-18. In the two previous problems,is used in two ways: first, as time in the rate problem,and second, as the scale factor in the similar triangle problem used to find three fifths of 25miles. Both of these situations resulted in an equivalent calculation:. How else could this be written?

  1. Using the portions web shown at right, work with your team to find two other ways to write the equation. For example, one way might be.
  2. If you did not already find it, what percent would be equivalent to? Use this percent to write a statement in words and symbols that is equivalent to.
  3. Use the idea of scalingto find the following values. Write an expression using either a fraction or a percent, and then find the result.
  4. 90% of 25 miles
  5. 8% of $75
  6. 25% of 144

7-19.Josea went out to dinner at an Indian restaurant. The total bill was $38. She wanted to leave a 15% tip.

  1. If you use the idea of scaling to find the tip amount, what would she need to multiply by? As you talk about this with your team, consider:
  2. How could you represent this multiplier as a fraction?
  3. How could you represent it as a decimal?
  4. Does it make a difference which representation, fraction or decimal, you use to solve this problem?
  5. Which do you think will be easier?
  6. How much should Josea leave for the tip? Show your calculations.
  7. If Josea changes her mind and wants to leave a 20% tip instead, how much will this be?

7-20. While shopping for a computer game, Isaiah found one that was on sale for 35% off. He was wondering if he could useas a multiplier to scale down the price to find out how much he would have to pay for the game.

  1. If Isaiah usesas a scale factor (multiplier), will he find the price that he will pay for the game? Why or why not?
  2. 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 percent’s.
  3. Howmuch will Isaiah have to pay for the game if the original price is $40? Show your strategy.

7-21.Ameena’s boat travels 35 miles per hour. The best fishing spot in the lake is 27miles away from her starting point.

  1. If she drives her boat forof an hour, will she make it to the best fishing spot on the lake?
  2. How long will Ameena need to drive to get to the best fishing spot on the lake? Express your answer in both a portion of an hour and in minutes.

7-22.Use the triangles below right to answer the questions that follow.

  1. What is the scale factor from A to B?
  2. What is the scale factor from B to A?
  3. What is the relationship of the scale factors?

7-23.Simplify each expression.

  1. 5.3 – 2.8x– 7.1 + 3.9x

7-24.Copy the diagram below on your paper. Use the given information to fill in all of the missing labels.

7-25. Alan is making a bouquet to take home to his grandmother. He needs to choose one kind of greenery and one kind of flower for his bouquet. He has a choice of ferns or leaves for his greenery. His flower choices are daisies, carnations, and sunflowers.

  1. Draw a tree diagram to show the different bouquets he could make. How many are there?
  2. What is the probability that he will use ferns?
  3. What is the probability that he will not use sunflowers?
  4. What is the probability that he will use leaves and carnations?

726. Read the Math Notes box in this lesson and use the information to complete the following problems.

The daily high temperatures in degrees Fahrenheit for the last two weeks in Grand Forks, North Dakota were7, 1, –3, 0, 4, –1, 2, 5, 7, 7, 3, –2, –4, and –5.

  1. Calculate the median temperature.
  2. Find the first and third quartiles (Q1 and Q3).
  3. What is the interquartile range (IQR)?

Lesson 7.1.2

  • 7-16.·hr = 15 miles
  • 7-17.See below:
  • 25 miles·= 15 miles
  • Sample response: Both problems have a distance of 25 and 15 miles; in the first problemis time in hours, while the other usesas a scale factor; the computation of25 miles·= 15is the same in both cases.
  • 7-18.See below:
  • Sample answers: three fifths of twenty-five, 25(0.6) = 15, 60% of 25 = 15,(25) = 15
  • 60%. 60% of 25 is 15
  • i. (0.9)(25) = 22.5
    ii. (0.08)($75)= $6
    iii.(144) = 36
  • 7-19.See below:
  • The scale factor is 15%.. 0.15. It does not matter which you use. Student responses regarding which will be easier will vary.
  • 5.70. One possible equation: 0.15($38) = $5.70
  • One way to write it:($38) = $7.60
  • 7-20.See below:
  • will give him theamount 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.
  • See diagrambelow. He could use 65%, which is 100% minus 35%.
  • (0.65)(40) = $26
  • 7-21.See below:
  • No, she will only go a little over 23 miles.
  • Approximately 0.77hours or 46.3 minutes
  • 7-22.See below:
  • The scale factors are reciprocals.
  • 7-23.See below:
  • −
  • −1.8 + 1.1x
  • 7-24.60%of students = 42, total number of students = 70, 28 students = 40 %
  • 7-25. See below:
  • See sample diagram below. There are 6 possible bouquets.
  • ·=
  • 7-26.See below:
  • 1.5 degrees Fahrenheit
  • Q1=–2, Q3=5
  • IQR=5–(–2)=7