Lesson 2.3.2

HW: 2-124 to 2-129

Learning Target: Scholars will fix a scaling error, choose appropriate scales, and plot data for which the placement of points must be approximated.

In this lesson, you will use all that you know about graphs to solve challenging graphing problems. Each of the situations in this lesson will require you to think hard about what a graph tells you and what the best way is to show it. As you work together to solve these problems, think about what makes the task challenging. Focus with your team on how you can get yourselves “unstuck” if your teacher is not immediately available. Does our data fit? Can we see it clearly?

2-121.Andre works in his family’s juice shop. He has invented the new Mathberry Madness smoothie, and word is getting around. He wants a graph showing how many new smoothies have been sold throughout the first month. He has gone through the cash-register records and gathered the data for some of the first 12days, shown in the table at right.

He wants to graph his data and use it to predict approximately how many Mathberry Madness smoothies he can expect to sell by Day 20. He has started the graph below right.

Your Task:

  1. Examine Andre’s graph. Can you use it to predict how many smoothies would be sold by Day20? Why or why not?
  1. Contribute your ideas to a team discussion and then work with your team to decide how to scale the axes so that you can graph Andre’s data accurately and make a prediction.
  2. Then, on your own paper, graph Andre’s data.
  3. Show where on the graph you would expect to place a data point for Day20 and explain how many smoothies are likely to be sold by then.

2-122. GRAPHING CHALLENGES

Your teacher will assign your team one of the graphing challenges shown below. Work with your team to plan an appropriate scale for each axis. Then create a graph and place the data on the graph. Be prepared to explain to the class how you created your graph and why it is accurate and easy toread.

Challenge A: The table at right shows the time it took five different students to get to the mall and how far they traveled to get there.

Challenge B:To use the pool at the Columbus Recreation Center, guests must pay one annual membership fee and then another small fee each time they swim. Jeffand his five friends kept track of how many times they visited the pool in one year and how much money they each spent.

2-124.Troyis a fan of baseball, and his favorite player is Moe Jauer of the Minnesota Triplets. Troy made a table displaying how many home runs Jauer hit during his first five seasons. Graph Troy’s data.

2-125. Saraturned in the two graphs below for homework, but her teacher marked them wrong. Explain to Sara what mistakes she made. Then choose one of her graphs to correct, copy it on your paper, and correctit.

2-126. If a setof xyaxes has 20 grid units in each direction and the greatest value of the data to be placed on the horizontal axis is 132, what would be an appropriate and convenient scale to use for this axis? Explain.

2-127.Simplify each expression.

2-128.For eachof the experimental results described, write the indicated probability.

  1. A coin is flipped 80 times. It lands tails 47 times. What is the P(heads)?2-128a HW eTool(CPM).
  2. A bag contains purple and orange marbles. Sam randomly takes out one marble and then returns it to the bag. He does this 18 times, and 12 of those times an orange marble is pulled out. What is P(green)? 2-128b HW eTool (CPM).
  3. Sarah pulls a card from a standard deck and then replaces it. She does this 30times, and 40% of the time it is hearts. What is the probability that she does not get hearts? (Note: For more information on standard card decks, refer to problem 1-68.)2-128c HW eTool(CPM).

2-129.Use yourreasoning about numbers to answer the following questions.

  1. If multiplying bymakes a positive number smaller, then what does dividing bydo to the value of the number? Explain your reasoning.
  2. If multiplying by 1 does not change the value of a number, then what effect does multiplying byhave? Explain your reasoning.
  3. If you find 80% of a number, do you expect the answer to be greater or less than the number? What if you find 120%? Explain your reasoning.

Lesson 2.3.2

  • 2-121. Students should recognize that there is no consistent pattern from which to determine scale on the graph as shown. It is reasonable to predict approximately100 smoothies.
  • 2-122. See answer graphs below:
  • Challenge A:
  • Challenge B:
  • 2-124. See graph below:
  • 2-125. See below:
  • Rescale the vertical axis evenly—the graph is a curve; see answer graph below.
  • Rescale both axes so that zero is at the origin—the end points are on the axes; see answer graph below.
  • 2-126. 132 + 20 ≈ 7 so scaling by any whole number from 7 up to 10 would be convenient.
  • 2-127. See below:
  • –
  • or 1
  • 2-128. See below:
  • 0
  • 60% or
  • 2-129. See below:
  • It makes it larger (in fact, four times larger) because dividing “undoes” multiplication.
  • It also does not change the value of a number because= 1.
  • Less than because 80% is less than 100%. Greater than because 120% is greater than 100%.