# Lesson 15

Where Are We Eating?

These materials, when encountered before Algebra 1, Unit 1, Lesson 15 support success in that lesson.

## 15.1: Estimation: Marathon Runner 2 (5 minutes)

### Warm-up

The purpose of an Estimation warm-up is to practice the skill of estimating a reasonable answer based on experience and known information, and also to help students develop a deeper understanding of the meaning of standard units of measure. It gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it (MP3). Asking yourself, “Does this make sense?” is a component of making sense of problems (MP1), and making an estimate or a range of reasonable answers with incomplete information is part of modeling with mathematics (MP4).

### Launch

Display the image for all to see. Ask students to silently think of a number they are sure is too low, a number they are sure is too high, and a number that is about right, and write these down. Then, write a short explanation for the reasoning behind their estimate. Students need to know the length of the marathon (26.2 miles) and that 225 minutes have passed for the runner to make it to mile 20.

### Student Facing

How long will it take the marathon runner to finish the marathon?

1. Record an estimate that is:
too low   about right   too high

### Activity Synthesis

Ask a few students to share their estimate and their reasoning. If a student is reluctant to commit to an estimate, ask for a range of values. Display these for all to see in an ordered list or on a number line. Add the least and greatest estimate to the display by asking, “Is anyone’s estimate less than $$\underline{\hspace{.5in}}$$? Is anyone’s estimate greater than $$\underline{\hspace{.5in}}$$?” If time allows, ask students, “Based on this discussion, does anyone want to revise their estimate?” Then, reveal the actual value and add it to the display (294.75 minutes). Ask students how accurate their estimates were, as a class. Was the actual value inside their range of values? Was it toward the middle? How variable were their estimates? What were the sources of error?

## 15.2: Groups of Runners (15 minutes)

### Activity

Students practice conceptualizing the distribution shapes of situations. In this activity, emphasis should be placed on students’ justification for their matches.

### Student Facing

These distributions represent marathon times for different groups.

1. Which display is most likely to represent the marathon times for people aged 20–30? Explain your reasoning.
2. Which display is most likely to represent the marathon times for every tenth person to cross the finish line? Explain your reasoning.
3. Which display is most likely to represent the marathon times for people aged 40–50? Explain your reasoning.

### Activity Synthesis

Select students to share their solutions and reasoning. Here are sample questions to promote class discussion:

• “Describe the shape of each distribution.” (Display A is a skewed right distribution. Display B is approximately bell-shaped. Display C is approximately uniform.)

## 15.3: Where Are We Eating? (20 minutes)

### Activity

In this activity, students extend their thinking about distribution shapes to using the shape to justify making a decison from a set of repesentations. In previous lessons, students matched distribution shapes to situations. Students practice applying the situations when they choose a representation and are able to eliminate the others. This activity prepares students to compare specific measures of several distribution shapes in a later lesson.

### Student Facing

Restaurant A

Restaurant B

Restaurant C

Restaurant D

Each histogram represents the number of star ratings for a different restaurant. The ratings range from 0–4, with 0 representing a very poor experience and 4 representing an excellent experience. For each question, explain your reasoning.

1. Which restaurant do reviewers like the most?
2. Which restaurant do reviewers like the least?
3. Which restaurant received mostly mixed reviews?
4. Which restaurant would you choose to try?