# Lesson 10

Estimation Exploration

## Warm-up: Estimation Exploration: No Driver Required (10 minutes)

### Narrative

The purpose of an Estimation Exploration is for students to practice the skill of estimating a reasonable answer based on experience and known information. Students are given some information about a parking garage and pictures of the interior and exterior.

Invite students to share the assumptions they used when they make and share their estimates. For example, students may share how they used the photos to estimate how many floors there were and how many cars could fit on each floor. They may share the assumptions they made about whether each floor held the same amount of cars or how the cars were arranged on the floors based on the picture that they used to estimate that there are 10 floors and each floor holds the same amount of cars.

### Launch

• Groups of 2
• Display image.

### Activity

• “What is an estimate that’s too high? Too low? About right?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Record responses.

### Student Facing

Here are pictures showing the exterior and interior of a parking tower in Wolfstadt, Germany. The parking is automated: each car goes up on a lift and is then placed in a parking space.

How many cars can fit in the tower?

Record an estimate that is:

too low about right too high
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### Activity Synthesis

• “What assumptions did you make about the parking garage to make your estimate?”
• Consider revealing the actual number of cars in the structure, which is 400. The parking structure has 20 stories and 20 cars per story.

## Activity 1: Dental Care (10 minutes)

### Narrative

In this activity, students use given descriptions and their knowledge of multiplication to make some estimates of the cost and time associated with brushing teeth. To complete the estimation, students will need to make some assumptions about what constitutes “a lifetime” and the cost of a single toothbrush. The activity gives students another example before they write their own Estimation Exploration activity.

Engagement: Provide Access by Recruiting Interest. Revisit math community norms to prepare students for working with an uncertain situation. Remind students about expectations for handling disagreements and provide sentence frames to support possible ways to come to a resolution.
Supports accessibility for: Social-Emotional Functioning

### Launch

• Groups of 2
• Solicit some ideas from students: “What kinds of things can we estimate in this situation?”

### Activity

• 4–5 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for the different assumptions that students make to answer the questions.

### Student Facing

Jada brushes for 2 minutes, twice a day. She changes her toothbrush every 3 months.​​​​​​

Based on this information, make some estimates and show your reasoning:

1. How many toothbrushes will she use?
2. How many dollars will she spend on toothbrushes?
2. About how many minutes would she spend brushing her teeth:

1. in a year?

### Activity Synthesis

• Select students who made different assumptions about cost and the length of a lifetime to share their responses and reasoning. Record their estimates.
• If time permits, invite students to share the new estimation questions they thought of for this situation. “How might you make those estimates?”

## Activity 2: Get Your Classmates to Estimate (15 minutes)

### Narrative

In this activity, students create an Estimation Exploration activity that focuses on multi-digit multiplication. Students may choose to present a situation (as in the toothbrush example), something observed in the classroom (such as a large shelf filled with books), or an image (as in the warm-up). They need to anticipate the reasoning strategies others might use to make an estimate.

### Required Preparation

• Gather two magazines or other sources of images for each group of 3–4 students.

### Launch

• Groups of 3–4

### Activity

• “Work with your group to create an Estimation Exploration activity that involves a large number of objects or a large quantity.”
• “Be sure to consider different strategies that others might use to make an estimate.”
• 11–12 minutes: small-group work time

### Student Facing

It’s your turn to create an estimation problem.

1. Think of situations or look around for images that would make interesting estimation problems. Write down 4–5 ideas or possible topics.
2. Choose your favorite idea. Then:

• Write an estimation question that would encourage others to use multiplication of multi-digit numbers to answer.
• Record an estimate that is:

too low about right too high
$$\phantom{\hspace{1.9cm} \\ \hspace{1.9cm}}$$ $$\phantom{\hspace{1.9cm} \\ \hspace{1.9cm}}$$ $$\phantom{\hspace{1.9cm} \\ \hspace{1.9cm}}$$

Be prepared to explain your reasoning.

### Activity Synthesis

• Clear up any confusion and allow them a few minutes to revise their design, if needed.

## Activity 3: Facilitate Your “Estimation Exploration” Activity (10 minutes)

### Narrative

In this activity, students facilitate the Estimation Exploration activity they created for another group in the class. If time allows, encourage students to run the activity for multiple groups.

MLR8 Discussion Supports. Synthesis: During group presentations, invite the student(s) who are not speaking to follow along and point to the corresponding parts of the display.

### Launch

• Combine every two groups of 3–4.
• Give each group a piece of poster paper to record their written scenario (if they have one) and to record responses.

### Activity

• “Take turns facilitating your estimation activity with the group you’re partnered with.”
• Remind groups to switch roles halfway through the allotted time.

### Student Facing

Follow these steps to facilitate your Estimation Exploration activity for another group:

• Give them 1 minute of quiet think time.
• Give them 1–2 minutes to discuss together.
• Invite them to share their estimates and how they made them. Record their ideas.
• If you know the actual number or quantity, consider revealing it.

### Activity Synthesis

• See lesson synthesis.

## Lesson Synthesis

### Lesson Synthesis

Invite students to reflect on their process. Discuss questions such as:

“How was the process of creating an Estimation Exploration activity different from answering one?” (Creating the activity is more involved. It requires researching, thinking of possible ways to estimate, actually making estimates, and maybe revising the question. Doing the activity only involves finding a way to estimate and explaining it.)

“What did you learn as you facilitated your Estimation Exploration?” (The estimates that others find could be close or far from our estimates or the actual number. Others might use other strategies that we did not think of or make assumptions that are very different than ours.)

“If you had a chance to revise your activity, would you change anything? What would you change?”