Lesson 10
Estimation Exploration
Warmup: 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 

\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\)  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\)  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) 
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
Activity Synthesis
 “What assumptions did you make about the parking garage to make your estimate?”
 “What information would help you make a more accurate 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.
Supports accessibility for: SocialEmotional Functioning
Launch
 Groups of 2
 Read the first paragraph of the task statement.
 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:

In a lifetime, approximately:
 How many toothbrushes will she use?
 How many dollars will she spend on toothbrushes?

About how many minutes would she spend brushing her teeth:
 in a year?
 in a lifetime?
 Think of another estimation question you could ask about this situation.
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
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 multidigit 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 warmup). 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
 Provide access to magazines or other sources of images.
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: smallgroup work time
Student Facing
It’s your turn to create an estimation problem.
 Think of situations or look around for images that would make interesting estimation problems. Write down 4–5 ideas or possible topics.

Choose your favorite idea. Then:
 Write an estimation question that would encourage others to use multiplication of multidigit 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.
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
Activity Synthesis
 Encourage students to ask lingering questions about designing their activity.
 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.
Advances: Speaking, Representing
Required Materials
Materials to Gather
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:
 Display your image or present your scenario.
 Ask your classmates: “What is an estimate that’s too high? Too low? About right?”
 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.
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
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?”
Cooldown: Reflection (5 minutes)
CoolDown
Teachers with a valid work email address can click here to register or sign in for free access to CoolDowns.