Lesson 10

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.

• Groups of 2
• Display image.

• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Record responses.

• “¿Qué suposiciones hicieron sobre el estacionamiento para hacer su estimación?” // “What assumptions did you make about the parking garage to make your estimate?”
• “¿Qué información les ayudaría a hacer una estimación más precisa?” // “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.

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.

• Groups of 2
• Read the first paragraph of the task statement.
• Solicit some ideas from students: “¿Qué tipos de cosas podemos estimar en esta situación?” // “What kinds of things can we estimate in this situation?”

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

• 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. “¿Cómo podrían hacer esas estimaciones?” // “How might you make those estimates?”

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.

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

• Groups of 3–4
• Provide access to magazines or other sources of images.

• “En grupo, creen una actividad tipo ‘Exploración de estimación’ en la que haya un número grande de objetos o una cantidad grande” // “Work with your group to create an Estimation Exploration activity that involves a large number of objects or a large quantity.”
• “Asegúrense de pensar en las distintas estrategias que podrían usar sus compañeros para hacer una estimación” // “Be sure to consider different strategies that others might use to make an estimate.”
• 11–12 minutes: small-group work time

• 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.

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.

• 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.

• “Dirijan su actividad de estimación. Háganlo por turnos con el grupo que se hicieron” // “Take turns facilitating your estimation activity with the group you’re partnered with.”
• Remind groups to switch roles halfway through the allotted time.

• See lesson synthesis.