# Estimating Volume: The Money Munchers

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

- Model a situation.
- Make sensible, realistic assumptions and estimates.
- Use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

## Introduction

In this unit, students choose and use mathematics to model a problem situation:

- Before the lesson, students attempt
*The Money Munchers*task individually. You then review their solutions and create questions for them to answer in order to improve their work. - At the start of the lesson, students work individually, answering your questions about the task.
- Next, students work collaboratively in small groups. Their task is to produce a better solution to
*The Money Munchers*problem than they did individually. Then, in the same small groups, students analyze responses to*The Money Munchers*task written by students in another class. - In a whole-class discussion, students compare and evaluate the solution methods they have seen and used.
- In a follow-up lesson, students review their individual and joint solutions and write about what they have learned.

## Materials required

- Each student will need a copy of the task sheet
*The Money Munchers*and the*How Did You**Work*? questionnaire. - Each small group of students will need a new copy of the task sheet
*The Money Munchers,*a sheet of poster paper, and a copy of the*Sample Responses to Discuss.* - Provide calculators for students who choose to use them.
- There is a projector resource to support whole-class discussions and to help introduce activities.

## Time needed

15 minutes before the lesson, a 1-hour lesson, and 10 minutes in a follow-up lesson. Timings given are approximate and will depend on the needs of your class.

## Lesson Type

## Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*