# Using Space Efficiently: Packing a Truck

## Mathematical goals

This lesson unit is intended to help students to:

- Reason precisely and defend their conclusions.
- Use mathematics to model a scenario concerning volume.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt the
*Packing It In*task individually. You review their responses and formulate questions that will help them improve their work. - At the start of the lesson, students read your comments and consider ways to improve their work.
- In pairs or threes, students work together to develop a better solution, producing a poster to show their conclusions and their reasoning.
- Then, in the same small groups, students look at some sample student work showing different approaches to the problem. They evaluate the strategies used and seek to improve the arguments given.
- In a whole-class discussion, students compare different solution methods.
- Finally, students reflect individually on their learning.

## Materials required

- Each student will need a copy of
*Packing it In*and*How Did You Work?*and some blank paper to work on. Provide calculators for students who wish to use them. - Each pair of students will need the three
*Sample Responses to Discuss*, a piece of poster paper, a marker and some glue. - Have graph paper and if possible, unifix cubes or small cardboard boxes available.
- There is a projector resource to support whole-class discussions.

## Time needed

## 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:*