# Designing a 3D Product in 2D: A Sports Bag

## Mathematical goals

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

- Recognize and use common 2D representations of 3D objects.
- Identify and use the appropriate formula for finding the circumference of a circle.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt the
*Designing a Sports Bag*task individually. You review their work and formulate questions that will help students to improve their solutions. - At the start of the lesson, students respond individually to the questions set. Then in groups, they combine their thinking and work together to produce a joint solution in the form of a poster.
- In the same small groups, students evaluate and comment on sample responses. They identify the strengths and mistakes in these responses and compare them with their own work.
- In a whole-class discussion, students explain and compare the strategies they have seen and used.
- Finally, students reflect on their work and their learning.

## Materials required

- Each student will need a copy of
*Designing a Sports Bag*, some plain paper, a mini-whiteboard, a pen, and an eraser. - Each small group of students will need a new copy of
*Designing a Sports Bag*, some poster paper, a marker, and copies of the*Sample Responses to Discuss*. Provide calculators, rules, and squared paper for students who request them. An optional*Formula Sheet*is available for use as required.

## Time needed

25 minutes before the lesson, a 95-minute lesson (or two 50-minute lessons), and 15 minutes in a follow-up lesson. Timings are approximate. Exact timings 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:*

- 7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
- 7.G: Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.