# Designing 3D Products: Candy Cartons

## Mathematical goals

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

- Select appropriate mathematical methods to use for an unstructured problem.
- Interpret a problem situation, identifying constraints and variables and specify assumptions.
- Work with 2- and 3-dimensional shapes to solve a problem involving capacity and surface area.
- Communicate their reasoning clearly.

## Introduction

This activity will take two lessons. The lessons are structured in the following way:

- Before the first lesson, students tackle the problem individually. You review their work and write questions to help students improve their solutions.
- At the beginning of the first lesson, students respond to your questions. They then work collaboratively in pairs to produce a better solution, using their designs to construct a carton.
- To launch the second lesson there is a whole-class discussion. Then in small groups students evaluate and comment on sample solutions, followed by a whole-class discussion about the work.
- Finally, in a follow-up lesson students review and evaluate their work on the problem.

## Materials required

- Each student will need a mini-whiteboard, a pen, an eraser, a copy of the task sheet,
*Design a Candy Carton*, and a copy of the*Design Review*questionnaire. - Each small group of students will need a large sheet of paper for making a poster, a sheet of light, letter-sized cardboard, scissors, a glue stick, highlighter pens, and a copy of each of the
*Sample Responses to Discuss*. - Provide calculators, rules, protractors, pencils, grid and plain papers, compasses, and cylindrical counters (such as checkers pieces) for students who wish to use them.
- You may also want to bring a couple of cartons to the class.
- There is a projector resource to support whole-class discussions.

## Time needed

20 minutes before the lesson, two one-hour lessons, and 15 minutes in a follow-up lesson. Timings are approximate; exact timings will depend on the needs of your students.

## 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:*