# Maximizing Area: Gold Rush

## Mathematical goals

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

• Interpret a situation and represent the variables mathematically.
• Select appropriate mathematical methods to use and communicate their reasoning clearly.
• Explore the effects on a rectangle’s area of systematically varying the dimensions whilst keeping the perimeter constant. Interpret and evaluate the data generated, identifying the optimum case.

## Introduction

• Before the lesson, students attempt the Gold Rush task individually. You then look at their responses and formulate questions for students to think about as they review their work.
• At the start of the lesson, students use the questions posed to think of ways to improve their work. Next, they work collaboratively to produce a better solution than they did individually.
• In a whole-class discussion students compare and evaluate the different methods they used.
• Working in the same small groups, students analyze some sample responses, then, review as a class the methods they have seen. In a follow-up lesson students reflect on their work.

## Materials required

• Each individual student will need a copy of Gold Rush, some plain paper, a mini-whiteboard, pen, and eraser, and a copy of the review questionnaire How Did You Work?
• Each group of students will need a sheet of poster paper and the Sample Responses to Discuss.
• Provide calculators, rulers, and squared paper for students on request. String cut into equal lengths or popsicle sticks may also be helpful in representing the situation.

## Time needed

20 minutes before the lesson, a 120-minute lesson (or two 60-minute lessons), and 10 minutes in a follow-up lesson. Timings are approximate. Exact timings will depend on the needs of your class.

## Mathematical Practices

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

## Mathematical Content Standards

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