# 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.

## 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
- MP7: Look for and make use of structure
- 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.