Read more about the purpose of the MAP *Classroom Challenges*…

## 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.
- Explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant.
- Interpret and evaluate the data generated and identify the optimum case.

- Communicate their reasoning clearly.

### 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 reflect on their individual responses and use the questions posed to think of ways to improve their work. Next, students work collaboratively in small groups to produce, in the form of a poster, a better solution to the
*Gold Rush*task than they did individually. - In a whole-class discussion students compare and evaluate the different methods they used.
- Working in small groups, students analyze sample responses to the
*Gold Rush*task, then, in a whole-class discussion, review the methods they have seen. - Finally, students reflect on their work.

### Materials required

- Each individual student will need the task sheet
*Gold Rush*, some plain paper, a mini-whiteboard, a pen, an eraser, and the review questionnaire*How Did You Work?* - Each small group of students will need a large sheet of paper for making a poster, and copies of the
*Sample Responses to Discuss.* - Provide calculators, rulers and squared paper for students who choose to use them. String cut into equal lengths or popsicle sticks may also be helpful in representing the situation.
- There are some projector resources to support whole-class discussion, and introduce activities.

### Time needed

20 minutes before the lesson, 120-minute lesson (or two 60-minute lessons). Timings given are only 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:

- MP1: Make sense of problems and persevere in solving them
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics

### Mathematical Content

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

- 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.

### Resources

#### Lesson (complete)

- maximizing_area_gold_rush_complete.pdf ( 6351.7K PDF/Acrobat 10 Jul 2012)

#### Projector Resources

- maximizing_area_slides.ppt ( 2579.5K MS PowerPoint 10 Jul 2012)

A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP *Classroom Challenges* for the first time.

We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.

The Beta versions of the MAP Lesson Units may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved. Please send any enquiries about commercial use or derived works to map.info@mathshell.org.

Can you help us by sending samples of students' work on the *Classroom Challenges?*