Maximizing Area: Gold Rush
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.
- 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.
- 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.
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.
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.