## The Track Problem Answer Key - Section 1: Homework Review: The Track Problem

# Extreme Couponing: Pizza Edition

Lesson 7 of 14

## Objective: Students will be able to use proportionality to solve an area problem.

## Big Idea: In Extreme Couponing, students use a variety of tools to convince each other of which coupon offers the customer a better deal.

*50 minutes*

Students review the Track Problem by discussing in their small groups. Since students sometimes interpret the straightaway or width of the track differently or incorrectly, it is important that the group agrees on a problem solving approach and answer. I debrief the problem as a whole class by having a student volunteer present his/her thinking, which also gives me the chance to address the idea of attending to precision when considering the number of digits of pi students used when carrying out their work (**MP3**). After this discussion, I have at least two students read their explanations out loud and give everyone an additional minute or two to make modifications or additions to their own written explanations.

#### Resources

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Extreme Couponing: Pizza Edition forces students to grapple with a rather challenging task: determining whether doubling the sector angle or radius of a pizza slice provides a better deal. The coupon image engages students, posing them with a question they want to answer. In the past, some of the best solutions involve students using a compass and straightedge and/or tracing paper to illustrate their ideas (**MP5**).

We debrief the task by having at least a couple of groups share out their solutions so we can critique each other’s reasoning and make connections (**MP3**).

*NOTE: I found the original coupon image and problem on Dan Meyer’s blog.*

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Sectors of Circles
- LESSON 2: Making Sense of Area Formulas for Triangles, Parallelograms, Trapezoids, and Kites
- LESSON 3: Making Sense of Area Formulas for Regular Polygons and Circles
- LESSON 4: Strategies for Decomposing 2-D Figures
- LESSON 5: Sector Area Application: The Grazing Goat
- LESSON 6: Surface Area and Area Differentiation
- LESSON 7: Extreme Couponing: Pizza Edition
- LESSON 8: Area "Quest"
- LESSON 9: Introduction to Volume: Origami Boxes
- LESSON 10: Origami Boxes Gallery Walk
- LESSON 11: Volume Formulas, Cavalieri's Principle, and 2-D Cross-Sections
- LESSON 12: Real World Volume Context Problems
- LESSON 13: Ratios of Similarity and 3D Solids Generated by Revolving 2D Figures
- LESSON 14: Volume "Quest"