## The Track Problem Answer Key - Section 3: Homework: The Track Problem

# Sector Area Application: The Grazing Goat

Lesson 5 of 14

## Objective: Students will be able to solve and explain a sector area application problem.

#### Group Area Assessment

*40 min*

I give the Area Group Assessment to assess my students’ understanding of area. Like other group assessments, groups may ask me only one question while working on the assessment, which encourages them to rely on each other to make sense of the work before consulting me.

#### Resources

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#### The Grazing Goat

*30 min*

In The Grazing Goat problem, students interpret and solve a real-world context by applying their understanding of sector area (**MP1**). To solve the Grazing Goat problem, students need to interpret the real-world context and apply their understanding of sector area (**MP1, MP4**). Students may struggle and have difficulty grasping how the tether wraps around the barn changing the radii. To differentiate, I might encourage students to sketch a diagram that represents the situation; if they really struggle, I tell students to draw a scale model and to use their compass to visualize the area in which the goat can graze. I have found that giving students a short piece of string, which they can wrap around the corner of their binder, helps them understand the relationship between the tether and the radius. Students can choose from any of these tools to strategically think through the problem (**MP5**).

After about 20 minutes of work, I ask students to work on justifying their answers individually so I can assess each of their understanding.

#### Resources

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#### Homework: The Track Problem

*10 min*

Before the end of class, I make sure to read the The Track Problem out loud to students to make sure they understand what the problem is asking of them and to ensure my expectations are clear. I tell students they must:

- Show clear calculations for each sub-area
- Explain how he/she found the length of the “straightaway”—words like “perimeter,” “arc length,” and “semi-circle” should appear in the explanation
- Justify why your answer makes sense with the situation—why is it reasonable?

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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"