Sector Area Application: The Grazing Goat

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

Big Idea

Students use a variety of tools (graph paper, compasses, string) and strategies to solve the Grazing Goat problem in their groups.

Group Area Assessment

40 minutes

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.    

The Grazing Goat

30 minutes

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.

Homework: The Track Problem

10 minutes

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:

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