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One of my favorite projects that we do all year is this Area of a Sector Real World Activity. I love it because it’s steeped in real world application, works great as a group activity (but can be done individually as well!), and requires students to justify their thinking. Additionally, students get to be creative and explore an open-ended problem.
What is The Area of a Sector?
A sector is a portion of the circle enclosed by two radii and the arc that connects them. Think of it like a slice of pizza or pie! You calculate the area of a sector with the equation A=(θ/360)*πr2.
How Does the Activity Work?
In order to practice finding the area of a sector and apply the knowledge to a real world situation, I give students a blueprint of a house. Then I tell them that they need to install security cameras on the house. There are different sized cameras with different attributes:
- How far the camera can accurately “see” varies (the radius, r)
- The maximum distance it can rotate varies (the angle, θ)
Then students decide with their group mates the best locations on the house to place the security cameras. Students must be able to justify their location choices.
How Can I Extend this Activity?
Take this activity to the next level! Here are some extension ideas. These increase the rigor and difficulty of the project for an honors class or any early finishers.
- Have students pitch their ideas and choose the option that keeps the house safest. Make it a friendly competition with an optional prize!
- Calculate the percent of the yard that is now visible through security cameras.
- Have students create a blueprint of their own house and choose locations for security cameras.
- If students feel that the given cameras do not provide enough security, what kind of camera would they build to make the house more secure? Give the radius and degree angle that they feel is best.
- Have students color the blueprint and hang them up as posters!
The project is great for a Geometry or Pre-Calculus class to get students talking to each other and applying math knowledge to the real world. Click here to buy the resource in my TpT store. Tell me in the comments how you would use this activity and if you use any of the extension ideas! How would you raise the rigor of this activity?
Let’s continue the conversation in the comments or on my social media: @mathymrs.j on IG.
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Happy teaching!
Natasha