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Lesson 4: Area of a Sector
• Calculate the area of a sector. Lesson Narrative
In this lesson, students build on what they have learned over the previous several lessons about the relationships between circles and radian measure in order to calculate the area of a sector. Students explore areas of sectors by analyzing pizza slices for their cost e ciency.
Students model with mathematics when they come up with a way to measure how “good a deal” a slice of pizza is and report the best deals from a data set with the help of technology (MP4).
Required Materials Scienti c calculators
Spreadsheet technology Required Preparation
For the “Pizza Palooza” activity, you will need access to spreadsheet technology. The spreadsheet will need to be pre- lled with Elena’s data from that activity. Acquire devices that can run GeoGebra (recommended) or other spreadsheet technology. It is ideal if each student has their own device. (A GeoGebra Spreadsheet is available under Math Tools.)
Student Learning Goals
• Let’s calculate areas of pizza slices. 4.1 Equal Slices
Warm Up: 5 minutes
This warm-up invites students to reason about areas of circles and sectors of circles in a context where area can be used to think about cost-e ciency. This context will be explored heavily throughout the lesson.
Student Task Statement
At one pizza shop, a personal pizza has a radius of 10 cm and costs $5. Another shop takes a pizza with radius 30 cm, cuts it into 8 slices of equal area, and charges $5 per slice. Which is a better deal? Explain your reasoning.
Student Response
The per slice option is more pizza for the same price. The personal pizza has area
square centimeters, whereas the slice has area square centimeters, which is greater than square centimeters.
Unit 7 Lesson 4: Area of a Sector
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