Pizza Pi-rates! Exploring Circles in the Real World

Introduction (5 minutes):

Pizza Passion: Start by engaging students with a discussion about pizza. What are their favorite toppings? What shapes do they usually see pizzas in?
Circle Review: Briefly review the definitions of a circle and its key parts:
Center: The point in the middle of the circle, equidistant from all points on the edge.
Radius: A line segment from the center to any point on the circle.
Diameter: A line segment that passes through the center and connects two points on the circle.
Chord: A line segment that connects any two points on the circle.
 

Activity 1: Pizza Proportions (15 minutes)

Sharing is Caring: Present an image of a whole pizza. Ask: "If you're sharing this pizza with a friend, how would you cut it to ensure you both get equal amounts?"
Guide them to understand that cutting along the diameter creates two equal halves.
More the Merrier: Show a picture of a pizza cut into more slices (e.g., 8 slices).
Discuss: "What part of the circle helps ensure each slice is the same size?" (radius)
"If you connect the two points where a slice is cut, what part of the circle have you created?" (chord)
Pizza Sizes: Show images of pizzas with different diameters.
Discuss how the diameter relates to the overall size and how it might affect the number of slices.
"If a pizza has a diameter of 12 inches, what is its radius?" (6 inches)
 

Activity 2: Pizza Design Challenge (15 minutes)

Creative Chefs: Divide students into groups. Each group is tasked with designing their own unique pizza.
Circle Constraints: Provide specific criteria related to circle parts:
"The pizza must have a diameter of 14 inches."
"Use pepperoni slices to create chords of different lengths on your pizza."
"The center of the pizza must have a special topping."
Pizza Presentation: Have each group present their pizza design, explaining how they incorporated the circle elements.
 

Activity 3: Real-World Pizza Problems (15 minutes)

Pizza Pricing: Present a scenario: "A small pizza with a 10-inch diameter costs $8. A large pizza with a 14-inch diameter costs $14. Which pizza is a better value?"
Guide students to use the diameter/radius to estimate the area and compare the price per "size" of pizza.
Pizza Box Design: "You're designing a box for a circular pizza. How can you use the diameter of the pizza to determine the dimensions of the box?"
Discuss the need for the box to be slightly larger than the pizza's diameter.
Pizza Delivery Zones: "A pizza place delivers within a 5-mile radius of their store. If your house is 3 miles from the store, can they deliver to you? Why or why not?"
Connect the concept of radius to a real-world delivery zone.
 

Wrap-up (5 minutes):

Review the key parts of a circle and how they were used in the pizza activities.
Encourage students to look for examples of circles and their parts in their everyday lives.
 

Assessment:

Observe student participation and group work.
Collect student pizza designs and explanations.
Assign word problems involving pizza and circle concepts for homework.

differentiation: Provide pre-cut circles and have them label the parts.

extension: Use the PBS Pizza Video linked in the resources tab to extend this geometry lesson beyond the second dimension with the introduction of the Gaussian curvature.

Use the performance task linked in the resources tab to assess student learning outcomes.