Even when writing essays, humor is frequently used as an attention grabber to engage readers and to put them in a positive mindset for reading the rest of the essay. This idea also applies to engaging students in the math classroom. The pictures featured in this blog includes many different possible math applications.
One such problem is using different shaped and sized pizzas to determine surface area and perimeter, and to improve comparison and mathematical reasoning skills. A common math problem requires the students to compare the size and price of a circular pizza to the size and price of a square and/or rectangular pizza. This will have the students calculate the surface area of each pizza and compare them to see which one is larger. Next, the students will have to compare the prices of each pizza to see which pizza is a better deal. Additionally, you can have the students discover pi by having them compare the circumference and surface area of small, medium, and large pizzas. A couple questions that you can ask the students are:
- What is the surface area of each pizza?
- Which pizza is the better deal?
- What is the circumference of a circular pizza with an area of ____ square inches?
- If the crust is 1 inch wide, what is the surface area of the pizza excluding the crust?
- If the pizza has an average of 4 pieces of pepperoni per square inch, how many pieces of pepperoni are on each of the pizzas?
- What is the ratio of circumference to surface area of the circular pizzas? Why is that number familiar?
- To have the students show examples of their reasoning skills, you can ask them to explain how they got their answer for any of the problems just listed.
To further engage the students, you can actually order the pizza and have the students perform their calculations on actual pizzas and then let them eat the pizzas.
There are many common core state standards that you could teach through a pizza lesson, but the following standard is the one that fits the activity described above.
CCSS.MATH.CONTENT.7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
I like your post and how this lesson offers many different things you can teach with circles.
I think that another lesson that could be taught is finding arc lengths as well as area of sectors. So students could maybe see which slice of pizza is more cost efficient by finding the area of the sector.
CCSS.MATH.CONTENT.HSG.C.B.5
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.