Monday, May 11, 2015

Pizza Investigation - Large or Small?

A practice investigation to help us prepare for our final unit test, was the pizza investigation. When doing this activity, we had to define which pizza was a better deal and why. Some of the calculations we did was for the unit price and the area of the pizza's.

Down below you can see the full document. Or, you can click the link to access the google document.


Pizza… Which one is a better deal?
Topics to be covered in this investigation:
Area and Circumference of circles, unit price (unit rate), percentage increase, proportional thinking, literal equations  (d=c/pi), volume and surface area.


Part I:
Your Task: Compare the two pizzas below and determine which one is a better deal.  
On the pizza menu, you have a choice between these two pizzas:
Large: Small:
12 inch pizza for $10.99 9 inch pizza for $7.99


Values:
Large pizza: Area: 113.04
Unit price: $0.973
Small pizza: Area: 63.59
Unit price: $0.13
Explanations:
The large pizza is a better deal because the unit price is lower. Therefore you can get more pizza per square inch for a cheaper price.


Extension Questions
  • How much should the small pizza cost if the two pizzas are supposed to be equal in value?  
$7.78
  • What is the percentage difference between the original price of $7.99 and the new price?
2.63%
  • Explain why this new price would make the pizzas ‘proportional’ in price.
Since their unit prices are the same, none of the pizza’s are over-priced. The two pizza’s now have the same value per square inch.


Part II:
A large pizza has a circumference of about 66.9 inches and costs $13.85. A small pizza has a circumference of about 50.2 inches and costs $9.50. (Hint: what does it mean if a pizza is “66.9 inches” ?)

  • How much is does each pizza cost per square inch?
Large pizza: Area: 356.15
Unit price: $0.038
Small pizza: Area: 200.96
Unit price: $0.047
  • Compare the two pizzas to find out which one is a better deal or if they are proportional in price.
The large pizza is a better deal. This is because the unit price is lower. Because of this, you can get more pizza per square inch.


Part III:
Research and answer the guiding questions below for Volume and Surface Area.

Volume is the the measurement of the space inside an object. We use this to determine how much something can hold or how big it is.
Surface area is the measurement of all the sides of a 3-dimensional figure. We use this to determine how large something is.
  • What are some everyday applications or examples where we might use volume?
We could use the volume of an object to know if it fits in our locker. For example, if I want to fit a big bag in my locker, I could use the volume.
  • What are some everyday applications or examples where we might use surface area?
Architects could use the surface area for blueprints and such when building.


Extra Problem:
A 12 inch pizza comes in a square box that is 13 inches across, and 2 inches deep.  
442 inch.
338 inch2
The makers of this pizza want to save money by using less cardboard in the box, so they make a round box with a diameter of 13 and a depth of 2 inches.
  • Do you think the pizza will fit in this new box?  Why?
Yes, because the diameter of the pizza is 12, so it would fit in a pizza box with a diameter of 13. If the pizza were in the box, it would still have 1 inch to fill up.
  • How much less cardboard will they need to make the new box?  (what percent of the original box is this?)
78.5%
  • What is the volume of the new box?
265.33%

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