Area of whole pie is 3.14 x 7 x 7 or 153.86
Area of non crust is 3.14 x 6 x 6 or 113.04
Area of crust is 153.86 - 113.04 or 40.82
40.82/153.86 is 0.2653 or about 26.5%
Even a simple problem can go in a different direction when the student isn't seeing what the teacher is. It didnt' help I had a student working on cylindrical volume just before seeing the problem. For me, when I read a 1" crust, I thought, "Oh, it is a deep dish Pizza." and pictured a thin 1 inch tall cylinder containing a volume of pizza sauce and ingredients because a pizza is after all a three dimensional object. I saw the problem as pi x r ^2 x 1inch ( 3.14 x7x7x1), but was then stumped at how to figure sauce volume so I could subtract it. What if the problem also ment 1" thick, would that now make my cylinder 2 inches tall? Then I noticed how odd my answer still matched the same measure as the area of a two dimensional circle. How both a cylinder and circle could be the same? (It took awhile to remember they are not and only are not because one is square inches and one is cubed inches but we so often forget how important the measurement unit is.). Off I went wandering in speculation of what the question ment to ask. So I find myself back her days later still thinking about how a stray I went and wondering how often that is happening for my students, but they don't have the time or knowledge to let me know what happened.
Comments
Did anyone use this with their classes? and would anyone use this to show distributive property and or order of operations with this problem?
I want to use this problem now that we've covered area and I'd like to confirm my answer.
I have about 27 percent. The whole pizza is 154, the center is 113, so the crust is 41 which is 27 percent of 154.
(Radius of pizza is 7 and of the part without the crust is 6.)
Right or am I missing something?
A 14" pizza with a 1" crust:
7" radius for the entire pizza
6" radius for the pizza only
Yields:
113 1/7 (or 113.04) square inches for the pizza, depending on which approximation of pi
154 (or 153.86) square inches for the entire pizza, depending on which approximation of pi
Using fraction or decimal pi approximation still yields 73.5% of the entire pizza is pizza. Which gives 26.5% of the entire pizza is crust.
I wanted to make sure I wan't missing something before I used it in class.
Area of whole pie is 3.14 x 7 x 7 or 153.86
Area of non crust is 3.14 x 6 x 6 or 113.04
Area of crust is 153.86 - 113.04 or 40.82
40.82/153.86 is 0.2653 or about 26.5%
Isn't the bottom of the pizza considered crust?
Even a simple problem can go in a different direction when the student isn't seeing what the teacher is. It didnt' help I had a student working on cylindrical volume just before seeing the problem. For me, when I read a 1" crust, I thought, "Oh, it is a deep dish Pizza." and pictured a thin 1 inch tall cylinder containing a volume of pizza sauce and ingredients because a pizza is after all a three dimensional object. I saw the problem as pi x r ^2 x 1inch ( 3.14 x7x7x1), but was then stumped at how to figure sauce volume so I could subtract it. What if the problem also ment 1" thick, would that now make my cylinder 2 inches tall? Then I noticed how odd my answer still matched the same measure as the area of a two dimensional circle. How both a cylinder and circle could be the same? (It took awhile to remember they are not and only are not because one is square inches and one is cubed inches but we so often forget how important the measurement unit is.). Off I went wandering in speculation of what the question ment to ask. So I find myself back her days later still thinking about how a stray I went and wondering how often that is happening for my students, but they don't have the time or knowledge to let me know what happened.