3.3+Sharing+Pizza

29.January.2009**
 * T.C.

Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them. What methods are there for comparing things?
 * Big Idea:**
 * Essential Questions:**

Sharing Pizza 3.3 [[image:pizza.png link="image:  cartoon_pizza.gif align="center""]]
Question:** If the pizzas at a table are shared equally by everyone at the table, will a person sitting at a small table get the same amount of pizza as a person sitting at a lage table? Explain your resoning.
 * A.
 * Answer:** If you are sitting at the big table you will get more than if you are sitting at a small table. Because if you do the math 4/10=.4x100=40 so therefore if you sit at a large table you get 40% of a pizza but at the small table you only get 38% because 3/8=.375x100=37.5=38 so 38% of a pizza if you sit at a small table. Another way to think of it is if you are at the large table you get 1/10 of every pizza so total 4/10 of a pizza and if you are at the small table you will get 1/8 of every pizza so total 3/8 of a pizza. And a denominator that fits 8 and 10 is 80 so you find how many times 10 goes into 80 = 8 and how many times 8 goes into 80 = 10 so then x the numerator whatever it took the denoninator to get to 80. So 4x8=32 so 32/80 at the large table and 3x10=30 so 30/80 at the small table and 32/80 gets you more pizza, so you get more at the large table!

Question:** The ratio of large tables to small tables in the dining room is 8 to 5. There are exactly enough seats for the 240 campers. How many tables are there of each kind?
 * B.
 * Answer:** There are 16 large tables and 10 small tables in the dining room. There are 240 seats which is as many seats as campers 240/240. I figured this out by x the number of large tables by the number of seats and the same for the small tables. Which was 8x10=80, 80 seats at the large tables. And 5x8=40, 40 seats at the small tables, so 80+40=120 so 120 seats but that was only half the amount of campers so then i doubled each amount of tables and got 240 seats!


 * Follow-Up**

Question:** How were ratios important in thinking about the problem?
 * 1.
 * Answer:** They are helpful because in question B it shows you the part to part ratio of how many tables there are. And on the answer I used a part to whole ratio for the number of seats to the number of campers.

Question:** How many pizzas will the cook need in order to put four on each of the large tables and three on each of the small tables?
 * 2.
 * Answer:** The cook will need to cook 94 pizzas.They will need 30 for all the small tables and 64 for the large tables. I found this by x the number of pizzas per table by the number of tables so for the small tables its 3x10=30 so 30 for all the small tables and for the large tables its 4x16=64 so 64 pizzas for all the large tables and all together 94 pizzas because 30+64=94.