Page 160 - Learning to Learn

READING EXPERIENCE 6: M ETHODOLOGIES: UNLOCKING PROCESS KNOWLEDGE
160 L EARNING TO LEARN: BECOMING A SELF-GROWER
Step Explanation
2 Identify key issues Enough pizza must be bought for at least one meal.
One small pizza will not be enough.
Chuck does not mind having leftovers.
3 Collect data and
information
Chuck has $25.
The menu lists three sizes: the small for $5, the medium for $8, and the
large for $11.
The small pizza has six slices, and the medium and large pizza each have
eight slices.
The small pizza is 8 inches in diameter, the medium is 12 inches in
diameter, and the large has a 16 inch diameter.
In examining this information, Chuck decided that the number of slices
really does not provide any helpful information. He is interested in the
quantity of pizza, not the number of slices.
4 Identify
assumptions
All pizzas ordered will be cheese only—no toppings.
The goal is to get the most pizza for the least amount of money.
5 Break the problem
apart
One aspect to look at is the comparative sizes of the pizzas. This is one
sub-problem. Then, using cost, Chuck can calculate the amount of pizza
per dollar.
6 Model sub-
problems
Comparison of pizzas:
Small pizza: 8 inch diameter (4 inch radius): Area = πr2= 16π
Medium pizza: 12 inch diameter (6 inch radius): Area = 36π
Large pizza: 16 inch diameter (8 inch radius): Area = 64π
Pizza per dollar:
For the small pizza, Chuck gets 16π ÷ 5 = 3.2π units per dollar.
For the medium pizza, Chuck gets 36π ÷ 8 = 4.5π units per dollar.
For the large pizza, Chuck gets 64π ÷ 11 = 5.8π units per dollar.
7 Integrate solutions Given the models, it looks like one large pizza is the best deal. But let’s
look at some other options.
If Chuck buys two small pizzas at $10, they only get 32π of pizza, vs. 64π
for $1 more. Not a good deal.
If he buys a small and a medium pizza at $13, they get
(16 +36)π = 50π; less than one large pizza and for more money.
It looks like buying a large pizza makes the most sense and Chuck has
enough money as well.
8 Test and validate Is this convincing? It does appear that a large pizza is the way to go.
9 Generalize the
solution
The method of finding a common comparison, in this case units of pizza
(via area) per dollar, can be generalized. Often, when buying items, one
needs to make this kind of comparison. Sometimes, you may be surprised.
Is 5 cans for a $1 better than 19¢ per can? Is an all-day ticket at an
amusement park for $40 better than $2 per ride?
10 Communicate the
solution
Chuck and Evelyn should order a large pizza for $11, and
Chuck will have the leftovers for a tasty breakfast.