Super clever math

First, it snowed. Then it rained and froze again and such, so there was kind of icy snow. Then it snowed about 3". Then I went sledding. The first few runs were great -- really fast, and smooth, and all -- but then the snow got "sledded off" so there was just this icy snow stuff. That was perfectly fine for sledding, so I continued. When I looked at my tray afterwards, though, there are all these deep lines in it from the sharp edges I sledded over. Oops! Last year there was so much snow that this was never an issue.

I made the quiz that the regular math students took today, and I made a worksheet that the advanced math students are doing for homework tonight. I was really proud of that worksheet. If they can exert enough effort and brain power to do it, they will learn something without having to explicitly have it taught to them, just like the Exeter math curriculcum. It goes like this:

(5) 6 people are sharing 9 pizzas. (Don’t worry, they’re mini pizzas.)

(a) If each pizza is cut into four slices and everyone eats the same amount, how many slices does each person eat? (6) (slices/person)
(b) If each pizza costs $5 and everyone pays an equal amount, how much does each person pay? ($7.50) (dollars/person)
(c) If each pizza costs $5 and is cut into 4 slices, how much is it per slice? $1.25 (dollars/slice)
(d) Multiply your answers to (a) and (c). Why is this the same as your answer for (b)? (6 x $1.25 = $7.50)
(e) If you didn’t already, add units to your answers. For example, the units of (a) are slices/person.
(f) Redo (d), this time including the units when you multiply. (6 slices/person x 1.25 dollars/slice = $7.50 dollars/person

The answers to each problem are in the parantheses, but of course the students don't have that on their worksheets. The idea is that if they can get through (d), they will make a synapse connection. If they can do and understand (f), they will figure out dimensional analysis (the thing you use to convert meters/sec to miles/hr) before I teach it to them tomorrow. So tonight I have to figure out exactly what I am going to do in class tomorrow. Sounds like fun!