Monday's Math Problem via @NCTM:
Batman and Robin each order a pizza. The circumference of Batman's pizza is 20 percent greater than the circumference of Robin's pizza.The area of Batman's pizza is what percentage greater than the area of Robin's pizza?...for about two seconds.
But instead, I gave this:
What We Did
1. Decided that the best question was: Which pizza is a better deal?
2. Misconception: Comparing diameters to determine which pizza is preferable. This leads to believing that two personal pizzas are a better deal than one large. (Note to self: Let them think this as long as you can. It's kinda fun and the truth hits them harder if they're committed to their initial opinion. )
3. Realized that area is the way we measure which one gives us the most pizza.
4. Determine area of each pizza and calculate $/sq".
5. Sidebar: Is $/sq" or sq"/$ a better rate to use? Let them decide, but make them justify.
6. Extension: What are we really paying for? Not the crust. Assuming that the average pizza contains about 1" of crust on the circumference, removing it takes the personal pizza from $.14/sq." to $.28/sq".
7. Synthesis: We brought out the laptops and put our data into Excel. I allowed them to enter the diameter and cost for each pizza then showed them how to use the function and fill features to have the program do the number crunching for them. I'm actually disappointed with myself for not doing this earlier in the year. I often forget how powerful Excel is for teaching math.
8. Conclusion: If you order a personal pizza, eat your crust!
9. Reflection I wasn't prepared to handle the question on rates. I think in terms of $/sq" and assumed that my students would too. I also took an opportunity for student ownership away by drawing the two 7" pizzas inside of the 14" instead of allowing the student who came up with the idea a chance to shine.
I'm taking this one on the road and will swap classes with other teachers in my department to see how their kids handle it.
10. What else would you have done with this lesson?