I want to make one of those measuring tools for spaghetti. ItÕs a board with holes of various sizes in it. ThereÕs a hole through which you stick enough spaghetti to feed 2 people, another hole for 3 servings, another for 4. I know that the hole for 2 servings has a diamter of 1 inch. How large should the other holes be?
guess and check
find area for 1 person, then set up and solve equaations for other numbers of people
area ratios: diameter of hole for 3 servings is the square root of 3/2 times the diameter of the hole for 2 people.
see pattern in data for 1, 2, 3, 4 servings, note constant second differences, find quadratic function for prediction
Does pattern hold for 0 servings?
Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!
Last updated 30 November, 2004