MATH 5030 Spring 2009 honors credit extra assignments

Extra assignment 1 due Monday, February 16:

1) Refer to problem 3 on page 249 of the Activity Manual. Consider an extension of problem 3: what if you have 4 lines in the plane, 5 lines in the plane, in general n lines in the plane, in each case, what is the largest number of disjoint regions into which that many lines can divide the plane? Try to find a formula in terms of n, the number of lines in the plane. See if you can explain why that formula is true for all n.

2) Problem 10 a – f on pages 415, 416 of the textbook.

Extra assignment 2 due Friday, April 3:

Problems 3, 4 on pages 492, 493 and problem 19 d on page 576 (do parts a – c too but don’t hand them in).

Extra assignment 3 due Monday, April 27:

(1) Problem 8 on page 584, (2) problem 9 on page 609, and (3) We used methods of “moving chunks,” “putting inside a bigger shape and taking away,” and “putting inside a bigger shape and taking half” to find areas of shapes in terms of areas we already knew how to find. For each of these methods, describe at least one example of similar reasoning students can use with numerical calculations (especially with mental math and in scaffolding the learning of basic multiplication/division or addition/subtraction facts) and discuss how the reasoning is similar to the reasoning we used when finding areas.