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GRED 505 (Topics in mathematics for elementary teachers)
Assignment 1: Partition of integers into summands
Part 1. Partitions with regard to the order of summands.
Brain Teaser. There are stamps of denomination 1 cent, 2 cents, 3 cents, and 4 cents. In
how many ways can Andy make postage of 4 cents out of these four types of stamps if
the order in which the stamps are arranged on an envelope matters? Solve this problem
by making an organized list (that is, answer the question by actually listing all
combinations of the stamps). As an example, figure 1 shows two different ways of
making 4 cents in postage.
Figure 1. 4=1+2+1 and 4=1+1+2
Alternative task 1 (adapted from classroom idea 1B for grades 1-2 of New York State
mathematics core curriculum). Provide students with four two-color counters. Have
students create different combinations of red and yellow counters, record each
combination they find and stop when they believe they found all of them. (As an
example, figure 2 shows two such combinations.)
Figure 2. Two combinations of red and yellow counters.
Instructor Sergei Abramovich
1c
2 c
1c
1c
1c
2 c
