Teaching Mathematics via Cooperative Problem Solving
The Locker Problem
Students at an elementary school have decided to try an experiment. When recess is
over, each student will walk into the school one at a time. The first student will open
all the first 100 locker doors. The second student will close all of the locker doors
with even numbers. The third student will change all the locker doors with numbers
that are multiples of three. (Change means closing locker doors that are open and
opening locker doors that are closed). The fourth student will change the position of
all locker doors numbered with multiples of four; the fifth student will change the
position of the lockers that are multiples of five. And so on. After 100 students have
entered the school, which locker doors will be open?
Dr. Kimani — pkimani@fullerton.edu
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Using what you learned from the locker problem can you complete this table?
Number Prime Factorization Odd or Even # of factors Exact # of factors
529
23 x 23
126
2x3x3x7
441
3x3x7x7
169
13 x 13
11, 025
3x3x5x5x7x7
841
29 x 29
Classifying Numbers According to their Prime Factorization
Discussion: What generalizations can you make about prime factorization and the
number of factors?
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
X
X
X X
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Dr. Kimani — pkimani@fullerton.edu
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