Volume 8 Math Stars Worksheet Page 18
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35Vol. 8 No. 5
About these newsletters...
The purpose of the MathStars Newsletters is to challenge students beyond the classroom
setting. Good problems can inspire curiosity about number relationships and geometric
properties. It is hoped that in accepting the challenge of mathematical problem solving,
students, their parents, and their teachers will be led to explore new mathematical hori-
zons.
As with all good problems, the solutions and strategies suggested are merely a sample of
what you and your students may discover. Enjoy!!
Discussion of the problems...
1. [6x] Since the can will hold three balls and the diameter of a ball is 2x, the height of the can must be
at least 6x.
2. [6 feet or 72 inches] Volume = length x width x height or 72 = 3 x 4 x height. Height = 72÷ 12 = 6.
(8 - 8)
8
3. Answers will vary. Here are some : (8 - 8) x 8 + 8 = 8;
8 x 8
= 8;
8 x( 8÷8)
= 8;
(8 - 8)÷8 + 8 = 8.
4. [4, 1] (4 x 3) - 1 = 5
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5.
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6. [13, 25] This is an example of the Pigeonhole Principle. It can easily be modeled with a calendar
and a set of student names. a) Once 12 names have been drawn, if each has a unique birthday month,
the next name guarantees a match. b) Again, if 24 names have been drawn and they are all paired, then
the 25th name will produce a triple.
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