Volume 8 Math Stars Worksheet Page 14
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35Vol. 8 No. 4
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
horizons.
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. (a) (3, 4, 5), (5, 12, 13), (8, 15, 17); b) (8, 15, 17), (12, 35, 37), (48, 55, 73) and many more. . .]
2. (2/3) Since one-half is twice one-fourth, double one-third to arrive at two-thirds, or solve the pro-
portion: 1/4 : 1/3 or 1/2 : x.
3. (These each have 11 factors: 96, 90, 72, 60) After examining lists of factors, deficient, abundant,
perfect and amicable numbers could be explored.
4. ( a) triangle, 0; quadrilateral, 2; pentagon, 5; hexagon, 9; heptagon, 14; octagon, 20; nanogon,
27; decagon, 35 b) 209 c) If n is the number of sides then there will be n(n - 3) diagonals.)
2
5.( 7/2, 9/2, 11/2) The numerators are the odd numbers while the denominators are all two.
6. (14.28 units) The perimeter of the arc is one-fourth the circumference of a circle with radius four; to
that length you must add two radii for a total 6.28 + 8 = 14.28.
7. (There are two ways he could have scored: three 3-pointers, one 2-pointer and one 1-pointer
or, two 3-pointers, and three 2-pointers.)
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