Volume 8 Math Stars Worksheet Page 11
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35Vol. 8 No. 3
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. (36˚) The angles are complimentary, therefore their sum is 90˚. A proportion ( 2
=
x ) or
linear equation (2x + 3x = 90) will yield the desired results.
5
90
2. (1 and 23) Students may wish to explore solution if the conditions are changed. i.e. Which two
integers . . . or which two numbers. . ..
3. (13.76 square units) The area of the square is 64 square units. The area of the circle is 50.24
square units.
4. (1) The largest possible sum for 7 + B has a one in the ten's place.
n
5. (a) 28; b) 1.5 x 2
+ 4, where n is the number of the term; c) Bode's Pattern describes the
relative distances of the planets from the Sun in our solar system.) This is a most challenging
problem. The actual numbers in Bode's Pattern approximate the relative distances.
6. (P(6) = 12/64) There are 64 possible sums, many of which are repeats. The sum six occurs 12
times, therefore, P(6) = 12/64.
7. ( a) 183; 9 and 8 in the ten's place 7 and 6 in the one's place, actual numbers can vary; b) -88;
10 - 98) This problem can be explored with varying conditions i.e. one or more repeats allowed, only
positive integer differences, one decimal point allowed, etc.
8. ( 57, 105, 193) Related to the Fibonacci sequence, this problem affords students some similar
explorations.
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