Problem Solving Worksheets With Answer Key - Math Stars Page 15
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39Vol. 7 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...
2
2
1. (256) The first perfect square after 100 is 121, (11
), but the sum of its digits is 2
. Continuing, the
2
first square that fits the criteria is 256, (16
), and the sum of its digits is 13, definitely not a perfect
square.
2. (210; no; 225 > 210) Friday 1 + 3 + 5 + ...+ 29 = 225
Saturday 1 + 2 + 3 + ...+ 20 = 210 This
might be a good place to introduce little Gauss and his technique for summing an arithmetic progres-
sion.
3. (Adam owes Jose $1 and Don owes him) $2 The total amount spent was $20. Each person's
share is therefore $5. Steve spent that amount and owes no one. Jose spent $3 more than his share.
Adam spent only $4 and Don spent only $3, thus they owe Jose $1 and $2, respectively.
4. (187 trips) Hint: two children can row over but one must return to allow an adult to cross.
5. (42) 25 - 1x1 squares, 12 - 2x2 squares, 5 - 3x3 squares.
6. (Answers will vary.)
7. (3, 7, 19) One less cut than the number of pieces required.
8. (8, 4, 2, 1, .5)
9. (53; 43 and 68) (a)Students should follow the clues and eliminate those primes which do not fit.
(b) A guess and check strategy can be employed for this problem.
10. (D (7,6) ) Students should use the definition of a rectangle, and the grid to determine the fourth
vertex. Establishing right angles and/or equal, opposite sides will enable them to solve the problem.
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