Problem Solving Worksheets With Answer Key - Math Stars Page 30
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39Vol. 7 No. 8
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. [66,660] Each digit appears six times in each of the four places. Therefore the sum of the ones
places is 6(1 + 2 + 3 + 4) or 60. Each subsequent column will total 66 ( 60 plus the regrouped 6 from
the previous column).
2. [76 meters] One plot is 6 by 8 meters i.e. a = 6 meters and b = 8 meters. (These are the only factors
of 48 that fit the diagram.) The perimeter is 6a + 5b or 36 + 40 or 76 meters.
3. [80 inches] The ratio 3 : 5 :: 48 : x will yield the desired dimension. You may wish to note that the
most attractive ratio, 3 by 5, is a pair of consecutive Fibonacci numbers, as are 5 by 8, 8 by 13 and
other often-used ratios. The Golden Rectangle and Golden Mean could also be explored at this time.
4. [$22,598.00] Students can explore the relationship 105% of ?? = $23,727.90 or examine the concept
of 105% as 21 parts (20/20 + 1/20). The dealer makes $23727.90 ÷ 21 or $1,129.90, while the car
costs 20 times that amount or $22,598.00.
5.[55 pieces] 0,0; 0,1, 1,1; 0,2, 1,2, 2,2; 0,3, 1,3, 2,3, 3,3;. . . 0,9,1,9,2,9, 3,9, 4,9, 5,9, 6,9, 7,9, 8,9, 9,9
1 + 2
+
3
+
4
+ . . .
+ 10
6.Answers will vary.
7. [1,073,741,823¢ or $10,737,418.23] A calculator with memory function is especially useful to
solve this problem. Also making a chart will help students see the sum of the 30 addends as a function
of the earlier day's amount i.e.
Day
1
2
3
4
5
6
7
8
9
10
11
12
Gift
.01
.02
.04
.08
.16
.32
.64
1.28
2.56
5.12
10.24 20.48
Total .01
.03
.07
.15
.31
.63
1.27
2.55
etc.
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