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Math Problem Solving Techniques

Eight problem solving strategies and practice activities for 9 to 12 year olds.

Math Problem Solving Techniques by David Stephenson
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This book has been created to assist educators faced with the difficult task of presenting, explaining, teaching, and practising problem solving techniques and skills. This book provides:  a) a brief overview of eight problem solving techniques. Each technique is accompanied by a worked example that teachers should talk through with the class to give a full explanation of the sub-skills and thinking processes through which students may proceed. We realize that there are many more problem solving techniques than those presented here, and that problem solving techniques are never used in complete isolation. However, for the purpose of teaching we have broken the techniques into separate usable approaches to problem solving. b) four practice questions with each of the eight techniques. These should be used as teaching exercises, changing the numbers as required to consolidate the technique being taught. c) a non-graded mixture of 100 different problems requiring use of the problem solving techniques. These can be written on the board, photocopied or pasted onto cards. Allow students to work through at their own pace, omitting problems initially if they feel ill equipped to solve them. Students can return to those problems later on as their repertoire of problem solving skills increases. The ability to solve problems at whatever level of complexity provides the solver with an intrinsic sense of self-worth. As educators, we should provide as many opportunities as possible to raise students' self esteem - providing them with these eight techniques to solve problems is a great commencement point.


Ready-Ed Publications; June 2001
64 pages; ISBN 9781863971102
Read online, or download in secure PDF format
Title: Math Problem Solving Techniques
Author: David Stephenson; Rod Jefferson
Strategy 2: Guess and Check
(Using 2 variables)

As the title suggests, this strategy arrives at a verifiable solution by hypothesizing possible answers, checking back to see which fits the problem, and modifying answers from the results of previous checks. In this strategy the teacher’s role is to guide students towards:

a) a probable or likely starting point;
b) working in the right direction with large enough gains to quickly solve the problem.
i.e. The guessing game: I'm thinking of a number between 1 and 1000.
Can you guess it in 10 tries?

The most successful students achieve this by eliminating as many numbers as
possible with each guess, e.g. 500 lower, 250 higher.

An example to work through:

Billy has 56 marbles in his collection. If he had 14 more 'catseyes' type than 'bullets' type, how many of each marble did he have?

Teaching Strategies

Decide what you are trying to find out.

Read the question for clues of where to start, i.e.
a) In this question, the number of catseyes and bullets is ‘given’:
No. catseyes = bullets + 14; No. of bullets = catseyes - 14.
b) There are more catseyes than bullets.

As there are more catseyes than bullets, make the first guess about the number
of catseyes, and make the estimated number higher than half of the marbles:

Half of 56 marbles = 28, therefore catseyes = 30?
catseyes = 30,
bullets = 30 - 14 = 16.

If there were 30 catseyes, the total number of marbles would be 46, 10 less than the actual total.

Halve the difference between the two totals, and add it to the previous guess:
30 catseyes + 5 = 35.
bullets = 35 -14 = 21.

Total marbles equals 56.

Therefore, the second guess is correct. Billy has 35 catseyes and 21 bullets in his