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Math Problem Solving Techniques
Eight problem solving strategies and practice activities for 9 to 12 year olds.
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(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
collection.
