Posted on : 2011-08-10

The word ‘heuristic’ is taken directly from the Greek verb, *heuriskein* which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics.

**Three: Going through the process**

Example:The figure is made of 17 sticks. Move 4 sticks to form 8 squares.
Solution: |

· Pupils can apply the ‘work backwards’ method when given a problem that provides the final result and that requires them to find the initial quantit

There were some chocolates in a basket. Michael and three of his friends took 8 chocolates each. 25 chocolates were given to Shirley. There were then 11 chocolates left in the basket. How many chocolates were there in the basket at first?
Using the ‘work backwards’ method, first find the number of chocolates taken away by Michael and his three friends. 4 × 8 = 32 chocolates Then, find the total number of chocolates taken away from the basket. 32 + 25 = 57 chocolates Number of chocolates in the basket at first =
57 + 11 = 68 chocolates |

Example:
Jacky had $56 more than Jill. When he spent $108, Jill had thrice as much as what he had left. How much did Jacky have at first? Solution: 2 units → $108 - $56 = $52
1 unit → $52 ÷ 2 = $26
$26 + $108 = $134 Jacky had $134 at first. |

**Four: Changing the problem**

· By restating a problem in another way, pupils can view the problem in another perspective.

Example:
Find the sum of 10 + 12 + 14 + … + 146 + 148 + 150.
There are 75 numbers in the sum 2 + 4 + 6 + … + 146 + 148 + 150. There are 4 numbers in the sum 2 + 4 + 6 + 8. 75 – 4 = 71 Hence, there are 71 numbers in the sum 10 + 12 + 14 + … + 146 + 148 + 150.
There are 35 pairs of 160 and a ‘80’. 10 + 12 + 14 + … + 146 + 148 + 150 = 35 × 160 + 80 =5680 |

· When facing a complex problem, pupils can split the problem into smaller parts and start by solving the simpler parts. After doing so, the problem is simplified and solving the problem is much easier.

*Written by Gui Yan Tong*

Check out the series "Use of Heuristics in Problem Solving" by EPH and have more practice on the different types of heuristics |

**Extra!**

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