Heuristics are general rules of thumb of what students can do to tacke a problem when the solution to the problem is not obvious. Below are the 4 main types of heuristics. A sample question for each sub-type is given as a general guide.
1) To give a representation e.g. drawing a diagram/model, make a list, make a table, use equations Draw a diagram Q1 Some flower pots are placed along a street at equal distances. The distance between the 1st and the 4th flower pot is 18 m. The distance between the 1st and the last flower pot is 54 m. How many flower pots are there altogether?
Draw a model Q1 Mary's age is 1/3 of John's age. Sean's age is thrice that of John's. If Sean is 32 years older than Mary, how old is John?
Make a list Q1 Two dice are thrown. How many combinations will result in the sum of their faces being even?
Q2 A teacher assigns Taylor, Amy and Vanessa each duty to clean the classroom every day. These duties are cleaning the table, mopping the floor and emptying the waste paper basket. In how many different ways can she assign the duties to the three students?
Make a table Q1 Mr Chen has a square plot of land for planting apples and a smaller plot for planting carrots. The total area of both plots of land is 58m2. What is the perimeter of each plot of land?
Use equations Q1 A steel cuboid measuring 35 cm by 7 cm by 7 cm is melted and cast into 5 identical cubes. What is the length of the side of each cube?
2) To make a calculated guess e.g. guess and check, look for patterns, make suppositions/assumptions Guess and Check/ Make suppositions/assumptions Q1 Sammy has 30 pieces of 5-cent and 10-cent coins. The total value of the coins is $2.40. Find the number of 5-cent coins that Sammy has.
Look for patterns Q1 Jane saved $1 in the 1st week and $4 in the 2nd week. Each week, she saved $3 more than the week before. a) How much money did she save in the 5th week? b) In which week did she save $22?
3) To go through the process e.g. act it out, work backwards, before-after Act it out Q1 Arrange 9 coins to form a triangle such that there are 4 coins on each side.
Work backwards Q1 There were some marbles in Box A and B. 25 marbles were transferred from Box A to Box B. 40 marbles were then transferred from Box B to Box A. In the end, there were 150 marbles in Box A, which was twice the number of marbles in Box B.
Before/After Q1 There were 352 members in a social club. 75% of them were female and the rest were male. Later in the year, some female members resigned and the number of female members was 3/7 that of the total number of members in the club. How many female members resigned?
Q2 Christina is 4 years old and her mother is 36 years old. In how many years' time will Christina's mother be thrice as old as her?
4) To change the problem e.g. restate the problem, simplify the problem, solve part of the problem Restate the problem - to express the given information in another way such that the solution to the problem is more direct. Letters are used as symbols to represent unknown values or items.
Q1 A dictionary and a magazine cost $30. The same dictionary and 3 such magazines cost $48. How much money did each magazine cost?
Simplify the problem Q1 If 3 chefs can peel 3 potatoes in 3 minutes, how many potatoes can 30 chefs peel in half an hour?
Solve part of the problem Q1 Mr Ali made a long distance call to India that cost $8.49. The call cost $4.35 for the first 3 minutes and 46 cents for each additional minute. How much time did he spend on the phone?