Math heuristics, explained for parents

A scary word for a simple idea

"Heuristics" sounds like something you need a degree to understand. It is not. A heuristic is just a problem-solving strategy, a way in when the answer is not obvious. Your child is taught a set of them in school. You probably use several yourself without ever naming them. This guide gives you the names and shows a few in action, so you can spot which one a problem needs and nudge your child toward it.

Why they matter for the PSLE

PSLE problem sums are rarely a straight calculation. They are puzzles where the first challenge is working out how to even start. A child who only knows formulas freezes. A child with a toolbox of strategies always has somewhere to begin. Heuristics are that toolbox, and the real skill is not memorising all of them. It is picking the right tool for the problem in front of you.

The strategies your child is taught

MOE's maths framework groups the heuristics into four families. You do not need to drill these. You just need to recognise them.

To give a representation (make the problem visible): draw a diagram or model, or make a systematic list.

To make a calculated guess: guess and check, look for a pattern, or make a supposition (assume a value and see where it leads).

To go through the process: act it out, work backwards, or use the before-and-after concept.

To change the problem: restate it in your own words, simplify it, or solve part of it first.

A few in action

The names make more sense once you see them work. Here are three of the most useful, with real numbers.

Draw a model. A pole is painted so that one third is red and the rest is white. The white part is 4 metres longer than the red part. How long is the pole? Draw the pole as three equal sections. One is red, two are white. The difference between white and red is one section, and that difference is 4 metres. So one section is 4 metres, and the whole pole is three sections: 12 metres. The drawing does the heavy lifting, the maths becomes obvious.

Guess and check. A farm has chickens and rabbits. There are 8 heads and 22 legs. How many rabbits? Start with a sensible guess: suppose all 8 are chickens. That is 16 legs, but we need 22, so we are 6 short. Swapping a chicken for a rabbit adds 2 legs. Six extra legs means three swaps, so 3 rabbits and 5 chickens. Check: 5 chickens (10 legs) plus 3 rabbits (12 legs) is 22. Correct.

Work backwards. I think of a number, multiply it by 3, then add 6, and get 30. What was the number? Run the steps in reverse: 30 minus 6 is 24, then 24 divided by 3 is 8. Start from the end, undo each step, and the answer falls out.

The frame underneath them all: Polya's four steps

For any problem, it helps to teach your child a simple rhythm: understand the problem, make a plan, carry it out, then check back. Most rushed mistakes come from jumping straight to step three without a plan.

The skill that actually matters

Here is what most practice misses. The point is not to be good at one heuristic. It is to choose the right one. A common trap is a child who reaches for the bar model on every single problem, including the ones that really call for guess and check or working backwards. They get stuck, not because they cannot draw a model, but because a model was the wrong tool for that question. So when you practise together, the most useful question is not "can you do a bar model?" It is "which strategy fits this problem, and why?"

How to build it at home

You do not need worksheets for this. Build it into ordinary moments. Estimating the grocery total is guess and check. Working out what time to leave to arrive on time is working backwards. Splitting a pizza fairly is fractions and diagrams. When your child does homework, resist solving it, and ask instead which strategy they want to try, then let them talk through why. Over time the strategies stop being a list to memorise and become habits of thinking.

When that clicks, "I don't know where to start" turns into "let me try drawing it first." That shift is the whole game.

If you want your child to see which heuristic each problem uses, the worked solutions in StudyLah name the strategy, not just the answer.