Problem-solving method
Guess and check, explained for parents
It is not what a child does when they have given up. Here is why the wrong rows earn marks in a problem sum, what a proper table looks like, and when to trade it for something faster.
- Used from
- P3
- Taught at
- P3–P6
What this method is
Try a sensible value, check it against the question, and use how wrong you were to choose the next try. Your child meets it from Primary 3, usually as the first heuristic they are taught by name.
The name does it no favours. This is a search with a record, not flailing. Each row narrows the range, and a marker gives credit for the table itself, so three tidy rows with two "wrong" answers is the method working exactly as intended.
When to reach for it
These are the words in a question that point at this method. You do not need to be able to solve it to spot them.
“altogether there are 8 heads and 22 legs”
Two totals describing two kinds of thing. This is the classic shape, and it is worth recognising on sight.
“a box of 8 pencils costs $6.40”
Two item types with one combined constraint, which is exactly what a guess can be tested against.
“How many of each”
You need two numbers rather than one, and they trade off against each other. Fixing one fixes the other.
“the numbers are consecutive”
A tight range to search, so the table converges in two or three rows rather than wandering.
Watch it work
A farm has chickens and rabbits. There are 8 heads and 22 legs altogether. How many rabbits are there?
| Chickens | Rabbits | Legs | Check |
|---|---|---|---|
| 4 | 4 | 24 | too many |
| 5 | 3 | 22 | correct |
Start with a sensible guess
4 chickens, 4 rabbits → 4 × 2 + 4 × 4 = 24 legsHalf and half is nearly always a good opening. It does not need to be close, it needs to be written down where the next guess can learn from it.
Read the direction of the error
24 legs against the 22 wanted → too manyToo many legs means too many rabbits, because rabbits are the four-legged ones. That sentence is the entire method, and it is the part children skip.
Adjust and check again
5 chickens, 3 rabbits → 5 × 2 + 3 × 4 = 22 legsSwap one rabbit for one chicken and test again. Two rows is enough here because the numbers are small, and a marker wants the rows your child actually used.
Write the answer under the table
there are 3 rabbitsAs a sentence, below the table rather than inside it. The table is the working, and the sentence is the answer, and they are marked as two different things.
The one it gets confused with
Two of these look like guess and check on the page. The difference is what makes you stop writing rows.
Are the numbers big? Supposition gets there in one calculation instead of several rows, and it is the faster method once a child trusts it.
Are you hunting for the one that fits, or counting every possibility? This stops when it finds. A list stops when it is complete.
Does the question hand you the final result? Then undo the steps, because there is nothing left to guess at.
How can you tell it has clicked?
Look at whether the wrong rows survived. A child who rubs out each failed attempt has understood the guessing and missed the checking, and they lose the marks that were sitting in the rows they erased.
The other tell is the Check column. Too many and too few, written as words, mean your child is reading the direction of the error rather than starting fresh each time.
One thing to try tonight
If they are stuck and the numbers are small, give them permission to write a wrong answer down. That is usually the unlock.
The first row is meant to be wrong. Its job is to say which way to move. A child who will not write anything until it is right cannot start this method at all.
Where your child will meet it
Want the bigger picture on how these methods fit together? Maths heuristics, explained for parents
See which methods your child reaches for
StudyLah names the method in every worked solution, so you can see whether the problem was the method or the arithmetic.