Problem-solving method
Working backwards, explained for parents
The method for a child who says they have no idea where to start. Here is how to spot one in a problem sum, what undoing a step actually means, and the one line that catches a mistake.
- Used from
- P4
- Taught at
- P4–P6
What this method is
When a question tells you where things ended up and asks where they started, you run the steps in reverse and undo each one. Every operation has an opposite. Going forwards × 3 comes back as ÷ 3, and + 6 comes back as − 6.
It is the method that most reliably rescues a child who has no idea where to start, because the one number they definitely have is the last one.
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.
“at first”
The classic. You are being asked for the beginning and handed the end, which is the shape this method is for.
“he was left with 89”
A final state, stated as a number. That is not the answer, it is where your chain starts.
“in the end, she had”
The same signal in different words. Read to the end of the question before deciding there is nothing to go on.
“How many did she have to begin with”
The question is pointing backwards itself. Reading it aloud is often enough for a child to hear the direction.
“then she gave away half of what was left”
A chain of steps in order, and the order is what you reverse. Write the steps down before undoing any of them.
Watch it work
I think of a number. I multiply it by 3, then add 6, and get 30. What number did I start with?
Write the steps in the order they happened
? → × 3 → + 6 → 30Nothing is being solved yet. Getting the chain onto the page in the right order is the part children skip, and every reversal below depends on it.
Start at the end and undo the last step
30 − 6 = 24The last thing done was add 6, so the first thing undone is add 6. Last in, first out, the same as taking off shoes and socks.
Undo the step before that
24 ÷ 3 = 8Multiply by 3 comes back as divide by 3. Naming which operation is being undone out loud is what stops the two from getting swapped.
Check it forwards
8 × 3 = 24, then 24 + 6 = 30Run the answer through the original steps and land on the number you were given. This costs one line and catches a flipped operation, which is the only mistake this method really makes.
The one it gets confused with
All three deal with something that changed. The difference is the shape of the change, and it is usually visible in the question.
Is it two states, or a chain of steps? Two states get two pictures. A chain gets reversed one step at a time.
Do you actually know the end value? If you do, do not guess. Guessing is for when nothing in the question is pinned down.
Is "what was left" a fraction of something? Then draw it. Bars handle a fraction in the chain better than arrows do.
How can you tell it has clicked?
Ask which number in the question they are most sure about. A child with the method says the last one, without hesitating. It is the fastest check on this page.
Then watch for the forwards check. A child who does it unprompted has understood that reversing is error-prone, and that is the real lesson here.
One thing to try tonight
Do it out loud with something ordinary. We need to leave at 8. Getting there takes 20 minutes, and you need 15 to get ready. When do we start?
Most children can do that in their head long before they will do it on paper. Naming it as the same thing they meet in maths is the whole intervention.
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.