Problem-solving method
The assumption method, explained for parents
Pretend they are all chickens. Here is why deliberately assuming something false is a real method for problem sums, the five beats it always follows, and when it beats guessing.
- Used from
- P4
- Taught at
- P4–P6
What this method is
Pretend, on purpose, that everything is one kind of thing. The total that gives you is wrong in a known direction, and the size of that error tells you exactly how many to swap back. One calculation instead of several rows of guessing.
Singapore tuition teaches it as five fixed beats, sometimes called ATEDO: assume, total, excess, difference per swap, then divide. A parent who knows those five can follow any supposition working their child writes.
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.
“8 heads and 22 legs”
Two kinds of thing with two totals. This is the shape the method was built for, and it recurs from Primary 4 upward.
“scored 3 points for each correct answer and lost 1 for each wrong”
A gain and penalty question. Assume every answer was correct, then trade down until the score matches.
“some $2 notes and some $5 notes”
Two denominations and one total value. Assume all of the cheaper kind and work up from the shortfall.
“the last task took 30 minutes longer”
An odd one out. Assume every task took the same time, then account for the extra separately.
“How many of each kind”
The answer is a split between two kinds, and supposition finds it without hunting for it.
Watch it work
A farm has chickens and rabbits. There are 8 heads and 22 legs altogether. How many rabbits are there?
Assume they are all chickens
8 chickens → 8 × 2 = 16 legsThis is knowingly false, which is the part that feels wrong to say out loud. It is allowed precisely because you are going to correct it, and the correction is the method.
Compare with the real total
22 − 16 = 6 legs unaccounted forSix legs have nowhere to go. That number is the shortfall, and everything left to do is working out what it means.
Find what one swap changes
a rabbit for a chicken → 4 − 2 = 2 more legsTurning one chicken into one rabbit adds exactly two legs, every time. This is the step children guess at, and it is worth saying aloud rather than writing.
Divide
6 ÷ 2 = 3 swaps, so there are 3 rabbitsThe shortfall divided by what one swap is worth. Three swaps means three rabbits, and the eight heads give you the five chickens for free.
Check it
5 × 2 + 3 × 4 = 22 legsOne line, and it confirms both numbers at once. Worth the ten seconds on a method whose only real risk is a subtraction the wrong way round.
The one it gets confused with
The first of these solves the very same questions, which is why knowing when to switch matters more here than anywhere else on this page.
Are the numbers small? Then a two-row table is quicker and just as valid. This method earns its keep when guessing would take many rows.
Is it really two kinds of thing being counted? If the question compares amounts rather than counting two types, draw it instead.
How can you tell it has clicked?
Ask what they assumed and why. A child with the method names the assumption in one sentence and knows it is false. A child without one describes the arithmetic they did and cannot say where the first number came from.
Watch for a table appearing. It means guess and check has been reached for instead, and while that may still get the answer, it is the slower road on the questions this method is set for.
One thing to try tonight
Ask what if they were all chickens? and let them tell you what goes wrong.
The answer they give, that there would not be enough legs, is the method. Everything after it is arithmetic, and the hard part is already done.
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.