6 mistakes learners make with multi-step problems, each one named and explained.
Say what the question asked for, then check your answer is that thing.
The answer is the age or amount at the later time rather than now.
The equation is built around the future situation, so the future numbers are the ones in front of you.
Question. In 5 years their ages total 31. How old is Sara now?
A common answer. 19, her age in five years
The answer. 14
Why. The question asks for now, so the five years have to come back off.
Write now and later as two separate columns. Answer from the column the question names.
The calculation runs on past the answer, giving a value for more than was asked.
Once a repeating step is established it is easy to apply it one extra time.
Question. 24 pencils at 8 per pack, £1.20 a pack
A common answer. £4.80, which is four packs
The answer. £3.60
Why. 24 divided by 8 is 3, so three packs.
Check the intermediate number against the question. Three packs is 24, which is what was needed.
One fraction, one person or one deduction is handled and the other is never applied.
The first step is the one the question names first, and completing it feels like progress enough.
Question. 24 chocolates, Maya eats a third and her brother a quarter, how many are left
A common answer. 16, with only Maya's share taken off
The answer. 10
Why. Both shares have to come off: 8 and 6, leaving 10.
Underline every person or quantity in the question and tick each one off as you use it.
The answer is correct but belongs to the person the question did not ask about.
Both values come out of the same working and both are correct answers to something.
Question. Sara is twice her brother's age, and in 5 years their ages total 31. How old is Sara?
A common answer. 7, her brother's age
The answer. 14
Why. Sara is the older one, so hers is the doubled figure.
Circle the name in the question before you start, and check it against your answer at the end.
An intermediate value is given as the final answer.
The intermediate value is a real result and arriving at it feels like arriving.
Question. 8 pencils cost £1.20, how much for 24
A common answer. £2.40, the cost of 16
The answer. £3.60
Why. 24 pencils is three packs, not two.
Reread the question after you get a number. It says what the answer has to be.
The arithmetic is done correctly on a quantity the question did not ask you to use, such as the change instead of the amount spent.
Every number in a word problem looks equally usable, and the one that is mentioned last is often the one still in mind.
Question. Pencils cost 45p, paid with £5, change £1.40. How many pencils?
A common answer. 1.40 / 0.45 = 3
The answer. 3.60 / 0.45 = 8
Why. The change is what came back, not what was spent.
Write down what each number in the question is before using any of them.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.