Reasoning and 11 Plus

Common mistakes in multi-step problems

6 mistakes learners make with multi-step problems, each one named and explained.

All common mistakes

Say what the question asked for, then check your answer is that thing.

A future value given where the present was asked for

What it looks like

The answer is the age or amount at the later time rather than now.

Why it happens

The equation is built around the future situation, so the future numbers are the ones in front of you.

A worked example

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.

Put the two side by side

In five years: 19.
Now: 14.

Write now and later as two separate columns. Answer from the column the question names.

One step too many taken

What it looks like

The calculation runs on past the answer, giving a value for more than was asked.

Why it happens

Once a repeating step is established it is easy to apply it one extra time.

A worked example

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.

Put the two side by side

Four packs: 32 pencils.
Three packs: 24 pencils.

Check the intermediate number against the question. Three packs is 24, which is what was needed.

Only one of two steps carried out

What it looks like

One fraction, one person or one deduction is handled and the other is never applied.

Why it happens

The first step is the one the question names first, and completing it feels like progress enough.

A worked example

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.

Put the two side by side

One share removed: 16 left.
Both removed: 10 left.

Underline every person or quantity in the question and tick each one off as you use it.

The other person's value given

What it looks like

The answer is correct but belongs to the person the question did not ask about.

Why it happens

Both values come out of the same working and both are correct answers to something.

A worked example

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.

Put the two side by side

Brother: 7.
Sara: 14.

Circle the name in the question before you start, and check it against your answer at the end.

The problem stopped one step short

What it looks like

An intermediate value is given as the final answer.

Why it happens

The intermediate value is a real result and arriving at it feels like arriving.

A worked example

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.

Put the two side by side

Two packs: £2.40.
Three packs: £3.60.

Reread the question after you get a number. It says what the answer has to be.

The wrong number from the question put into the calculation

What it looks like

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.

Why it happens

Every number in a word problem looks equally usable, and the one that is mentioned last is often the one still in mind.

A worked example

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.

Put the two side by side

£1.40 is the change.
£3.60 is what the pencils cost.

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.

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