Grasp Maths

11+ Prep

Multi-step worded problems: a strategy

Learn a reliable method for breaking a multi-step worded problem into smaller steps, instead of guessing which operation to use.

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Lesson overview

Multi-step reasoning — working out what to calculate, and in what order

The hardest part of a multi-step 11+ problem usually isn't the arithmetic -- it's working out WHAT to calculate first. These questions combine two or more separate ideas (like mean averages, ratio, percentages, or unit conversions) into one worded scenario. The method is always the same: find the totals or starting values you actually know, work out what the question is really asking for, then find the smallest missing piece before working towards the final answer.

Turn the words into known values first

Before calculating anything, list every number the question gives you and what it means.

Don'tStart calculating as soon as you see two numbers in the question
DoWrite down what each number represents before deciding what to do with it

A number described as 'the mean of 4 numbers' behaves completely differently from a number described as 'one of the numbers' -- read carefully.

Work out what the question is actually asking for

Multi-step questions often ask for something that isn't directly given anywhere in the question.

Example'What is the 5th number?' when you're only given a mean and 4 other numbers
ReframeThe 5th number = (total of all 5) minus (total of the first 4)

If the final answer isn't a number you can read straight off the question, work backwards from what you DO know towards it.

Chain the steps: each answer feeds the next calculation

In a genuine multi-step question, your answer to step 1 becomes an input to step 2.

Write down each intermediate answer clearly -- it's very easy to lose track of what a number represents halfway through a multi-step question.

Worked example — mean average, missing value

The mean of 4 numbers is 8. Two of the numbers are 6 and 9. What is the sum of the other two numbers?

KnownMean = 8, count = 4, two of the numbers are 6 and 9
Asked forThe sum of the OTHER two numbers -- not their individual values
  1. The question isn't asking for a value given directly -- it's asking for a sum you have to derive, so work out the total first.
  2. Total of all 4 numbers = mean × count = 8 × 4 = 32.
  3. Total of the two known numbers = 6 + 9 = 15.
  4. The sum of the other two numbers = total of all 4 minus the total of the two known ones = 32 - 15 = 17.

Try it

Work through each question in steps: known values first, then what's being asked, then the calculation.

Question 1

The mean of 5 numbers is 10. Four of the numbers are 8, 9, 11 and 12. What is the 5th number?

Question 2

A recipe for 4 people needs 200g of rice. Which calculation gives the amount needed for 10 people?

Question 3

A recipe for 4 people needs 200g of rice. How many grams are needed for 10 people?

Question 4

A question gives you a percentage discount and asks for the final price after TWO separate discounts are applied one after another. What's the key thing to remember?

Question 5

A coat costs £80. It's reduced by 25%, then a loyalty card takes a further 10% off the SALE price. What is the final price, in pounds?

Common mistakes

Watch for these when working through the lesson.

  • Starting to calculate before working out what each number in the question actually represents.
  • Applying a second percentage change to the ORIGINAL amount instead of the amount after the first change.
  • Losing track of what an intermediate answer represents partway through a multi-step chain.
  • Assuming the final answer is a number given directly in the question, when it actually has to be derived.

Related topics

These ideas fit closely with this lesson.

  • Percentages and ratio reasoning
  • Mean averages
  • Non-verbal reasoning: shape codes and pattern rules

Practice next

Ready for real questions?

This lesson builds the method for multi-step worded problems. Head to 11+ Prep practice for real multi-step reasoning questions with adaptive difficulty and scaffolded hints when you get one wrong.