11+ Maths Word Problems: A Step-by-Step Approach

11+ Maths word problems require not only strong mathematical ability but also careful reading and interpretation. These questions assess a child's capacity to translate real-world scenarios into mathematical equations and then solve them accurately. Success in this area is a significant component of achieving a good score in the 11+ exams.

This guide outlines a structured approach to tackling 11+ Maths word problems, breaking down complex tasks into manageable steps. By consistently applying these methods, children can improve their problem-solving skills and confidence.

Maths: word problems 11+ at a glance

Step 1: Understand the Question Fully

Before attempting any calculations, children should read the entire question carefully, at least twice. Encourage them to highlight or underline key information, such as numbers, keywords (e.g., 'total', 'difference', 'per', 'ratio'), and the specific question being asked. Identifying what information is given and what needs to be found is the crucial first step.

For example, if a question mentions 'twice as many' or 'three-quarters of', ensure these relationships are clearly understood before proceeding. A common error is to begin calculations based on a partial or incorrect understanding of the problem scenario.

Step 2: Plan Your Approach

Once the question is understood, the next step is to formulate a plan. This involves identifying the operation(s) required (addition, subtraction, multiplication, division, fractions, percentages, etc.) and determining the order in which they should be performed. Drawing diagrams, tables, or model-making can be extremely helpful for visualising the problem, especially for topics like time, distance, or sharing.

This planning stage helps to organise thoughts and reduces the likelihood of making errors during the calculation phase.

Step 3: Execute and Check

With a clear plan in place, children can then perform the necessary calculations carefully. Encourage them to show their working out. This not only helps in tracking steps but also allows for partial marks in some exams even if the final answer is incorrect.

After arriving at an answer, the final and critical step is to check the solution. This can involve:

This checking process is vital for catching careless errors and ensuring accuracy under exam conditions.

Try Maths: word problems 11+ practice questions

Question 1
A baker bought 25 kg of flour. He used 3/5 of it to bake cakes and 2.5 kg to bake biscuits. How much flour does he have left?
Answer: 7.5 kg. Total flour = 25 kg. Flour for cakes = (3/5) * 25 kg = 15 kg. Flour for biscuits = 2.5 kg. Total flour used = 15 kg + 2.5 kg = 17.5 kg. Flour left = 25 kg - 17.5 kg = 7.5 kg.
Question 2
Sarah cycles at an average speed of 12 km/h. How long will it take her to cycle 30 km?
Answer: 2 hours 30 minutes. Time = Distance / Speed. Time = 30 km / 12 km/h = 2.5 hours. 0.5 hours = 0.5 * 60 minutes = 30 minutes. So, the time taken is 2 hours 30 minutes.
Question 3
A garden measures 8 metres by 6 metres. If a path 1 metre wide is built around the outside of the garden, what is the new total area (garden + path)?
Answer: 80 square metres. Original garden dimensions: Length = 8 m, Width = 6 m. With a 1-metre path around the outside, the new length = 8 + 1 + 1 = 10 m. The new width = 6 + 1 + 1 = 8 m. New total area = Length * Width = 10 m * 8 m = 80 square metres.
Question 4
Three children, Ben, Chloe, and Daniel, share 72 sweets in the ratio 2:3:4. How many sweets does Chloe receive?
Answer: 24. The ratio is 2:3:4. Total ratio parts = 2 + 3 + 4 = 9 parts. Total sweets = 72. Value of one ratio part = 72 / 9 = 8 sweets. Chloe's share = 3 parts * 8 sweets/part = 24 sweets.

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Frequently asked questions

What specific maths topics are most common in 11+ word problems?

11+ word problems frequently test arithmetic (all four operations), fractions, decimals, percentages, ratio, proportion, time, money, measurement (length, mass, capacity), area, perimeter, and basic algebra embedded in word contexts.

How can I help my child improve their reading comprehension for word problems?

Encourage regular reading of various texts. For word problems specifically, practise highlighting keywords, identifying the 'question' part of the sentence, and rephrasing the problem in their own words. Discussing problems together can also help clarify understanding.

Should my child always 'show their working' in 11+ exams?

Yes, where space is provided, showing working out is highly recommended. It helps demonstrate understanding even if a calculation error occurs, potentially earning partial marks. For multiple-choice questions, showing working on scrap paper helps to avoid errors and allows for checking.

Are word problems typically harder in CEM or GL Assessment exams?

Both CEM and GL Assessment include word problems. CEM often places a greater emphasis on comprehension and multi-step problems, sometimes requiring more abstract thinking. GL Assessment can have a wider range of question types, including straightforward and multi-step problems, but generally focuses on curriculum knowledge application.