How to Solve 11+ Multi-Step Word Problems: A Parent’s Guide

“A bus leaves the station with 15 passengers. At the first stop, 7 people get off and 4 get on. At the second stop, a third of the passengers get off…”

Does this type of question make your child’s head spin? You’re not alone. Multi-step word problems are consistently one of the trickiest areas of the 11+ Maths exam.

Why? Because they are not just a test of calculation. They are a test of comprehension, logic, and a child’s ability to stay calm and organised under pressure. Examiners use these questions to identify students who can think clearly and apply their knowledge to real-world scenarios.

At elevenplus.com, we believe that any child can master these problems with the right framework. It’s not about being a “maths genius”; it’s about having a clear, repeatable strategy.

This guide will walk you through our proven R.U.D.E. method, a simple 4-step framework to decode any word problem with confidence.

The R.U.D.E. Method: Your 4-Step Framework

Panic is the enemy of logic. When faced with a wall of text, children often rush, misread the question, and lose easy marks. The R.U.D.E. method forces them to slow down and think methodically.

• Read
• Underline
• Draw
• Estimate & Execute

Let’s break down each step.

Step 1: Read the Question Twice

The first step is simple but crucial. Read the entire question once to get a general sense of the scenario. Then, read it a second time, much more slowly. Rushing this stage is the single biggest cause of mistakes.

Step 2: Underline the Key Information

As you read the second time, use your pencil to become a detective. You are looking for clues. Underline:

• All the numbers and values.
• The specific question being asked (it’s often buried at the end).
• Mathematical Keywords: Actively hunt for and circle operational words like “total”, “difference”, “more than”, “altogether”, and “change”. This tells you which calculations you’ll need to do.

This act of underlining separates the signal from the noise and helps your child focus on what truly matters.

Step 3: Draw a Simple Diagram

Trying to hold all the information in your head is a recipe for disaster. A simple drawing, chart, or bar model can turn an abstract problem into a concrete one. It doesn’t need to be a work of art; it just needs to organise the information visually.

Step 4: Estimate & Execute

Before you do any calculations, get a rough idea of what the answer should be. This “common sense check” helps to spot mistakes later. Then, execute the calculations step-by-step, writing each one down clearly. Don’t try to do too much in your head.

Worked Example 1: A Simple Problem

Let’s apply the R.U.D.E. method to a typical question.

Question: David buys a magazine for £1.75 and a chocolate bar for 80p. He pays with a £5 note. How much change does he receive?

R – Read: Read the question twice to understand the scenario.

U – Underline:

• magazine for £1.75
• chocolate bar for 80p
• pays with a £5 note
• How much change does he receive? (Here, “change” is a keyword for subtraction).

D – Draw: A simple bar model works perfectly here.

[Image: A bar model showing the £5 total, with sections for £1.75, £0.80, and a question mark for the change.]

E – Estimate & Execute:

• Estimate: The total cost is roughly £1.80 + £0.80 = £2.60. The change should be around £2.40.
• Execute:
  1. Convert units: First, make sure everything is in the same unit. 80p = £0.80.
  2. Find the total cost: £1.75 + £0.80 = £2.55.
  3. Calculate the change: £5.00 – £2.55 = £2.45.

The answer of £2.45 is very close to our estimate, so we can be confident it’s correct.

Worked Example 2: A More Complex Problem

Now let’s try a trickier, multi-step question.

Question: At a farm, a third of the 120 animals are sheep. The rest are either chickens or cows. There are three times as many chickens as cows. How many chickens are there?

R – Read: Read twice. This involves fractions and ratios.

U – Underline:

• 120 animals in total
• a third are sheep
• the rest are chickens or cows
• three times as many chickens as cows
• How many chickens are there?

D – Draw: A diagram is essential here. We can use a combination of a bar model and boxes.

[Image: A diagram showing a main bar for 120 animals. One-third is sectioned off and labelled “Sheep (40)”. The remaining two-thirds section is labelled “Cows & Chickens (80)”. Below this, show 4 boxes: one labelled “Cows” and three labelled “Chickens”.]

E – Estimate & Execute:

• Estimate: A third of 120 is 40. That leaves 80. If there are more chickens than cows, the number of chickens must be more than 40.
• Execute:
  1. Calculate the number of sheep: 1/3 of 120 = 120 ÷ 3 = 40 sheep.
  2. Calculate the remaining animals: 120 – 40 = 80 animals (these are the chickens and cows).
  3. Use the ratio: There are “three times as many chickens as cows.” This is a ratio of 3:1. In total, there are 3 + 1 = 4 parts.
  4. Find the value of one part (the cows): 80 animals ÷ 4 parts = 20. So, there are 20 cows.
  5. Find the value of three parts (the chickens): 20 x 3 = 60 chickens.

The answer is 60 chickens. This matches our estimate that the number would be more than 40.

Final Expert Tips

When looking at complex maths problems, keep the below in mind:

• Watch for mixed units! Always convert everything to the same unit (e.g. pence to pounds, or cm to metres) before you start.
• Answer the right question. Often, a problem will require multiple calculations. Double-check that your final answer is what the question actually asked for.
• Practice makes perfect. The more word problems your child attempts, the more familiar they will become with the patterns and the less intimidating they will seem.

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