# What is a word problem?

## What is a word problem?

**A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.**

Word problems are seen as a crucial part of learning in the primary curriculum, because they require children to apply their knowledge of various different concepts to 'real-life' scenarios.

**Word problems also help children to familiarise themselves with mathematical language** (vocabulary like fewer, altogether, difference, more, share, multiply, subtract, equal, reduced, etc.).

Teachers tend to try and include word problems in their maths lessons at least twice a week.

## What is RUCSAC?

In the classroom children might be taught the acronym **RUCSAC (Read, Understand, Choose, Solve, Answer, Check)** to help them complete word problems.

By following the acronym step by step children learn to apply a structured, analytical strategy to their calculations. They will need to understand what the problem is asking them to find out by reading the question carefully, choosing the correct mathematical operation to help them solve the query and finally checking their answer by using the inverse operation.

## Word problem examples for Years 1 to 6

The following are example word problems that apply to each primary year group.

**Year 1**

In Year 1 a child would usually been given apparatus to help them with a problem (counters, plastic coins, number cards, number lines or picture cards).

*Sarah wants to buy a teddy bear costing 30p. How many 10p coins will she need?*

Brian has 3 sweets. Tom has double this number of sweets. How many sweets does Tom have?

**Year 2**

In Year 2, children continue to use apparatus to help them with problem-solving.

*Faye has 12 marbles. Her friend Louise has 9 marbles. How many marbles do they both have altogether?*

Three children are each given 5 teddy bears. How many teddy bears do they have altogether?

**Year 3**

In Year 3, some children may use apparatus, but on the whole children will tend to work out word problems without physical aids. Teachers will usually demonstrate written methods for the four operations (addition, subtraction, multiplication and division) to support children in their working out of the problems.

*A jumper costs £23. How much will 4 jumpers cost?*

Sarah has 24 balloons. She gives a quarter of them away to her friend. How many balloons does she give away?

Children will also start to do two-step problems in Year 3. This is a problem where finding the answer requires two separate calculations, for example:

*I have £34. I am given another £26. I divide this money equally into four different bank accounts. How much money do I put in each bank account?*

- In this case, the first step would be to add £34 and £26 to make £60.
- The second step would be to divide £60 by 4 to make £15.

**Year 4**

Children should feel confident in an efficient written method for each operation at this stage. They will continue to be given a variety of problems and have to work out which operation and method is appropriate for each. They will also be given two-step problems.

*I have 98 marbles. I share them equally between 6 friends. How many marbles does each friend get? How many marbles are left over?*

**Year 5**

Children will continue to do one-step and two-step problems. They will start to carry out problem-solving involving decimals.

*My chest of drawers is 80cm wide and my table is 1.3m wide. How much wall space do they take up when put side by side?*

There are 24 floors of a car park. Each floor has room for 45 cars. How many cars can the car park fit altogether?

**Year 6**

In Year 6 children solve 'multi-step problems' and problems involving fractions, decimals and percentages.

*Sarah sees the same jumper in two different sales:In the first sale, the original price of the jumper is £36.15, but has been reduced by a third.In the second sale, the jumper was priced at £45, but now has 40% off.How much does each jumper cost and which one is the cheapest?*

In the past, calculators were sometimes used for solving two-step problems like the one above, but the new curriculum does not include the use of calculators at any time during primary school.

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