20 Word Problems For Year 6: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Word problems for Year 6 are an important part of the curriculum. For children to achieve success in the Year 6 SATs, in particular the more challenging reasoning element of the SATs assessments, it is essential they have the confidence to tackle a wide range of word problems.

Key to this success is regular exposure to the style and type of questions, covering the topics children could be presented with. Our collection of year 6 maths worksheets are is a great place to start.

To help child practice their problem solving skills, we have put together a collection of 20 word problems, organised by topic. This collection encompasses the types of questions children may encounter in the two reasoning papers.

Year 6 Maths Word Problems in the National Curriculum

The National Curriculum states that children need to be able to solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into simpler steps and persevering in seeking solutions. 

By Year 6, children can expect to be tackling a range of one-step, two-step and multi-step word problems. To achieve at least the expected standard in Year 6, pupils need to demonstrate the ability to solve word problems across a range of topics.

Place value 

Solving problems including ordering, rounding and negative numbers.

Addition, subtraction, multiplication and division

Solving multiplication, division and addition and subtraction word problems including one and two-step word problems and multi-step word problems in context, deciding which operations and methods to use and why.

Fractions 

Solving problems involving comparing, ordering and sequencing fractions; using the four operations and problems which require answers to be rounded to specified degrees of accuracy.

Ratio and proportion

Solving problems involving the relative sizes of two quantities; the calculation of percentages; involving similar shapes where the scale factor is known and can be found; and unequal sharing and grouping, using knowledge of fractions and multiples.

Measures

Solving problems including time word problems and involving the calculation and conversion of units of measure, using decimal notation up to three decimal places, where appropriate.

Statistics

Interpret and construct pie and line graphs and use these to solve problems.

Why are word problems important in Year 6 maths?

Word problems are an essential element of the Year 6 curriculum, because they require children to apply the knowledge they have learnt to ‘real life’ situations, for example, in money word problems. They shouldn’t just be taught as stand alone topics, but should be incorporated in lessons throughout the year, to ensure children have as much exposure as possible. 

Solving word problems helps children learn the skills needed to apply their knowledge of maths beyond the classroom and into the real world.

How to teach problem solving in Year 6

When teaching problem solving in Year 6, children need to firstly look carefully at the key information and think about what they already know. Secondly, what is the word problem actually asking? Which calculation(s) would be required and would it help to draw/represent the problem pictorially?

Here is an example:

Ahmed is buying clothes. He buys a t-shirt for £12.99 and a pair of jeans which cost £12.26 more than the T-shirt. He pays with a £50 note. What change does Ahmed get?

How to solve:

What do you already know?

• More than means I will need to add the price of the T-shirt and jeans together.
• Decimals numbers means I need to remember to line up the decimal points in my calculations.
• Calculating change means I will need to subtract the total for the jeans and T-shirt from the original amount. 

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

• To calculate the cost of the jeans, we need to add £12.99 and £12.26 = £25.25
• Ahmed pays using a £50 note. 
• To calculate the change Ahmed will get, we need to subtract £25.25 from £50.
• £50 – £25.25 = £24.75

Word problems in SATS

Problem solving is an important part of the preparation for the Key Stage 2 SATs, as this is the area children tend to find the most challenging. With two reasoning papers to complete, children will be expected to answer a wide range of word and number problem style questions. The best preparation for this is through regular exposure to these types of questions.

Addition word problems for Year 6 

Addition word problems at Year 6 include larger 6 or 7 digit numbers, decimal numbers and problems involving finding the inverse. These can be one, two and multi-step problems

Subtraction word problems for Year 6

Subtraction word problems in Year 6 include larger 6 or 7 digit numbers, decimal numbers and problems involving finding the inverse. These can be one, two and multi-step problems

Multiplication word problems for year 6

Multiplication word problems can include multiplying whole and decimal numbers by 1 and 2-digit numbers. A secure knowledge of times tables is helpful for children solving these questions confidently. 

Division word problems for Year 6

Division word problems in Year 6 can include division with whole numbers and decimal numbers, dividing by 1 and 2-digit numbers.

Fractions, decimals and percentage word problems for Year 6

Decimals, percentage word problems and fraction word problems can be stand alone, or they can involve converting between. For example, in questions using measures.

Ratio word problems for Year 6

Ratio word problems are often linked with measures. Children should be encouraged to draw bar models to solve problems involving ratio, as these question really benefit from a visual representation.

Mixed four operation word problems for Year 6

Mixed operation word problems require two or more operations to solve. Alongside the four operations, they can also include other topics, including fractions and percentages These can be two-step or multi-step questions and are worth 2 or 3 marks in SATs papers. 

Third Space Learning’s online one-to-one tutoring programmes include questions that combine skills students have learnt and test their understanding across a range of topics. Personalised to the needs of each individual student, our online tutoring programme works to identify gaps in learning, fill those gaps and reinforce students’ maths knowledge.

More word problems resources

Third Space Learning also offers a wide array of maths and word problems resources for other year groups such as word problems for Year 5, word problems for Year 4 and word problems for Year 3