25 Addition and Subtraction Word ProblemsYear 2 to Year 6 With Tips On Supporting Pupils’ Progress

Addition and subtraction word problems are synonymous with primary maths. Children encounter both operations very early on in their primary school journey. It is the understanding of both addition and subtraction facts that opens up a world within maths for children to tackle different mathematical concepts. For this reason, along with place value, understanding and applying these operations really does form the foundations of maths.

In Early Years (EYFS) children will be introduced to simple addition and subtraction word problems and they will visually explore how the total gets bigger when adding and how the total gets smaller when taking away. These skills, whilst basic, are built upon year on year up to Year 6 whereby children will encounter mixed word problems and complex word problems that involve two-steps in order to solve them.

But without forming this solid basis in EYFS and Key Stage 1 where children explore through the use of visuals, manipulatives and concrete materials, children will not be as confident with the written formal methods and solving complex multi-step word problems involving large numbers and decimals.

What are addition and subtraction word problems

Addition word problems and subtraction word problems are questions involving both operations, placed into context and given a real-life scenario. Rather than practising fluency through arithmetic, children are given math word problems to challenge them to interpret what a question is asking and what operation or multi-steps they need to do in order to find the solution.

In this blog we have put together a range of questions from Year 2 up to Year 6 to show the journey from one step word-problems, on to two-step problems and ending with more complex word problems that mimic those seen in the KS2 SATs. 

Addition and subtraction word problems in the National Curriculum

Addition and subtraction word problems in Year 2

Having already been introduced to simple addition and subtraction word problems worksheets in Year 1, where the focus is on representing simple number sentences visually, in Year 2 children continue to use pictorial representations and concrete materials to solve addition and subtraction problems.

Third Space Learning’s online one-to-one tutoring programme works to ensure children understand mathematical concepts by for example, using pictorial representations.

The word problems will typically focus around number, measures and simple money word problems e.g. adding coins together. Children will also be building their mental methods in calculating both addition and subtraction and be introduced to the different vocabulary both operations through quality first language and flashcards in lessons. By the end of Year 2, children will be expected to solve word problems using 1 digit and 2 digit numbers and will be introduced to the concept of regrouping and using a number line to solve the problems.

Addition and subtraction word problems in Year 3

Word problems for Year 3 signal the beginning of solving more complex word problems. Children begin to use more formal written methods and go beyond using a number line, although this may be applicable to some questions.

In Year 3 children begin to use column addition or subtraction to solve problems involving 3-digit numbers and their knowledge extends to adding and subtracting word problems involving topics such as fractions. They also consolidate their place value knowledge by being able to mentally add 3-digit numbers with ones, tens and hundreds. The concept of inverse is also important here to see the connection between addition and subtraction and how we can use the inverse to solve a problem within a maths activity.

Addition and subtraction word problems in Year 4

With word problems for Year 4, children make the next progression to solving two step word problems and moving from 3-digit numbers to 4-digit numbers. When seeing word problems in context children will have to decide what operation to use and what method is most efficient and accurate for the problem. They also will need to and understand why. 

Whilst working with larger numbers pupils will also need to think about the processes and strategies behind multi digit addition and how to use subtraction facts to assist in solving mixed word problems.

Addition and subtraction word problems in Year 5

As children progress to Upper Key Stage 2, they will encounter two-step addition and subtraction word problems for Year 5, they will be expected to solve contextual word problems by adding or subtracting both whole numbers up to 5 or 6 digit numbers, as well as decimal numbers.

 Whilst children will be increasing their ability to add larger numbers mentally, they will be tightening their grasp of adding and subtracting large numbers using the formal written methods. Children should also be encouraged to use the inverse, for example in subtraction word problems, addition can be used to check the accuracy of their answer and to consider how to effectively estimate the answer before proceeding with the formal written approach.

Addition and subtraction word problems in Year 6

In preparation for the SATs tests towards the end of Year 6, children will be solving increasingly more complex word problems in both addition and subtraction. Word problems will be given a real-life context and will involve large numbers in the millions, as well as decimal numbers. 

The multi-step word problems for Year 6 will also not be limited to purely addition and subtraction word problems but extend to using all four operations: addition, subtraction, multiplication word problems and division word problems and children will need to be able to interpret them successfully and apply their understanding in the correct manner.

Why are word problems important for childrens’ understanding of addition and subtraction

Word problems for addition and subtraction do not only bring the maths to life, they enhance understanding of both operations. From simple story problems where children use visuals and concrete materials to explain what is happening, to being able to solve complex multi-step problems, word problems go beyond a maths worksheet aimed purely at fluency in addition and subtraction.

Word problems from EYFS also help engage children in applying their phonics skills, build up their mathematical vocabulary, build up their problem solving skills and deepen their understanding of the inverse between addition and subtraction. 

Finally, the use of word problems also enables children to build up their strategies to solve such a problem: pictorial, mental methods or formal written methods. The key is to engage via the language arts and provide a context where children can decipher what to do, how to do it and apply their knowledge to real-life situations that make sense to them.

How to teach addition and subtraction word problem solving in primary school

Building on the arithmetic and fluency of adding and subtracting, the next step is to use concrete materials and pictorial representations to show what maths is happening. 

Children need to be able to read a word problem and successfully interpret what is happening by reading the question carefully and knowing what is asked. From here, children need to work out what operation is needed to solve the problem and solve it using one of the strategies in their armoury – hopefully the most efficient one for that problem!

Below is an example of an addition word problem that also includes subtraction:

In a countryside farm there are 4672 birds nesting in the trees.

A further 304 arrive to nest too but 561 depart for a better habitat.

How many birds are there in the countryside farm?

How do we solve this?

Firstly, we interpret the question to work out what we know:

• We know that at the beginning there were 4,672 birds.
• 304 more birds arrive….so we add this to the total above. We then get a new total of 4,976.
• 561 leave…so we take this away from the new total of 4,976 and we get the final total of 4,415.

How could this look pictorially?

Using the bar model method (suitable for Years 3 and 4) we could firstly do a bar model to add the 304 birds to the initial amount of 4,672.

Then we can take that total to show how many birds were left after 561 departed.

Alternatively, we could use the column method to represent this word problem too. It would look like this:

Then:

Addition and subtraction word problems for Year 2

In Year 2 pupils are required to work with both 1-digit and 2-digit numbers. This is a vital stage for children to visually understand the processes of both addition and subtraction and so using a template to represent the word problems pictorially is a great way of allowing children to show what they interpret the question to be asking, and how to resolve it.

Addition and subtraction word problems for Year 3

In Year 3, children are required to be confident at adding and subtracting 3-digit numbers and they will begin to use the formal method of column subtraction or addition. Children will also notice that the type of word problems are a little more complex in using measures, time, money as ways of incorporating an addition or subtraction word problem.

Addition and subtraction word problems for Year 4

Children in Year 4 consolidate their knowledge of adding and subtracting with 3-digit numbers before advancing to 4-digit numbers. They will also begin solving more complex word problems and multi-step problems too. This is also the perfect opportunity to begin self-checking their answers by using the inverse as they will also encounter decimal numbers and fractions within word problems.

Addition and subtraction word problems for Year 5

As children begin Upper Key Stage 2 they will become familiar working with larger numbers, 5 and 6 digit numbers, as well as decimals. Word problems are typically more complex and are mainly two-step problems together with the use of multiplication and division as well. They will again be encouraged to check the accuracy of their answers by using the inverse.

Addition and subtraction word problems for year 6

In preparation for the SATs, children in Year 6 need to be able to add or subtract when using 6 or 7 digit numbers, as well as decimal numbers. Addition and subtraction word problems in the SATs may also include fraction word problems and they will be two-step or multi step word problems to interpret and solve.

Looking for more resources

Third Space Learning offers a diverse and extensive library of maths resources. For more word problems resources, take a look at our packs of percentage word problems, ratio word problems and time word problems.