# 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.**

- What are addition and subtraction word problems
- Addition and subtraction word problems in the National Curriculum
- Why are word problems important for childrens’ understanding of addition and subtraction
- How to teach addition and subtraction word problem solving in primary school
- Addition and subtraction word problems for Year 2
- Addition and subtraction word problems for Year 3
- Addition and subtraction word problems for Year 4
- Addition and subtraction word problems for Year 5
- Addition and subtraction word problems for year 6
- Looking for more resources

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.

All Kinds of Word Problems Addition and Subtraction

Test your students' problem solving skills with this pack of addition and subtraction word problems worksheets.

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.

#### Question 1

Mrs. Molloy had 18 glue sticks in her class but 6 had to be chucked away as the glue lids had been left off. How many does she have left now?

**Answer: 12 glue sticks**

This could be solved in several ways. We could represent this pictorially with 18 glue sticks and cross out 6, we could show this on a number line and count back 6, or we could show it in the bar model method. Here are images of how this could look:

Pictorially:

Number line:

Bar model:

#### Question 2

The school bus arrives at a bus stop and 5 children get on the bus. At the next stop, 7 more children get on and at the final bus stop, 4 more children get on the bus.

How many children are now on the school bus altogether?

**Answer: 16 children**

5 + 7 + 4 = 16

#### Question 3

a) Sahana was collecting football stickers and counted 32 in total. Hannah had 25 football stickers too. How many do they have altogether?

b) If Sahana then gave 11 of her stickers to her friend Kevin, how many stickers does Sahana have left now?

**Answers: a) 57 b) 21**

In part one 32 + 25 = 57.

In part 2, if Sahana had 32 to start with and gives away 11 so this would be, 32 – 11 = 21.

#### Question 4

Flowers come in bunches of 10. Miss. Spalding buys 3 bunches for her house. How many flowers does she have in total?

**Answer: 30**

10 + 10 + 10 = 30 or a multiplication fact that 10 x 3 = 30

#### Question 5

Who has the most books – class 1 or class 2?

Class 1 had 37 books and were then given 15.

Class 2 had 60 books but lost lost 6.

**Answer: Class 2 had the most.**

Class 1 is 37 + 15 = 52 books

Class 2 is 60 – 6 = 54 books

### 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.

#### Question 1

176 poppies were growing in a field.

Over the spring months another 210 poppies grew in the field.

How many were there at the end of spring?

**Answer: 386 poppies**

176 + 210 = 386

It may be worth informing pupils that unlike subtraction, it does not matter what way round we carry out the addition with two or more different numbers. For example, it doesn’t have to be the biggest number first, but it is essential we do this in subtraction.

We could represent this in simple column addition as such:

#### Question 2

Alice has saved £120 from her birthday.

She spends £35 on a plushie.

How much does she have left?

**Answer: £85**

120 – 35 = 85. Here we do need to borrow from the tens column and give to the ones column in order for subtraction to be possible.

#### Question 3

Ariana scored 156 Dojo points last term. This term she has scored 137 more. How many points has she scored altogether?

Katie has 50 points less than Ariana. How many did she have?

**Answer: Ariana had 293 Dojo points altogether and Katie had 243 Dojo points.**

First we have to add Ariana’s together: 156 + 137 = 293.

Secondly, we have to subtract 50 from Ariana’s total, so 293 – 50 = 243.

#### Question 4

Year 3 were asked what their favourite fruit was between strawberries and bananas. If there there are 145 children in Year 3 and 72 like strawberries the most, what is the most popular fruit? Strawberries or bananas?

**Answer: Bananas wins with 73 children preferring them to strawberries.**

145 – 72 = 73.

#### Question 5

If assembly starts at 9:00am and finishes at 9:15am, then maths is an hour and 10 minutes long before break time. How many minutes is it from assembly to break time?

**Answer: 85 minutes. This could also be one hour and 25 minutes if asked to convert.**

15 + 60 (one hour) + 10 = 85 minutes.

### 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.

#### Question 1

James and Bernard have 820 marbles between them.

However, James has 148 more than Bernard.

How many does Bernard have?

**Answer: Bernard has 336 marbles.**

Additional information: James has 484 marbles.

How to solve this:

As there are two people, James and Bernard, and between them they have 820 marbles, we halve that to work out how many they would have each if divided equally.

The answer would be 410 as 820 divided 2 is 410.

But James has 148 more, so we halve 148 and get 74.

This is because we will then take 74 from Bernards 410 and they will go to James. 410 – 74 = 336.

So for Bernard we subtract 74 from the 410, and for James we add 74 to his 410. This gives a difference of 148.

#### Question 2

I have £25.

I need to buy a birthday present for £6.50, lunch for £9.75 and a train ticket for £5.50.

Will I have enough?

**Answer: Yes! Not only will I have enough, I will have £3.25 left.**

25.00 – 6.50, 9.75 and 5.50 = £3.25

#### Question 3

A private jet can hold fuel for 8,689 miles.

To travel around the UK, it will use 7,863 miles worth of fuel.

To get to France is another 710 miles. Will the private jet have enough fuel?

Prove it.

**Answer: Yes because 8689 – 7,863 = 826**

Therefore, we would still have enough fuel for 826 miles and France is under this at 710 miles.

#### Question 4

A return ticket to Japan is £1550.

Jack has saved £865 and Olivia has saved £379. Have they saved enough?

If not, how much more do they need to save?

**Answer: No they do not have enough. They need another £306.**

865 + 379 = 1,244.

1,550 – 1,244 = 306

#### Question 5

Team Allstars are training for the big race. They spend 1928 minutes training in February and then 5674 minutes training in March.

Their rivals, the Dream Team, spend 7642 minutes training in February and March combined. Who spent the most time training for the big race? What is the difference in training times?

**Answer: Team Allstars spends 7,602 minutes training so the Dream Team spent longer training. The time difference was 40 minutes.**

### 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.

#### Question 1

11,347 cupcakes were baked for an event. 8,692 were sold at £3 each.

How many cupcakes were left and how much money was made?

**Answer: There were 2,655 left and £26,076 was made from selling the cupcakes.**

11,347 – 8,692 = 2,655

8,692 x 3 = £26,076

#### Question 2

A cruise ship had 12,469 passengers in April and 14,738 in May. How many more passengers were aboard in May?

**Answer: 2,269 passengers**

14,738 – 12,469 = 2,269

#### Question 3

At the beginning of the school year, there are 11, 499 pencils. The school receives an extra 3,575 midway through the school year but they use 9,223 during the year.

Maria works out how many are left at the end of the school year by doing the following calculation:

*9,223 + 3,575 = 12,798. Then 12,798 – 11,499 = 1,299 pencils left.*

Explain the mistake Maria has made and work out how many are actually left at the end of the year.

**Answer: Maria has completed this question incorrectly because she had to add the extra 3,575 to the initial 11,499. This would give her 15,074. She then had to subtract 9,223 from this to give the amount left at the end of the year which would be = 5,851**

#### Question 4

A car showroom sells 3 Mercedes sports cars for £72,731 each and 2 Porsche sports cars for £107,299 each. How much did they make in total? What is the difference between the total the Mercedes sports cars made compared to the total the Porsche sports cars made?

**Answer: The Mercedes total cost was £218,193 and we can do this either by adding £72,731 three times, or multiplying it by 3.**

**The total cost for the 2 Porsche cars was £214,598. If we then subtract £214,598 from £218,193 we will get the difference which is £3,595.**

#### Question 5

Martin is trying to work out would be longer in length. Eight pieces of string that are 1.6m in length each or 12 pieces of string that are 0.8m in length. What is the total length of string if we added both of them together?

**Answer: Eight lots of string at 1.6m each is 12.8m in total (either repeated addition or multiplying by 8) and 12 pieces of string at 0.8m are 9.6m in total. Altogether we add them up and get 22.4m.**

### 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.

#### Question 1

A toy shop is holding a buy one get one half price offer on the new computer. The computer costs £290.50 for one. How much would 2 cost in the offer?

**Answer: £435.75**

To find the cost of the second one we divide £290.50 by 2 and get £145.25 and then add it to the cost of the original one.

£290.50 + £145.25 = £435.75

#### Question 2

Sonic the Hedgehog 2 is playing at two different huge outdoor cinemas that both hold 250,000 people. One cinema has 218,745 people watching the film and the other has 187,681.

How many people are watching the film? How many more people could watch the film?

**Answer: There are 406,426 people watching the film. 93,574 more people could watch the film.**

This is: 218,745 + 187,681 = 406,426

93,574 more people could watch the film.

This is: 500,000 – 406,426 = 93,574

#### Question 3

Jagat buys snacks for his friends and himself. When he weights the bag, it weighs 1.2kg but when he removes just the chocolates it weighs 990g.

When he removes just the crisps it weighs 830g.

How much more do the crisps weigh than the chocolates?

**Answer: The chocolates are lighter as they weigh 210g. The crisps weigh 370g. So the crisps weigh 160g more than the chocolates.**

Convert 1.2kg into grams = 1200.

Then 1200 – 990 = 210g for the chocolates

Then 1200 – 830 = 370g for the crisps

370 – 210 = 160g difference

#### Question 4

Griffin is thinking of a number,

He adds 1,728.

He subtracts 352.

He divides it by 4.

His answer is 958.

What number did he start with?

**Answer: 2,456**

To do this we start with 958 and follow the rules backwards by doing the inverse.

958 x 4 =3,832

3,832 + 352 = 4,184

4,184 – 1,728 = 2,456

#### Question 5

Ben bought 1.4 litres of orange juice for him and 15 friends to enjoy. How much juice would they all get?

If all 16 children wanted 100ml of juice each how much does each child need extra and how much juice would that be altogether in litres?

**Answer: 87.5ml of juice each is the original serving.**

**They would need a further 12.5ml each to have 100ml in their cup.**

**12.5ml x 16 children would be an extra 200ml.**

**Add that to 1.4 litres it would equal 1.6 litres.**

### Looking for more resources

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