25 Division Word Problems for Year 2 to Year 6 With Tips On Supporting Pupils’ Progress

Division word problems are important in building proficiency in division. Division is one of the bedrocks of mathematics alongside addition, subtraction and multiplication. Therefore, it is vital that pupils have a deep understanding of division, its function within arithmetic and word problems, and how to apply both short division and long division with success.

Division itself is the mathematical process of breaking a number up into equal parts and then finding out how many equal parts you can have. It may be that you have a remainder following this division or you may have no remainder and so a whole number as your answer.

What are division word problems?

Division word problems are an extension of the arithmetic method whereby they are word problems with division at the heart.Pupils will be expected to use the process of division to find a solution to the word problem.

Typically, word problems use a story as a scenario and are based on a real life situation where pupils are expected to interpret what the word problem is asking and then apply their division knowledge to find the answer. Division can also be introduced early through the idea of grouping before advancing to the formal method of short division and long division.

To help you with the division journey, we have put together a collection of division word problems which can be used for children between Year 2 to Year 6 – also aimed at both 3rd grade and 4th grade pupils in America.

Division word problems in the national curriculum.

Division word problems in KS1

The national curriculum states that division and word problems should be encountered from Key Stage 1 and throughout our pupils’ primary school journey. Practical resources such as counters, dienes cubes and base ten can be used to supplement the teaching of division.

In Key Stage 1 the focus is on simple addition and subtraction word problems, however, it is standard practice to introduce the concept of grouping and sharing small quantities and to calculate the answer using concrete objects and pictorial representations. It is at this point that the idea of finding fractions of objects can also be introduced and that whilst multiplication of two numbers can be done in any order (the commutative theory), the division of one number by another cannot.

Division word problems in KS2

As children enter Lower Key Stage 2 they begin to develop their mental and written strategies for division. Pupils will begin to use their multiplication knowledge and times tables to assist in their solving of division problems and how they can use the corresponding division facts and multiplication facts to answer questions. 

By the end of Year 4, pupils are expected to recall their multiplication and division facts for multiplication times tables up to 12 x 12. They should also use their knowledge of place value, and known and derived facts to assist with simple division such as dividing by 1 and halving.

Introducing short division 

Short division is the next step in Lower Key Stage 2. Pupils practise their fluency of short division, also known as ‘the bus stop method’, in order to answer division word problems that have a whole number answer, and those with a remainder.

Before entering Upper Key Stage 2, pupils encounter division word problems and multi step problems with increasingly harder numbers going from a simple short division problem, such as, ‘If we have 30 pupils in our class and we are divided into groups of 5, how many pupils will be in each group?’ to ‘If there are 56 books in our library and they are shared amongst 7 children, how many books would each child get?’

Introducing long division 

As our pupils enter Upper Key Stage 2, long division is introduced. By the end of KS2 pupils should be fluent in both multiplication and division and the written strategies, and be able to apply knowledge in fraction word problems and percentage word problems. 

Year 5 pupils work towards being able to divide up to 4 digit numbers by a one digit number using short division and being able to interpret remainders in the correct context – even presenting the remainder as a decimal or fraction. Pupils should also be able to divide mentally and know how to divide by 10, 100 and 1000 and how place value works alongside dividing a number so it is 10, 100 or 1000 times smaller.

Year 6 pupils are expected to consolidate on the above formal methods of short division before being able to divide a four digit number by a two digit number using the formal method of long division and to again be able to understand remainders within this and present them in the correct context. 

This also flows into division word problems as children should be able to read a multi step problem and know how to correctly interpret it, apply their divisional knowledge and solve the problem successfully. The concept of multi step problems is built upon at each stage of the national curriculum.

Why are word problems important for childrens’ understanding of division?

Word problems, alongside the use of concrete objects and pictorial representations, are important in helping children understand the complexities and possible abstract nature of division.

Whilst children may understand that when we divide our answer will be smaller, before providing a child with word problem worksheets, just like with exploring arrays to support multiplication word problems, it is important to visually explore how division looks – from grouping and beyond.

Applying maths to real life situations

Word problems are important because they provide a real life context for children to understand division and how we encounter it in real life. By allowing children to see how division is used in everyday situations, children will find it more meaningful and relevant which in turn develops a deeper understanding of the four operations as a whole.

Building problem solving skills

Word problems are also vital to developing problem solving skills. Firstly, they must read and understand the problem before being able to identify the relevant information within the contextual problem and apply their knowledge to find a solution. This naturally builds critical thinking and a child’s ability to reason, which is an important skill for any mathematician.

Developing mathematical language skills

Finally, the importance of  moving from simple division word problems to more challenging ones enhances pupils’ vocabulary and language skills. For children to develop an understanding of vocabulary such as divisors, quotient and remainders means they must first understand these key words and apply it to the process of division and be able to communicate clearly what they are aiming to do.

Deepening understanding of the inverse relationship between division and multiplication

Division word problems also solidify the connection between multiplication and division. Understanding these inverse operations and being able to interchange the skills of multiplication and division will help make connections between different mathematical concepts and deepen pupils’ learning. 

How to teach division word problem solving in primary school.

Having taught the concept of division to pupils using concrete examples, for example how to group or share counters and cubes, the next step is to advance to division word problems. 

As with all word problems, it is important that pupils are able to read the question carefully and interpret it so they know what they are being asked. Do they need to add, subtract, multiply or divide? Do they need to solve a multi step problem and so need to do more than one step? They may decide what operation to do, in this blogs’ case – division, and then choose to represent it pictorially.

Example of a division word problem

There are 40 sweets ready to go in the party bags for Laura’s birthday. They are to be shared between 8 friends. How many sweets will each child get?

How to solve this:

Firstly we need to interpret the question. Laura has invited 8 friends to her party and she has 40 sweets to share equally between her friends. So we know:

• There are 40 sweets in total
• They are to be divided amongst 8 friends in total
• We therefore need to divide the total number of sweets (40) by the number of friends (8). So to solve this problem we could put the total number of sweets (the dividend – 40 ) in the ‘bus stop’ for short division and divide by the total number of friends (the divisor – 8). If we do this, we would get the answer of 5 – the quotient. Each friend would get 5 sweets each as 40 divided by 8 is 5.
• Alternatively, we could use the inverse – multiplication – to solve this problem. We may not know the division fact that 40 divided by 8 = 5 but if we look to the inverse we may know what numeral multiplied by 8 equals 40. If we did our 8 times table we would get the answer of 5 – the correct answer.

How can we show this pictorially?

We could show 8 circles – each circle to represent a child – and place a sweet in each circle until we have placed all 40 sweets. This would mean we have shared the sweets equally between the friends and would result in each child having 5 sweets.

We could represent the division word problem as a bar model. We could split the bar model into 8 sections. There are 40 sweets and so we share them between the 8 sections. We will again see each section gets 5 sweets.

The below visuals show how this would look:

Or: 

Word problems are an important aspect of our learning at Third Space Learning’s one-to-one tuition programme. Tutors will work with our tutees to break down the word problems and identify the correct operation needed to solve the word problem.

Examples of division word problems in the primary setting

Below are examples of what can be expected at each year group from Years 2 to 6. Through our tutoring programme at Third Space Learning, our tutees will become familiar with word problems throughout their learning. They will encounter word problems on a regular basis with each lesson personalised to develop the learning our tutees need. The word problems will increase their confidence, familiarity with vocabulary and mathematical understanding.

Division word problems are essential to developing problem solving skills and mathematical reasoning.

Year 2 division word problems

In Year 2 pupils use division facts for the 2, 5 and 120 times table and solve problems using concrete materials, arrays and see word problems in context.

Year 3 division word problems

With word problems for Year 3, pupils should begin using their recall of the 3, 4 and 8 times table to help with division word problems and be able to divide two digit numbers by one digit numbers using mental and short division.

Year 4 division word problems

With word problems for year 4, pupils should be using their full knowledge and recall of times tables to 12 x 12 to help with short division of 2 digit and 3 digit numbers by a 1 digit number. Word problems may also involve multi step problems. Remainders may also be within the answer.

Year 5 division word problems

Word problems for Year 5 centre around dividing a 4 digit number by a 1 digit number using the formal method of short division. They will also interpret remainders correctly depending on the context. Division and remainders is often demonstrated through money word problems.

Year 6 division word problems

Word problems for year 6 will be preparing for their SATs exams in May. They would be familiar with the concept of long division and needing to divide a 4 digit number by a 2 digit number using the formal methods of both short and long division.

More word problems resource

Are you looking for more word problems resources? Take a look at our library of word problems practice questions including: time word problems, ratio word problems, addition word problems and subtraction word problems.