Year 6 maths · Key Stage 2 · Number – addition, subtraction, multiplication and division

Year 6 order of operations, factors and multi-step problems

This Year 6 topic is about choosing and organising calculations as well as doing them. Children identify common factors, common multiples and prime numbers, learn that a calculation with several operations has an agreed order in which it must be worked out, and tackle word problems that take more than one step. They also use estimation to check answers and to decide how exact an answer needs to be.

Order of operations and multi-step problems, explained

A factor of a number divides into it exactly, and a multiple is a number in its times table. Year 6 asks for common factors and common multiples: those shared by two numbers. The factors of 18 are 1, 2, 3, 6, 9 and 18, and the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24, so the common factors are 1, 2, 3 and 6. The common multiples of 4 and 6 start 12, 24, 36. Common factors are the tool used to simplify fractions, so this connects directly to fraction work.

A prime number has exactly two factors, 1 and itself. Since Year 5, children have been expected to recall the primes up to 19 and to decide whether numbers up to 100 are prime by looking for a factor. 2 is the only even prime, and 1 is not prime because it has only one factor. Numbers such as 51 and 91 are good tests: they look prime but are 3 × 17 and 7 × 13. Children use the times tables and divisibility clues, such as digits adding to a multiple of 3, to find a factor quickly.

When a calculation has more than one operation, the answer would change depending on the order, so everyone follows the same rule: brackets first, then multiplication and division, then addition and subtraction, working left to right within each level. The memory aid is BIDMAS or BODMAS, depending on the school. The programme of study example is 2 + 1 × 3 = 5, but (2 + 1) × 3 = 9. Powers are part of the full rule, but at this stage most of the calculations are about brackets and the four operations.

Multi-step problems give a story and leave the child to decide what to do. “A café sells 135 teas on Monday and 28 fewer on Tuesday. Each tea is £2. How much money did it take over the two days?” needs a subtraction (135 − 28 = 107 teas on Tuesday), an addition (135 + 107 = 242 teas) and a multiplication (242 × £2 = £484). Children are taught to read the question, work out what each step finds, choose a method (mental or written) and say why. Bar models and short jottings are common.

Estimation is used in two ways. Before calculating, children round to get an approximate answer to check against: 38 tickets at £4.95 is about 40 × £5 = £200. And after calculating, they decide how accurate an answer needs to be: 478 children going on a trip in coaches that hold 50 need 10 coaches, because 478 ÷ 50 is a little under 10 and a part-filled coach still has to run. Schools often ask children to round to the nearest 10, 20 or 50 in context. Rounding to significant figures comes later, in secondary school.

Words your child will hear

Common factor: A number that divides exactly into two or more numbers. 6 is a common factor of 18 and 24.
Common multiple: A number that is in the times tables of two or more numbers. 12 is a common multiple of 4 and 6.
Prime number: A number with exactly two factors, 1 and itself, such as 2, 3, 5, 7, 11, 13, 17 and 19.
Composite number: A number with more than two factors, such as 15 (1, 3, 5, 15).
Order of operations: The agreed order for working out a calculation: brackets, then multiplication and division, then addition and subtraction.
Brackets: Symbols that group part of a calculation so it is worked out first.
Estimate: A sensible approximate answer, usually found by rounding the numbers first.

What the National Curriculum says

In Year 6, pupils should be taught to:

Identify common factors, common multiples and prime numbers
Use their knowledge of the order of operations to carry out calculations involving the 4 operations
Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
Solve problems involving addition, subtraction, multiplication and division
Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Work out 30 − (2 + 4) × 3 + 12 ÷ 4.

Look for brackets first. 2 + 4 = 6, so the calculation becomes 30 − 6 × 3 + 12 ÷ 4.
```
30 − (2 + 4) × 3 + 12 ÷ 4
30 − 6 × 3 + 12 ÷ 4
```
Next do the multiplication and the division. They are on the same level, so work through them from left to right. 6 × 3 = 18 and 12 ÷ 4 = 3.
```
30 − 18 + 3
```
Finally do the addition and subtraction, again from left to right. 30 − 18 = 12, then 12 + 3 = 15.
```
12 + 3 = 15
```
Check against the two common slips. Working strictly left to right after the brackets gives 30 − 6 = 24, 24 × 3 = 72, 72 + 12 = 84 and 84 ÷ 4 = 21. Doing the addition 18 + 3 before the subtraction gives 30 − 21 = 9. Neither is right: the answer is 15.

30 − (2 + 4) × 3 + 12 ÷ 4 = 15

Common mistakes and how to help

Working strictly left to right, ignoring the order

Children read a calculation like a sentence, so 2 + 1 × 3 becomes 3 × 3 = 9 instead of 2 + 3 = 5. Calculators that process keys in order can reinforce this.

What helps: Use a story: “2 sweets plus 1 bag of 3 sweets” is clearly 5. Then compare it with the bracketed (2 + 1) × 3 and see how the brackets change the meaning.

Thinking multiplication always comes before division, and addition before subtraction

BIDMAS lists the letters one after another, so children treat each pair as two separate steps. 30 − 18 + 3 then becomes 30 − 21 = 9.

What helps: Explain that the letters in a pair share a level and are done left to right. Drawing a ring round each level in a longer calculation makes this visible.

Believing that 1 is a prime number, or that every odd number is prime

1 seems to fit the “only divides by 1 and itself” idea, and odd numbers such as 9, 15 and 51 look prime.

What helps: Make factor lists. 1 has only one factor, so it doesn’t qualify. 9 has factors 1, 3 and 9. Spotting 3 × 17 for 51 shows why looking for a factor is better than trusting appearances.

Mixing up factors and multiples

The two words sound alike, and both involve times tables. A child lists 3, 6, 9, 12 when asked for the factors of 12.

What helps: Factors are few and finish at the number itself; multiples go on forever. “Factors fit into it, multiples are made from it” helps some children remember.

How to help at home

Number of the day. Choose a number up to 100 and ask your child to list its factors and say whether it is prime. Switch between a prime like 53 and a composite like 54 so they have to look for a factor each time.
Target number game. Give four small numbers and a target, and let your child use any operations and brackets to reach it. For example, make 24 from 2, 3, 4 and 6. It makes the order of operations purposeful, and there is often more than one answer.
Shopping-trip estimates. While shopping, round prices to the nearest £1 or 50p and keep a running estimate of the total. Compare it with the final bill and talk about whether your estimate was close enough to be useful.
Write your own story problems. Ask your child to invent a two- or three-step problem using a real situation: a party, a train journey or a sports match. Solving someone else’s problem, then your own, shows how the steps depend on each other.
Common multiple timetables. Planning when two events will line up is common multiple work. If one bus comes every 6 minutes and another every 8, when do they leave together? The first time is after 24 minutes, the smallest number in both the 6 and the 8 times tables.

Updated 20 October 2026.