In year 5, multiplication and division focusses on identifying multiples, factors, prime and composite numbers, multiplying and dividing numbers using formal written methods, multiplying and dividing numbers by 10, 100 and 1000, understanding square and cube numbers and solving problems with all of the above.
This page aims to provide you with all the Year 5 Multiplication and Division National Curriculum objectives, along with some guidance for each objective and a range of games and activities that can be used to meet the learning objective in a play-based way.
Teaching Year 5 Multiplication and Division:
| National Curriculum Objective | Things to think about … | Playful Learning Games |
| Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers. | Children should be familiar with the term ‘multiple’ but ensure that children are aware that a multiple of a number is any number that is in its times-table and it is what you get when you multiply a number by an integer. In year 5, children now find sets of multiples and start to make generalisations about them, e.g. ‘Find a rule to test if a number is a multiple of 8’. Concrete resources and the use of arrays are effective ways to help children understand and see patterns within sets of multiples, with the aim of them eventually being able to use times table knowledge and rules of divisibility. In year 5, children are also taught the term ‘common multiple’. In year 4, children learnt about factor pairs and this is continued in year 5, with children being clear between the difference between multiples and factors. They will also learn about common factors, factors that are shared by two or more numbers. | Multiples: Times Table Spot Spot the Common Multiples Factors: Factor Find Find the Factor Pairs Factor Dice |
| Know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers. | Children should use their knowledge of factors to help them identify prime numbers, numbers with only 2 factors and also composite numbers, numbers with more than 2 factors. The vocabulary and definition surrounding prime numbers should be looked at carefully as children can often become confused with this. It will become clear that most prime numbers are odd numbers but avoid misconceptions that every odd number is prime and also forgetting that 2 is a prime number. It can often be confused that 1 is a prime number when it is not. | Prime Cafe Is It a Prime Number? Factor Dice – Prime and Composite Numbers |
| Establish whether a number up to 100 is prime and recall prime numbers up to 19. | In year 5, children should try to remember and recall the prime numbers up to 19. The use of the games created should help them to remember and recall them. | Don’t Pick the Prime Prime Cafe Is It a Prime Number? |
| Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers. | Children have had experience in year 4 of multiplying a 3 digit number by a one digit number and in year 5 they will continue this with multiplying 4 digit numbers by a one and two digit number. Place value counters and charts are useful resources to use when first meeting this objective and the grid method when moving onto multiplying by a two digit number. Common misconceptions are similar to other formal methods of calculations, including not multiplying by zero correctly or not exchanging correctly. | Calculate and Find – Yr 5 Multiplication |
| Multiply and divide numbers mentally drawing upon known facts. | This objective is important so that children begin to choose the correct method for the calculation they are working out. We don’t want children using a formal method of multiplication or division when a simpler and more time-effective method could be chosen, such as partitioning, using known facts, factor pairs and number lines. | Find the Operation |
| Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context. | It’s important to recap short division methods that were taught in year 3 and 4 for this objective. Use of place value counters and part-whole models are useful for children to understand this objective. One of the main misconceptions is children working from right to left (as they do with addition, subtraction and multiplication) rather than left to right. | Calculate and Find – Yr 5 Division |
| Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000. | In year 4 children learnt to multiply and divide by 10 and 100 and now continue to develop this further by multiplying by 1000. Place value charts are a really useful tool for this objective and children should be secure in knowing in which direction the digits move when they are multiplying and dividing. | Multiply and Divide by 10, 100 and 1000 Decimal Dash |
| Recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3). | Square numbers – the result of multiplying a number by itself. Cubed numbers – the result of multiplying a number by itself and then by itself again. Visuals are a really good way to help children understand these concepts – see ‘Square It or Cube It’ for an activity suggestion. Common misconceptions can be that children see the notation for squared or cubed mean that you multiply the number by 2 or 3, rather than itself. | Square Number Bingo Square It or Cube It! |
| Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes. | This objective uses all of the skills learnt above to apply to multiplication and division. | |
| Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign. | This objective uses all of the skills learnt above to apply to multiplication and division. | |
| Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates. | This objective uses all of the skills learnt above to apply to multiplication and division. |