Developing conceptual understanding and procedural fluency in maths: Multiplication

Thank you to Caroline Clissold for this guest post.

Last month we focussed on helping children to develop their conceptual understanding and procedural fluency in addition and subtraction through looking at their progression and the effective use of manipulatives. This article explores multiplication and suggests ways that you can help children develop their conceptual understanding along with procedural fluency in this operation. Look out for a future article exploring division. As mentioned last month conceptual understanding is best achieved when the children are given manipulatives and visual representations. So the recommendation is that these are used throughout the school particularly when teaching something new, for example, a formal written method for:

  • addition in Year 3
  • multiplication in Year 4
  • division in Year 5
  • multiplying one-digit numbers with up to two decimal places by whole numbers in Year 6

Here is a suggested progression through multiplication: There are two structures for multiplication. These are scaling and grouping. Scaling (ratio, increasing in equal parts of something)A1P1     

Scaling or ratio first appear in Year R, when the children begin doubling.

Grouping (repeated addition)


As with addition and subtraction, early stages of multiplication can often involve a lot of counting. Cubes or similar manipulatives can take some of the counting away. Last month we suggested putting cubes together to make the numbers to 10 and then use these as manipulatives for simple addition and subtraction. These are also a great resource for simple multiplication.  



A1P4 without words

4 cubes multiplied by five equals 20.

Put four together five times and they match two blocks of 10 which is 20. Of course, if you have Numicon, then you can use that equipment! Straws and bead strings are also useful resources which help the children to develop their conceptual understanding of multiplication as grouping. A1P5 A1P6

In both key stages arrays are a key strategy for multiplication and division. They help to show the commutativity of multiplication and its inverse relationship with division, for example,

A1P7 with wordsA1P8 with words

20 divided into groups of 4 equals 5

  Arrays are also a good introduction to the grid method. A1P9A1P10 Modelling the array and the grid method are a good introduction to the written method. A1P11A1P12

To help the children develop their conceptual understanding, it would be good to model this on your whiteboard, have the children copy you with manipulatives and alongside this show how the written method works. When the children begin to multiply decimals, it is suggested that you repeat this process. Come back soon for our post on division!


Computing and ICT, Mathematics

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