Demonstrating, explaining and modelling involves showing children how to do something or providing an image to help them to understand something .
Models and images help children to understand the structure of numbers, and how they can be partitioned and combined.
Some examples of practical models and images are:
- beads, counters and pegs to help children learn to count, represent quantities, to develop their own images of numbers, subitise (recognise the amounts of objects, when small, merely by looking, rather than explicitly counting) and develop early calculation skills.
- number tracks and lines, and grids such as 100-squares to help children develop their understanding of how numbers relate to one another
- bead strings and counting frames, with each group of 10 distinguishable from the next, to give a linear image of tens and ones, and to provide model of finding complements of two-digit numbers;
- place value cards, place value charts and multibase materials to show how whole numbers and decimals can be partitioned in different ways;
- £1, 10p and 1p coins to show how each digit changes when multiples of 1p, 10p or £1 are added or subtracted;
- pegboards and other rectangular arrays to demonstrate the meaning of multiplication, including the commutative principle;
- empty number lines to support, record and explain calculations, e.g. 48 + 36 = 84
Diagrams are another form of model. For example, these diagrams all model ideas associated with multiplication:
What this looks like in the classroom
Subitising is a key step in helping children to move from seeing and manipulating practically to seeing and manipulating through imagining. It is the immediate recognition of a small number of objects without needing to count them. This is a key skill in the development of children’s ability to count. Children can be helped to improve their ability to subitise by being shown sets of counters for a short period and asked to say what they saw and how many they saw.
For example, children are shown the counters below for one second:
Those children who can subitise will be able to tell you that there are five counters without having to count them all individually. They might say that they saw a group of 4 counters and another counter. They might say that they saw a group of two, another group of two and a single counter.
This sort of activity will help children to develop an image of the numbers and count them ‘in their head’. If they are shown counters arranged in familiar ways they will recognise the number even more quickly. For example, children will recognise six counters swiftly if they are arranged the same way as on dice or dominoes, rather than in a random arrangement: