Demonstrating, explaining and modelling involve 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.
Careful choice of models and images can help children develop conceptual understanding, but it is important that the model or image you use helps children see the underlying structure that you want them to think about and doesn’t unintentionally limit the development of their understanding.
For example, if the only visual model of fractions that children see is the ‘chocolate bar’ image:
then they may fail to understand sufficiently the importance of fractions of a whole being equal sized divisions of the whole. They also need to see and discuss other shapes that have been divided up in different ways in order to explore this essential concept, for example images such as:
Images like these have the potential to help children develop a deeper conceptual understanding of what fractions are as they discuss why in each case the left hand image represents thirds but the right hand image does not.
Models and images for understanding and manipulating numbers in Years 1 to 3 is a very useful resource with a wide range of models and images to use in your teaching.
What this looks like in the classroom
Some examples of practical models and images are:
- number lines, tracks, grids such as a 100-square, to help children to see 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:
7 × 3 = (5 + 2) × 3
= (5 × 3) + (2 × 3)
= 15 + 6
||This is 27 × 30
||This is 27 × 4
||This is 27 × 34
12 × 6
Related information and links
How can practical resources support the development of mathematical understanding? is part of an NCETM CPD module.
Models and images - are you stuck in a rut? has ideas for some different models and images to support learning.
From Objects and Images to Mathematical Ideas and Models in Mind are NRICH discussion papers.