Tuesday, 7 April 2015
A mastery approach to maths includes the careful use of appropriate models and images to represent the mathematics to children, helping build procedural and conceptual knowledge. When considering all the resources out there to use, I am a big fan of ten-frames and twenty-frames  - rectangular frames into which counters are placed to represent numbers.

Children use these to model and visualise numbers to 20 and develop different mental strategies for manipulating these numbers. This resource is based on the Slavonic abacus (as advocated by Tandi Clausen-May) and represents quantity through a concrete and visual representation. Regular, repeated practice with it builds up a strong mental image for the child to get a 'feel' for number.
It builds on the idea of children subitizing – recognising and discriminating a small number of items, in this case counters. This is supported by grouping the counters in a frame of 5, which has been shown as just about the maximum number that people recognise without counting. Children are able to ‘see’ the number 5 and then can quickly ascertain other numbers or addition facts from this. If children can just 'see' 5 counters they don't have to count to recognise 7 counters, for example, they just know it is 2 more than 5.
This image is from a German twenty-frame app from i-tunes. There is also a website to access this online - all instructions in German, but the activities are accessible and effective.
I particularly like twenty-frames to help children learn the addition facts to 20 when crossing the tens. You just need two sets of 20 counters of two colours and a 5 x 4 grid – I’ve attached a file below that you can use with counters and number cards.

If we take 7+5 as an example, children can be asked to show this addition on the twenty-frame.

Alternative arrangements demonstrate and reinforce the different ways that 7+5 can be represented:

This can be seen as 6 + 6

This can be seen as 5 + 2 + 5

This can be seen as  10 + 2

So the ‘story of 12′ is being explored, while modelling 7+5 in different ways. Talking this through and asking them to explain their thinking gives a real insight into the way they visualise a calculation.

Download and print this twenty-frame and use with 2 sets of coloured counters.