**Louise Racher** is a primary mathematics adviser for HfL

The humble tens frame paired with double sided counters. Cheap, effective and perhaps a resource underused by schools in the UK. However, once you start using it you will soon realise the multitude of opportunities there are. The ten squares support pupils’ ability to benchmark from 5 and 10 and is a highly effective route to developing the idea of ‘ten-ness’ and the pattern of numbers leading to effective calculation and number sense. High performing jurisdictions such as Singapore use this model with pupils from a very early age; it is hugely popular in Singapore, America and now increasingly in Hertfordshire.

The word *subitise *is derived from the Latin to “suddenly see”. Familiar patterns which pupils first recognise are those displayed on dice and dominoes. When they have this patterning, research shows us that they possess a greater understanding of what digits represent. Seeing patterns within patterns allows pupils to make the transition from counting towards calculating. Children who do not have a strong sense of number (i.e. actually knowing and visualising the quantity of a number) are disadvantaged when it comes to the skill of partitioning which is vital for developing both mental and written fluency.

Consider the tens frame here. There are five counters on it.

How do you know there are five without the need to count? Understanding that the top row is full and knowing the importance of the bench mark to five is another integral piece of understanding which help pupils begin to calculate effectively. Maybe you see half of 10, or you know if it were doubled it would be 10. We don’t just want our children to know 5, but all the different numbers within that number and consider the full story of five. I am sure you can visualise how this pattern would continue.

**Reflection point – how would you work out 3 + 4?**

There are many ways the pupils may calculate this total: they could ‘count all’, ‘count the three’, then the four, then ‘count them all’. They may use the power of commutativity to switch 3 and 4, starting with 4 and then counting on 3 more. Maybe they will see double 3 and then add 1, perhaps they know double 4 is 8 and so they should subtract 1. There are many more strategies we could mention; no doubt your children will come up with many wonderful ways to find this total. If we want pupils to consider which strategy they feel would be most efficient then we do rely on the children securing a true sense of the numbers involved.

Therefore with this in mind, the power of the tens frame to help build that deeper understanding of the numbers from 1–10 (and beyond – just use two tens frames!) begins to be truly harnessed. Explore some of the activities below which can help pupils to bridge from subitising with lower numbers and then start to calculate more efficiently with numbers 1–20.

**Say what you see **– Exploring the patterns they see will help children build that ability to spot numbers within numbers. The use of the double-sided counter can support pupils to show those patterns. As pupils build confidence, they may well be able to structure number sentences to explain the patterns they see. See the examples below.

**Tens Frames Flash **– Display a pattern (for about 2 seconds – to ensure the pupils don’t have time to count) on the tens frame and then ask the pupils to replicate that pattern. Discussing how they know will help you identify if they are using the benchmarks to 5 and 10. For the pattern 7, a pupil may well say: *“I saw a full row. I know that is 5, then two more. Two more than 5 is 7.” *

The pupils can build towards playing this game in pairs; one builds the pattern, and uses a book to ensure their partner can’t see, they then lift the barrier for a short time to see if their partner can build the patterns.

**Fill it **– Similar to previous game. Show the pupils an image for a short time. But this time you will ask them to only place counters where they see the spaces. This supports the pupils understanding of complements to 10.

Tens frames are easy to print out and laminate. As well as providing a structure to the pupils’ understanding of number, they also give pupils freedom to manipulate number: to move counters around the frame, to move them on or off, to show patterns they see and help them internalise number patterns which they will be able to use as they develop their calculation strategies.

Go ahead, give them a go.