# Double sided counters

Updated: Oct 10, 2020

The models and images used in this blog are available to download at the end of the blog.

Double sided counters are nothing new to mathematics classrooms. These small plastic discs are versatile and can be used across the curriculum to unlock and deepen mathematical concepts. Here's how:

Double sided dexterous delights can represent and expose the structure of numbers from Early Years to Key Stage 3 and beyond. Using them with a place value grid allows focus on the value of each digit, understanding of the authority of the the position of digits in numbers and reading of numbers.

One of the most simple ways can be using 5 frames and 10 frames. Children may show number bonds to 5 and 10 to show the depth of their understanding in key stage 1.

In key stage two, where keeping 5 and 10 frames may still be effective, counters may represent different values (such as one counter representing 5 or 10 etc). They may also be used to represent decimals, fractions and percentages. For this reason, they have strong relationships and effective links with addition and subtraction.

Using them to introduce the concept of more than and less than can be a powerful way to introduce the concepts.

A number square and one double sided counter to obscure a number can be a powerful activity to develop reasoning and fluency around number. Finding **one more**, **one less,** **ten more** and/or **ten less **may be a good starting point for Key Stage one. *Changing* the language and questioning used can deepen the task for children at Key Stage two. **Find the number that is ten more than ten more than 41**, for example.

Introducing and strengthening understanding of inequality can be also achieved with double sided counters and lollipop sticks.

The activities above use carefully chosen numbers and positions of the counters to allow the tasks to be opened up to asking "**What is the same, what is different?**".

We spoke earlier about using 10 frames, part-whole models, 100 squares and number tracks for addition and subtraction. But how might double sided counters be used in Key Stage two and beyond to support addition and subtraction?

Using double sided counters can anchor the gap between concrete, pictorial and abstract representations of mathematics. The images below suggest how this could be achieved as children progress to standard methods of addition and subtraction. Children would physically combine the counters for additions to calculate the **sum** and remove counters from the whole number for subtraction to leave the **difference**.

These also allow for the authority of the place value to be a focus to keep learning tight on the value of the digits.

**Multiplication and division.**

Introducing multiplication as repeated addition is essential for understanding multiplication. Showing multiplication,* including doubles and halves, *can be a great way to start.

This can then lead to arrays to represent multiplication. Having children draw the representation and then write the equation can deepen children's conceptual understanding for how multiplication works.

The way children align and set out counters can prompt deep conceptual thinking as to the commutative nature of multiplication.

Division by grouping can similarly be an effective way to share and divide a whole.