By Matt Ellis, Assistant Headteacher and Maths Lead at Eastfield Primary School.

Teaching new areas of maths, especially fractions, can be a printing nightmare in schools, as we teachers often use images to support understanding. But do all these printed visuals actually support and scaffold learning for all children?

At our school, we believe that practical resources like Numicon manipulatives need to be at the forefront of our maths teaching. Using a concrete resource that children can physically manipulate can help support all learners, no matter how quickly they ‘grasp it’.

I always teach maths lessons with a tight structure:

• I model exactly what is expected.
• The children work together, replicating my model.
• The children work independently, using the scaffold to support their learning. 

I find it helps all children:

• to engage, allowing them to understand the structure of the question
• to work collaboratively and learn from each other
• to succeed in the maths classroom and grow in confidence.

Many schools recognise how helpful manipulatives are in teaching KS1 maths, but tend to limit their use to younger pupils and for intervention. However, at our school we have found Numicon resources to be equally helpful in addressing common misconceptions in KS2 maths topics.

Here are a few examples of common areas where misconceptions arise in KS2 maths learning, and how I use Numicon resources to tackle these tricky topics with my pupils.

How do we address children adding both the numerator and the denominator together?

In our school, we start the Fractions unit by revisiting this common misconception, and we address it by demonstrating how to make the whole number first. This could either be done as a starter in upper KS2 or as a lesson in lower KS2. We have found that focusing on or revisiting this can help children understand that when we add fractions together, the numerator changes in size but the denominator does not.

Top tip: use a Numicon tile that is greater than five, as this will allow children to add multiple fractions together.

Here is how to do it:

• Select a Numicon tile.
• Fill the whole tile with different coloured pegs (cubes will also work). This emphasises the difference between the numerator and the denominator. 
• Ask the children to write the fraction represented by each coloured item. We explicitly teach that the tile represents the whole and the peg represents the part.
• Ask the children to write the fractions in a number sentence. This shows that the denominator does not change and that the equal parts when added together increase in size.

Watch the video demonstration:

How do we make sure children are dividing by the denominator and multiplying by the numerator when finding fractions of amounts?

This is another area we explore thoroughly with the Numicon tiles. We have found that allowing children to manipulate and physically place the tiles on top of each other, alongside writing the calculation, helps them to remember how to work out fractions of amounts. Depending on the cohort, we teach this as a whole lesson in lower KS2, and in upper KS2 we replace the OF with an X multiplication symbol.

Top tip: Try not to pick large whole numbers or small denominators for the practical part as this can take children a long time to make. The purpose of this activity is that all children learn the written process through making and manipulating.

Here is how we do it:

• Make the total amount in Numicon tiles. In our example the total is 20, so ask the children to show you 20 first.

• Place the value of the denominator on top repeatedly until the total is covered. If the dominator is four, place the four tiles on top of the 20. Children will notice that they have placed five fours on top of the 20.

At this point ask the children to write down the calculation underneath their model (20÷4=5).

• Now ask the children to place the numerator representation on top of the denominator representation. In our example, the numerator is three, so place the three tiles on top of each four tile.

• Next, ask the children to count in threes until they get the correct answer. At this point, ask the children to write down the calculation underneath their previous number sentence (3 x 5 = 15).

• Remove the concrete representation and children are left with the written form, which they can copy into their books.

Watch the video demonstration:

How do we convert improper fractions into mixed number fractions?

Building on from making the whole (recapped here again), we carefully introduce counting beyond one whole using tenths and going past 10/10 using the Numicon Online interactive whiteboard software.

Top tip: This is a great resource found in the workspace section and it allows us to count in tenths at the front of the classroom alongside the children.

We reveal each number/tenth as we move along the first row of ten.

Once completed, we move the row out so the children can see that we have now made 10/10 or a whole row. We continue to count beyond the whole in tenths. For example: 11 tenths, 12 tenths, etc.

We then finally focus on how many tenths we have altogether and then focus the questioning to how many whole groups of ten are being shown and how many parts of the second group are being shown. We write this down as a representation underneath.

Once this has been introduced and practised multiple times, we move on to converting between both written forms.

Here is how we do it:

• We show an improper fraction.

• We ask the children to take a four tile out, as in the written form the denominator is four.
• We then count in quarters, using pegs (marbles or cubes can also work) until we make the whole.
• We ask children to then get another four tile out (repeat when needed) and continue to count on in quarters until they reach the amount of quarters shown.

At this point, we ask the children how many groups they have made and how many parts of the final group are shown. They write this underneath each group.

Once this area has been explored and children become confident making and representing using the tiles and the pegs, we then ask the children how many groups of four go into nine and how many are left over. This enables them to make connections with division and remainders.

Watch the video demonstration:

Why do we do it this way?

We do it this way because we are all on the journey from novice to master and concrete resources can support all learning!

Click here to read Matt Ellis’ most recent blog for us on ‘Key Stage 2 Maths: how can manipulatives support teaching Perimeter and Position and Direction?’.