By Matt Ellis, Assistant Headteacher and Maths Lead at Eastfield Primary School
We often see a lot of good ideas and support from school leaders when using manipulatives for Place Value and Number, and the Numicon resources certainly do this as well. But when we move towards other areas of the Primary Maths curriculum, do we still think about how we can use manipulatives to scaffold understanding so that all learners achieve within the sequence of lessons? If your school doesn’t, you’re certainly not alone.
This is something I have changed in my practice over the past few years. My approach to Maths is that we shouldn’t pre-judge children, and that all children should experience ‘the learning journey’ within their year group expectation. We should support all learners through scaffolds, no matter how well they do in an assessment.
We find that this helps:
- engage children, allowing them to understand the structure of the question.
- children to work collaboratively and learn from each other.
- all children to succeed within the Maths classroom and grow in confidence.
- to foster a more inclusive classroom – if all children are using manipulatives then those who are working below age-related expectations won’t stand out.
Here are a few examples of other areas of the Key Stage 2 curriculum where I use Numicon resources to support all children across a sequence of lessons within the same unit.
Finding the perimeter
How do we make sure children understand that the perimeter is the distance around the outside of the shape?
I find that spending time allowing children to count the holes around the outside of the Numicon tiles helps them to grasp the knowledge that the perimeter is the distance around the outside of the shape and not the inside. This starting point could either be a lesson in Lower Key Stage 2 or a recap in Upper Key Stage 2.
Top Tip: For those early graspers, ask them to find an odd-numbered perimeter using multiple tiles. It is impossible to do, but they will try their best to prove they can. It is a great way to check that the children have counted all sides correctly.
Here is how we do it:
- select a tile (even-numbered to start with)
- mark the starting point (one of the holes in the tile)
- mark each hole around the outside of the tile using a dash. (Be sure to use two different coloured pens – one for the horizontal dashes and one for the vertical dashes)
- count the total number of dashes.
- ask the children to write their answers using dashes as the unit of measurement.
How do we scaffold the learning when it comes to finding the missing length of a rectilinear shape?
This is another perimeter objective that’s worth investing time in so children can strip back the cognitive overload that this particular objective can present. In our school, we have found that allowing children to work with a partner when using the manipulatives supports their understanding and allows opportunities for discussion and collaboration. The children develop their understanding of how the smaller lengths can equal the longest length through manipulation and practical Maths. This allows them to focus on the vertical and horizontal lines when looking for the missing value rather than becoming overwhelmed with all the measurements.
Top Tip: Use two different coloured pens or pencils (like with the first perimeter outcome). One for the horizontal lines and one for the vertical lines. This small step allows the children to see that the two smaller sides = the longest side.
Here is how we do it:
- create a rectilinear shape using the Numicon tiles
- draw along the horizontal lines using the first coloured pen
- draw along the vertical lines using the second coloured pen
- write the value (length in holes) of each side next to each line.
At this point, ask children what they notice and encourage dialogue. In this step and once the children have discussed what they notice, we model how the two smaller sides equal the longest one.
- Repeat this to see if this is always, sometimes, or never the case with other rectilinear shapes.
Position and Direction
How do we teach Coordinates using the Numicon tiles and why have we found this effective?
A misconception I find when introducing Position and Direction is that when children write coordinates, they mix the X and Y axis when identifying corners within shapes or items on a grid. So we use the Numicon tiles and the peg boards to play our version of Battleships. We have found that this supports the understanding of going along the X-axis and then up the Y-axis.
Top Tip: use at least 5 or 6 tiles. Try sticking to tiles with the greatest value as the peg board has 100 dots. This can help reduce the time it takes for a game to be completed.
Here is how we do it:
- grab a baseboard and at least 5 or 6 large tiles
- write the values of the X and Y axis along one of the horizontal and vertical lines (this could be just numbers or a mix of letters and numbers)
- sit children opposite other and put a divide between them
- ask the children to place their tiles onto the baseboard or a photocopy of one
- children take turns calling out coordinates and writing down the coordinates they call out
- once all tiles have been ‘hit’ the game is over.
How do we support the understanding of translating a shape?
Building on coordinates within the Key Stage 2 Position and Direction unit, we introduce translation on a grid by using the baseboard and tiles to physically move tiles left or right and up or down. We find that this helps children to be precise with their counting and movement of the shapes. This helps them to clearly describe where a shape has been moved from and to and helps them understand the concept in a practical rather than abstract way.
Here is how we do it:
- grab a baseboard and a tile
- pair children
- write the values of the X and Y axis along one of the horizontal and vertical lines. (this could be just numbers or a mix of letters and numbers)
- ask Child 1 to place the tile in a position of their choice
- Child 2 now asks Child 1 to move it to another position on the board by using the correctly modelled language
- Child 1 marks a corner of the tile and from that corner, counts left or right and up or down (the instructions from Child 2)
- both children now write down the new coordinates of the new position.
Top Tip: Mark the starting point and each point the child counts, so it is clear how many places they have moved. This enables you to check they are moving correctly.
There is a fine line between using manipulatives as a scaffold to support children’s learning and it just becoming an activity, where children lose the ‘why’ to the lesson. In my experience, when introducing new learning, we should invest time with the resources, but we should try to think of different ways to stretch thinking. Fifteen minutes of focused learning is usually enough time to let children grow in confidence and move onto either a pictorial representation or an abstract method.
For more insights into how to get the most out of your school’s Numicon resources with your Key Stage 2 (P3-P7) pupils, sign up to our NCETM-accredited digital Professional Development workshop ‘Progression with Numicon for ages 8-11’.
Click here to read Matt Ellis’ previous blog for us on ‘Key Stage 2 Maths: how do I use manipulatives to teach Fractions?’.