The teaching model (using materials, then screening them before progressing on to using numbers alone) is a key feature of the Highland Numeracy Progression and is used to support conceptual understanding. Other ‘schemes’ or ‘programmes’ sometimes refer to this as CPA (Concrete-Pictorial-Abstract).
Although having something physical to manipulate is most likely more effective initially to support many children’s understanding, sometimes we don’t have the resources available or we want to show something to the whole class at one time. These free apps from ‘The Math Learning Centre’ are a great resource that can be used to support conceptual understanding. They can either be used as a web based app or for those who are using Chrome books, you can download the app from the Chrome Store.
One of my favourite ones on here is the ‘Partial Product Finder’. It’s a great resource to support children’s understanding of how you can partition numbers additively to make a multiplication problem easier to solve.
- Children can see visual representations of different ways that numbers might be partitioned.
- It also allows children to see clearly and easily the link between multiplication and area (hence the name ‘area model’)
- It could support links to a more abstract ‘area model’ where every individual square didn’t need to be drawn out/represented.