Half plus half equals one!
When we learn maths we develop understanding through visual models – these are “mental pictures” that explain a particular idea or concept. A “visual model” can be as simple as a using the slices of a cake to represent fractions, but they can explain some pretty complex ideas in advanced maths too. In this article I’m going to explore a few of the visual models we use in primary maths.
The Number Line
Most young learners are introduced to the number line at age 5 or 6. It’s a valuable visual model for progressing learners from counting one by one with their fingers towards memory recall of their number facts. Number lines really come into their own when learners see how they can split a calculation into two stages - making it easier to do:
I’ve written a previous blog article on number lines which goes into more detail. You can check it out here.
When learners first encounter multiplication they are usually introduced to Arrays. An “Array” is just 2D stack of counters as you can see:
Arrays are great because they also explain why it doesn’t matter which way round the numbers go in multiplication. In the case above you can see that four rows of six is the same as six rows of four – which explains why 4 x 6 is the same as 6 x 4 - otherwise known as the commutative law.
The Hundred Square
The hundred square allows learners to create patterns out of ideas in maths. Take for example the nine times tables in the image above – the pattern shows us an easy method for learning the 9 times tables – you could get to 4 x 9 = 36 in two steps by thinking 4 x 10 = 40 and then 40 – 4 = 36.
In Komodo we use a variety of visual models for learning concepts in maths. This helps develop understanding and it also teaches children to think visually about maths – so when they’re faced with a tricky maths problem they’re equipped with a range of visual tools to apply. Using visual models also helps learners develop an intuitive feel for numbers – a “number sense” that will stay with them for life.