Addition & Subtraction

Another week of Maths seminars is another week my mind's been blown open with ways of how I wish I was taught how to learn when I was in school. 

This week was all about addition and subtraction, something I thought I was pretty comfortable with. I didn't realise that there were two types of addition; aggregation and augmentation. Although the children wouldn't be aware of the two methods, it's helpful for a teacher to know the difference. If a child is struggling, it may be that one method will be easier for them to understand than the other. 

Aggregation is when there are two sets that come together - altogether would be the keyword.

Augmentation is when you start with something, and make it bigger - the keyword here would be more.

Other key phrases we were taught is partitioning and compensating. 

Partitioning is the splitting and recombining of numbers,

eg. 24 = 20 + 4

Compensating is when you add too much/little, then adjust it.

eg. 36 + 38

36 + 30 (-2)

As I didn't have much previous school experience, and the experience I did have was with older children, I was introduced to different resources we could use so the children could visualise the calculations. 

Multilink cubes are great for younger children in the enactive stage, as they can physically move around, add to or take away the individual cubes. 

Numicon is also great for those still in the enactive stage, as no only allows them to visualise the holes, but it also allows them to link a number to a colour. 

I had never seen Dienes blocks before, but they are an amazing resource to use to discuss place value. The children can visually see that ten 1s blocks are the same as one 10s block, and ten 10s blocks are equal to one 100s block. 

I particularly liked arrow cards, as this is a visual representation of partitioning. In this example, the children can see that 823 is the same as 800 + 20 + 3, and in turn, can see that 803 - 20 = 803 etc. 

One of the important messages was that we need to teach children that addition and subtraction are inverse processes. If they know one calculation, they also know the inverse. By introducing this link from the beginning, it makes it less scary to the children when it comes up later on. 

Another method to teach them is buy 1 get 3 free. For example, if you know 6 + 4 = 10, you also know 10 - 6 = 4, 10 - 4 = 6 and 4 + 6 = 10. 

When it comes to subtraction, the methods are similar, with partitioning and compensating being the inverse to the addition methods ie. partitioning is when you start with a number and split it into parts, and compensating is when you change a number and adjust it. 

Two new methods we were introduced to are reduction and difference. 

Reduction... if I have 10 cubes and I take away 4, how many do I have left?

Difference... what is the difference between 10 and 4?

It's interesting that these processes come as second nature to us as adults, but we may have struggled to grasp this concept as children. As teachers, it is our job to find which methods work best for each individual child.