How did you learn addition? It was probably pretty straightforward, something like “start in the 1s column and add those first,” then “carry” if necessary, and move on to add the numbers in the 10s column.

Many children today use the traditional method that we were taught, which is still an acceptable way to complete addition. However, using this method, many students lose the concept of place value or end up memorizing a procedure with a concept they don’t understand. Let’s take this example: 18+8. Many children will put the 18 in their head and count forward by ones until they’ve added 8 (18+1+1+1+1+1+1+1+1=26). As long as there are not errors in the counting, this works.

There is nothing wrong adding this way, however as numbers start to get bigger, this method can get cumbersome. But even more importantly, as we expect children to solve more complex math problems in the future, they will need to have a deeper foundation of number sense upon which to build and we can clearly see that this method is not promoting the skills they need. Instead of one-to-one counting, a child must learn to use their number sense to help them solve addition problems more efficiently and effectively.

In this week’s Math Mania Monday (Facebook Live Video), we featured some great strategies to help students on their journey in addition. Specifically, we featured decomposing/composing, compensation and partial sums as ways to solve addition in which students are using number sense instead of one-to-one counting. These methods allow students to explain their mathematical reasoning in a way that articulates higher order thinking and will in turn help them as they learn higher concepts in math. These same strategies can be used with whole numbers, decimals, fractions and measurement units.

Be sure to check out the video (inserted below) that explains these strategies in further detail, and scroll all the way to the end for a great one-pager for your reference!

### Addition Strategies:

Decomposing/composing:

Compensation:

Partial Sums:

Traditional with Place Value Discs

Use this addition helper sheet to have your students go beyond the traditional, and really show you how much mathematical power they have!

Get all the strategies for addition, subtraction, multiplication and division in one document: Three Ways + The Traditional

Dewi Williams says

Love the place value discs, I think the more of this kind of visual activity you can do the better – can be so much more engagin than a dull textbook!