Addition by Completing Groupings



This is just a quick visualization for mental addition problems. Although you can conceptualize the first example as teaching the concept of "carrying the one," I much prefer to think of this as a representation of regrouping as a technique for addition. One of the challenges with this is that it takes a lot of words to describe something intuitive, and this is ultimately an intuitive process. But the core idea is that "8 + 6" is in some ways a slower and more complex calculation than "6 - 2" (because the numbers of the first calculation are bigger), and so it is less mentally taxing to conceptualize the latter. (Don't worry about where the 6 and the 2 came from for now.) For one digit calculations, this doesn't show much benefit, but for larger calculations (such as "378 + 257") the value is more apparent.

The process can be broken into a sequence of questions:

Example 1: 8 + 6

This animation is on a perpetual loop with random one digit addition calculations that visualize this technique. It can also be used for practice

Example 2: 39 + 7

The trick to this one is that your brain is capable of converting the 39 to a 40 with relative ease, and 40 + 6 is an easy calculation.

Example 3: 48 + 37

If you are comfortable with one digit addition (and you should be), then it's not much to ask your brain to do 5 + 3 (or really, 50 + 30). (( Animations eventually? ))

Example 4: 378 + 257

This will take practice, but once you get it you will find this is not nearly as scary as it first appears. (( Animations eventually? ))