What is the name of this notation for sum?

Question

In my kid's school (age 6) they are using a variation of cuisenaire rods to learn mathematics. When they are doing the operations on paper the notation used is this one:, it's designed to ressemble the usage the make of the rods. I'm curious about the name it has and to look into references on it.

Answer 1

It's called addition by partitioning. One can partition a number into its digits, tens, etc. and then add these seperately.

Answer 2

Is the notation important?

To me, this looks like a graphical description of an arithmetic technique called adding from left to right.

It seems to outline that process. It is an old mental arithmetic strategy. After you master this technique, no notation is necessary. So that is why I question the importance of knowing what the notation is.

I first saw this in the first chapter somewhere of How to Calculate Quickly by Henry Sticker.

Answer 3

It is worthy to note that, in spite of the particular way we write it, the name of the properties which make the notation work is commutativity and associativity:

\begin{align*} 17+15&=(10+7)+(10+5)\tag{by the definition of 17 and 15}\\ &=(10+7+10)+5\tag{by the associativity}\\ &=(10+10+7)+5\tag{by the commutativity}\\ &=(10+10)+(7+5)\tag{by the associativity}\\ &=20+12\tag{by the definition of 20 and 12}\\ \end{align*}