# What is the name of this notation for sum?

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.

• I don't know that this has a name...it seems like a standard device to do arithmetic mentally. $17=10+7$, $15=10+5$ so $17+15=10+10+7+5=20+12=32$. I don't suppose that writing it graphically the way you present it here is terribly helpful...it all looks a bit hard to unpack. – lulu Feb 9 '19 at 22:19
• You might have better luck on matheducators.stackexchange.com – saulspatz Feb 9 '19 at 22:21

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

• +1 Indeed, that seems to be the right jargon. For a technique, even! – rschwieb Feb 9 '19 at 23:44
• Thanks a lot, this is just what i was looking for – aseques Feb 10 '19 at 20:40

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*}

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.

• It might be helpful for reference, if you work in education. No need to question the legitimacy of the question. ;-) – Mars Plastic Feb 9 '19 at 22:37
• @MarsPlastic I didn’t question the legitimacy of the question, just the focus. I am betting the person will get better results with the name of the technique rather than the name of the notation. – rschwieb Feb 9 '19 at 23:28
• Okay, I see your point now. Your answer sounded a little discouraging to me at first. – Mars Plastic Feb 9 '19 at 23:34
• @MarsPlastic It's possible that the poster doesn't even make a distinction between notation and technique. But one really ought to :/ – rschwieb Feb 9 '19 at 23:45