The Abacus Reigns #2

So my seven year old is being introduced to “the column method” for addition at the moment. He came home very upset yesterday because he couldn’t do it. After a few questions we realised part of the problem was that he didn’t know what the word “column” meant,  (take note!).

Being the annoying maths dad that I am, I asked him to get the trusty Base-10 Abacus out. He’s not quite old enough to groan in response but it won’t be long now!

We went through the idea behind column addition and lo’ and behold it started to click. Here’s how we did it:

Part 1

Here’s his sum (above). I highlighted the units / tens / hundreds with dotted lines, and we talked about the value of each digit. We also reproduced it on the abacus.

part 2

Next we added together all of our units. With the abacus there’s a clear “oops, no more units left” kind of moment, so we talked about exchanging our ten units for a single ‘ten’ in the next column over, because they’re worth the same. This in turn brings our units to zero, as shown on the abacus above.

part 3

Now we’re adding 4 tens. Well we have 3 tens at the moment, as we just exchanged ten units, so this will take us up to 7 tens. My son slid 4 beads up and counted how many there were altogether in the tens column. And how much is that worth? “70”. Goodo.

part 4

Finally we added two hundreds to our existing one hundred, to make three hundred. (not “three”, three hundreds, which is three hundred.). Finally we read out the complete answer as three hundred and seventy.

He insisted he didn’t need the abacus for the next question, and put it to one side.

Immediately he made this mistake:

final part

He’d got into the habit of exchanging ten units for a single ten, even if there weren’t ten units to exchange in the first place! So we went back to the abacus, and guess what? No problems, because we didn’t get past six beads. There’s no mistake in the answer in the picture above because I pointed out his error mid-sum.

I’m a big fan of spending time over the basics with physical representations of stuff. Maths is tricky, and if your confidence gets shot early on, it’s not exactly helpful. He came home today and demanded we do “ten column additions!!”. Good stuff.

 

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