Adding Multi-Digit Numbers Using an Abacus

Syd is actually really quick at math, but she gets frustrated SO easily, and so upset when she's incorrect, that we've been developing her skills at multi-digit addition systematically, with baby steps:

1. I had her daily building big numbers using Base Ten blocks for about two weeks, long after it was very, very easy for her. It's a good review!
2. I daily gave her a page of multi-digit addition problems that don't involve carrying, to complete by building both number using Base Ten blocks, physically combining them, and then counting the total. Syd was ready to move on from this activity after just three days, because that's a tedious way to add!
3. Because she found combining Base Ten blocks tedious, I was able to introduce the abacus without a tantrum by saying, "Hey, I do know a quicker, easier way to work these problems. Do you want to see it?" Mwa-ha-ha!

An abacus is dead easy to use, and almost completely interchangeable with Base Ten blocks, as well as intuitive for a kid who's used to them. We're using a vintage Playskool abacus from my own childhood--

but any elementary level abacus looks about the same.

We call the bottom row the units row, with the next row up the tens, and the next row up the hundreds, etc. At first, to work the problems, I showed Sydney how to simply build the first number on the abacus, using the units row and the tens row, and then to build the second number by counting on. So, for instance, first Sydney built, say, 14, using one ten and four units, and then built the number 34, adding three tens to the tens row and four more units to the units row. For carrying, I pulled back out the Base Ten blocks, and reminded Sydney that every time we had ten units, we needed to exchange that for one ten; it works the same on an abacus, but even easier, since there are no mistakes to be made. Every time you have ten units on an abacus, you HAVE to exchange it for one ten, or you can't continue to add the units!

Syd worked her multi-digit addition problems on the abacus for a solid week--

--quite happily (thank goodness!), and then I said to her, "You know what would be even easier?". I gave her a page of problems that don't require carrying, had her complete the first one the way that she was used to, then used her results on the abacus to point out that you could also solve this problem on paper simply by adding the ones, then the tens. She compared her answer when she did this to the answer that the abacus gave, tried both ways for a few problems, then decided on her own that solving these problems on paper is EVEN quicker and easier, yay!

Syd's now in the middle of her second week doing this, and although I haven't introduced carrying yet, I did introduce longer multi-digit numbers this week. You should have SEEN the fit that she threw when she saw that I wanted her to add a three-digit number to a three-digit number, up until the second that she realized that it was no different, and no more difficult, than adding two-digit numbers.

Sigh.