### An AHA! abacus moment in the life of a preschooler

I've been doing math lessons with my 3-year old using the 100-bead abacus. Usually we do a few problems where she tells me a two-digit number to make, and I tell her a number to make, back and forth. Today she asked me to make 51, and I asked her to make 68. These went smoothly since she's getting pretty good at this now.

Then we did a few "more than" problems. I said, "Let's say your sister has 5 cookies and you have one more than her. How many do you have?" This is a new concept to her, so we need to do it slowly and carefully with the abacus: first make her sister's cookies, then let her have the same amount, then give her one more.

Then we did a few subtraction problems such as 7 − 4. She moved 7 beads, then "took away", or moved the other way, 4 beads. How many were left? 3 beads. I also showed her the subtraction 50 − 10 = 40.

She started working on her own problem, "Let's do 9 − ..." and while she was thinking, I quickly proposed "... minus nine". Nine minus nine. Well, she moved nine beads (to make the number nine), then moved the beads the other direction, counting them one by one, and was left with none... and what a SURPRISE it was to her! She had to start giggling!

I immediately showed her another one, 4 − 4. She did 10 − 10 herself. And then I showed her 100 − 100, which made the greatest giggles of all!

It was just so cute I had to share. Plus, now you know several ways how to teach math concepts with the abacus.ðŸ˜Š

Then we did a few subtraction problems such as 7 − 4. She moved 7 beads, then "took away", or moved the other way, 4 beads. How many were left? 3 beads. I also showed her the subtraction 50 − 10 = 40.

She started working on her own problem, "Let's do 9 − ..." and while she was thinking, I quickly proposed "... minus nine". Nine minus nine. Well, she moved nine beads (to make the number nine), then moved the beads the other direction, counting them one by one, and was left with none... and what a SURPRISE it was to her! She had to start giggling!

I immediately showed her another one, 4 − 4. She did 10 − 10 herself. And then I showed her 100 − 100, which made the greatest giggles of all!

It was just so cute I had to share. Plus, now you know several ways how to teach math concepts with the abacus.ðŸ˜Š

## Comments

Example:

Let a**1 = a, let a**(n+1) = (a**n)x(a). Exponentiation.

Find all t such that 204**t gives a remainder of x (say, 8) when divided by p and a remainder of y (say, 15) when divided by q (p and q must be prime).

You get ridiculously large numbers, like (I'm making this up; didn't work it out) 204**(165+54n) for all n in Z+. This involves the Euclidean algorithm and also leads to Lagrange's theorem that the order of a subgroup divides the order of a group. It turns out to be rairly easy, really. Normal 8th graders can get it, if they like puzzles.

Denise

Sequel: the next day she wanted to go on and on with the same thing and giggle. I had to stop her so we'd get to do something else, too.