Tuesday, January 24, 2012

Following the Child: Our 3-y.o. and Addition

Every morning, without fail, our two older girls do math. It goes without saying that after breakfast they grab their math books and get started. So I guess it was only natural that our 3-y.o. wanted to do math, too.

Seizing upon her interest, over the past semester I introduced most of the math basics: the red and blue rods, the sandpaper numbers, the spindle boxes, numbers and counters, numbers 11 - 19, introduction to the decimal system, the "crisis of 9s," etc., until I got to the point when I thought she was ready for "shell math," an activity I read about in the New Child Montessori curriculum guide I bought a couple years ago (the other big Montessori investment we've made since our original purchase of Montessori materials four years ago).

Using addition sentences and answers from Montessori for Everyone (which I printed, laminated, and cut out), she would choose an addition sentence, choose the appropriate number of shells, and then find the appropriate answer card (here she is showing 1 + 1 = 2 and 3 + 5 = 8):

(For the shell math activity, I would select, say, 7 different math sentences and their corresponding answers; then I would set out the 7 answers in random order so she wouldn't be overwhelmed by all of the possible answers, a tip provided by Montessori for Everyone -- thanks!) 

She got so good at shell addition that I decided to see how she would do using stamp game units instead of shells; also, rather than matching an answer with a sentence, I wrote columnar equations and then let her write her own answer (here she is working on 4 + 4 -- she gets 4 unit stamps, 4 more unit stamps, lines up all the stamps, then counts how many she has altogether): 


She keeps the sandpaper numbers close by in case she needs help remembering how to write a number:

She got so adept at doing addition with stamp units that I ran out of equations -- there are only so many combinations you can do that add up to nine! 

I wanted to introduce equations with sums up to 18, but I wasn't sure how to do it. I didn't think she was quite ready for the full-blown bank game, and the addition strip board and addition charts didn't seem like they'd hold her interest. I was curious to see how she would do with a modified version of the bank game, so first I reviewed the overview of the decimal system and the "crisis of 9s" with her:

When she spontaneously said to me, "Mommy, I can make 10 like this..."

"...or like this..."

I thought she was ready! So here's how we did it:

First, I wrote some equations with sums up to 18. Here, she's working on 4 + 7:

I gave her a bank with 10s and units:

She puts 4 units in one cup, and 7 units in a second cup:

She pours all of the units into one cup:

Then she starts counting units. When she gets to 10 units, we say, "Stop!"

I remind her that there is "no such thing" as 10 units -- there's only one ten -- so she gives her units back to the bank and exchanges them for one ten:

She's left with one ten and one unit, so we get the number card for one ten and the number card for one unit, and she reads her answer to me: "One ten and one unit are eleven."

She writes down her answer, and voila!

She really seems to enjoy it and she's thriving, so even though it's a little unconventional, we're going to keep going with this fun modification of the bank game (bank game lite?) and see where she leads...

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