Order of Operations

From Deb:

We had a good first day back after vacation today. I mean yesterday, it's past midnight.

Madison, who has finally decided to take control of her own multiplication table learning, asked to create a 10 x 10 grid so she could see which ones she knew by heart and which she didn't. I printed out a grid from Excel so she didn't have to waste hours trying to make a nice one with rulers, etc. She completed all of the blank spaces, sometimes knowing the answers by heart, sometimes having to figure them out. I used it as our handwriting lesson, too, and believe it or not she was kind of enthusiastic about making it look nice, so things looked better than normal. She still kept reversing the 6's, though.

After she completed the grid, she had me test her on the tables. I put a small dot in the squares of the ones she knew by heart. Then, she took a highlighter marker and colored in all of the squares of the ones she knew, leaving the rest white. She figured out that she didn't know 38 of them, which translates to roughly 20 that she has to memorize since many of them are the same backwards-forwards.

20 seemed so manageable to her. She's going to devise strategies for doing the memorization. I'll leave her be on that for a while.

So that was the scheduled part of the day. But I love how sometimes learning happens just spontaneously rather than having been planned.

We were eating out for lunch (I want to mess up the kitchen as little as possible because of potential buyers seeing the house), and she asked me the difference between answers to equations that people knew, versus ones they had to figure out. So, she asked me, "Do you know the answer to 10 times 10 minus 10 plus 10 times 10?"

We then talked about how knowing the answer to parts of it makes the other parts easy to figure out, and that no one has memorized the answers to problems that have more than 2 steps; pretty much you just have to know the multiplication tables and your addition facts, to be able to do things that are much more complicated.

And THEN I gave her a shocker, which is that the answer to her question depends on how you group the parts of it. Really? The answer can be 1000, or 190, or 200, and probably others, depending on whether you don't use any parentheses at all to group them, or put parentheses in certain configurations. We talked about My Dear Aunt Sally as being the way to memorize the Order of Operations, and we did a couple of problems on napkins, both her above problem and things like

3 x 4 + 4 = 18
if there are no parentheses, and that this means

(3 x 4) + 4

But if you use a different set of parentheses like this:

3 x (4 + 4) then the answer is 24.

She loved this. She's glimpsing the fact that there is cool math beyond the multiplication tables.