Today I had one of the best classes so far in my career. And it happened when I went completely off book.
We were working on writing equations for systems of equations word problems. I want them to solve without a calculator but these particular problems were gross without one, so I just had them ID their first step and we talked about the different ways to solve particular problems. Which led to a conversation about which numbers were "easier" to multiply by hand...
I of course mention in passing that I had been thinking about why I don't like multiplying by 7 the other night when I couldn't sleep. (I then clarified that I do have a life sometimes...). So I wrote some numbers on the board and we talked about the patterns that made numbers easier to multiply.
Some ones that they hadn't heard of were 11 (10 +1), 9 (10-1) and 5 being (10/2) which then makes 15 easier.
My students had so many ah-ha moments and were so engaged in the conversation. They wanted me to go back and teach the third graders to see math this way. We talked about how I never learned math this way and have only recently (thanks to the #mtbos ) begun trying to think of numbers this flexibly. It was amazing to see their eyes light up as we talked.
I've already digressed before in this class (basically 9th grade Algebra I) about different ways to subtract. But I think this is important for several reasons
1) Allowing them to build number sense
2) Seeing multiple methods to solve
and 3) Help them see math as creative and flexible
And when half their state final is without a calculator...these skills are even more valuable.
But back to the title...
We also perhaps digressed even more briefly into the concept of bases. To me this brings up the "why?" and "what if?" which I believe are the central questions in mathematics. One of my very inquisitive students said her last math teacher asked her to stop asking "what it?". I can't even begin to convey to you what my face looked like. It literally brought tears to my eyes (which of course they noticed) as I emphatically begged her to keep asking that question. "I have taught you that is a great question to always ask, right???" "Yes, Ms. Hester...don't worry" *whew* Good...
And what followed was a great conversation about math, the beauty and patterns in math and the importance of asking questions.
It might not be on my pacing guide, but I hope that later students will remember today as a day that they really experienced and saw math in a different light.