Today, before the main part of the maths lesson, we looked at an equation on the board. I asked them not to calculate it (although some couldn't resist of course);
37 + 25 = ■ + ●I asked, "What do you notice?"
Aditi started us off by saying it was balanced. Brilliant! We'd done some work on balanced equations earlier in the year, so I was really pleased to hear this as the first thing.
There were some other good points, and then Justus said the two numbers could be instead:
38 + 25
We looked slowly at what he'd done. Justus said that you could always do this, take it from one addend and give it to the other. Most of the class agreed.
That's going up on the Claims Board.
"What other pairs of numbers could we have?" I asked.
And then there were a flood of answers.
Alonso gave us:
-1 + 63
and then there were lots of sums with minus numbers in too!
James gave us:
-38 + 100
On other occasions (like this), I've used Cuisenaire rods to help in representing the pattern. Today the ideas seemed to flow so well without this, but another time I might use them again for something like this.
Sometimes I think you are reading my mind. It can be scary. I had been thinking of different ways of representing 2+3 and had imagined filling up a whole page with numbers and expression that mean the same thing as 2 + 3. If a student had to add up 2+3 and wrote that the answer was 0! + ln e + log 10 + (-16 + 18) would that be reason to celebrate or to tell her to get with the program? Let me know if any of your pupils try out this concept on their math tests...:)ReplyDelete