 bombaysapphire: weebecka: If there are two routes through division, why would there only be one route through multiplication since the processes are inverses of each other?
The two routes through division arise because multiplication is commutative: 3 x 7 = 7 x 3 so if I split 21 into 7 groups there are 3 in each group. If I split it into piles of 7 then there are three of them. I could postulate the argument that because multiplication is commutative so is division since the process are inverses of each other. That is not the case.
Nice logic. The reasons for there being two routes through multiplication because there are two routes through division are, however, more compelling than division being commutative because multiplication is. Addition is commutative but subtraction is. Yet the ways of picturing addition and subtraction link easily to each other. I didn't feel the earth tremour by the way. bombaysapphire: How long do you find your starter takes weebecka? If it generates meaningful discussion then it must be difficult to keep it to a short timeframe.
If you just do one pair of numbers it takes, on average, pretty normal
starter time (5 mins ish). Sometimes I allow a bit longer because it's
worth it. I find it easy to set up because I just write SDPQ and two numbers on the board, then can focus on settling the class and dealing with issues as they arrive. I always make them write the words - sum, difference, product, quotient before their answers. They hate me for it but they sure know the vocabulary. bombaysapphire: I have found that different "always, sometimes, never true" activities are a good way to generate discussions which I would guess cover similar areas.
I like always, sometimes, never activities a lot - they keep students working and discussing efficiently at the boundaries of their knowledge. But I don't really find they cover the same area.
|