Use "reduce ahead"
12052017, 09:26 PM


I start this lesson sequence with "If I multiply [student name] by one, he/she is still [student name]." Continue this silliness, and start to substitute 3 over 3 for the one. Then exaggerate with something like 3,492 over 3,492. This focuses the multiplicative identity concept. Then reverse it with questioning if dividing by one or a form of one has the same result.
When we get to actually multiplying, I introduce "reducing ahead" so that I don't have to do "big arithmetic." Students really buy into it when they see that it saves them a mess at the end of the problem.This "simplifies", pun intended, the work.
This idea also ties in to other topics when we think about what's inside numbers. As PP suggested, seeing the numerators and denominators as their prime factorizations, which lends itself to finding the giant ones (ones in fraction form).
