When the answers don’t match, I agree with Christopher, it opens up an interesting conversation about place value. Moved on to the partial products and transcribed the same products from the lattice. Looking at this, my first thought is that the student did the lattice first (one of my least fav methods), where the digits are separated to not denote place value and put the answers in the boxes. That is, I would much rather that the boy wonder where the 210 in the partial products algorithm disappears to in the lattice. The contrast became a good learning opportunity.īut I do find it troubling that the abstraction of the lattice led to mistakes in the partial products algorithm, rather than the other way around. Is 7×3 in this problem really seven times 3? We agreed that it was 7 tens times 3, which is 21 tens, or 210. As parent of this guy, I used his noticing that the answers didn’t match (by a lot!) to turn the conversation towards place value. I am not the teacher in the classroom in question here, so I cannot say how this error, and others like it, gets dealt with. But efficiency is at the cost of thinking. The lattice (like the CCSS-mandated standard algorithm) implores us not to think about place value as we work. The task was to do a set of multiplication problems two ways-once with the lattice algorithm, and once with the partial products algorithm. To be fair, the student in question *did* notice the two different answers, which led to my noticing them, which led to a photograph and the submission to math mistakes.įrom my perspective, this is an elegant example of Constance Kamii’s claim that algorithms unteach place value.
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