7 x 7 = 49 6 x 8 = 48 5 x 5 = 25 4 x 6 = 24 10 x 10 = 100 9 x 11 = 99 One of my 3rd Graders pointed this out while we were looking at the multiplication table. Great! Challenge: make a diagram that explains this to a 3rd Grade class. What I did is below... (1/2)
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Replying to @mpershan
I did these in my head in the time it took to read them. Was there something I missed? Of value that is.
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Replying to @stampingout
Of value? I have no idea what you consider of value but there is an interesting mathematical pattern here. In algebra we'd express it as (n + 1)(n - 1) = n^2 - 1.
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Replying to @mpershan @stampingout
I have a colleague who does some mental math this way ... for example by seeing situations like 33 * 27 as (30-3)(30+ 3) = 900 -9 = 891. They are quite good as seeing situations that are amenable to this structure.
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Replying to @brianwfrank @stampingout
I have colleagues that do this too! That would be a bit much to expect from my students at this point. This pattern came up when I was showing my kids a multiplication table for the first time and kids were just noticing stuff and asking questions about it.
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Whenever both factors in a product have the same parity, this trick, long popular with mental calculators, may be used. Provided one has memorized the first twenty or so squares and is good at subtraction, ab = [(a+b)/2]^2 - [(a-b)/2]^2 turns most products into differences.
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