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October 31

Base-Ten Shortcut

Hello. I'm trying to teach some mental math shortcuts to elementary students. We've been look at what I've called the "base-ten shortcut:" x + 9 = x + 10 - 1; x + 8 = x + 10 -2. With two digit subtraction, it gets a little hairy (and maybe rendering it useless). I'm not sure how to explain the maths of a problem like 79 - 46, which would become 80 – 50 -1 + 4. Why subtract 1? It would seem that you should add 1 because in the addition version of the shortcut, you must subtract both digits in the ones place. Are there maybe 4 or 8 versions of this that I'm missing? Is there a real name for this shortcut? Thanks, Schyler (exquirere bonum ipsum) 14:39, 31 October 2014 (UTC)[reply]

these tips or stuff similar to it are highlighted in this fancy website which also may be of use to you when teaching. specifically sections on "Aim for 10" and "compensation method", the latter of which recommends that, in a problem like 79 - 46, you need only perform that trick for one of the two numbers..doubt there's a formal name for mathematical shortcuts however ~Helicopter Llama~ 16:42, 31 October 2014 (UTC)[reply]

Seems kind of silly to use a shortcut for 79 - 46 since there's no borrowing involved. But the reasoning being used is probably 79 - 46 = (80 - 1) - (50 - 4) = 80 - 50 - 1 + 4. The idea might be more useful for something like 76 - 49 = 70 + 6 - (50 - 1) = 70 - 50 + 6 + 1 = 27. Or how about 233 - 89 = 200 + 30 + 3 - (100 - 10 - 1) = 200 - 100 + 30 + 10 + 3 + 1 = 144? --RDBury (talk) 17:50, 31 October 2014 (UTC)[reply]

Thank you for the replies. I like that website, HL. Also, thanks for that connection RD, it will help me to activate the students' prior knowledge better. Schyler (exquirere bonum ipsum) 18:39, 31 October 2014 (UTC)[reply]