And on TW, Susan Russo used difference of two squares, which I hadn't thought of.
Cool!
https://twitter.com/Dsrussosusan/status/1628146466098188289?s=20

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I am happy with those 3 versions of mentally computing 83 x 97.

Please share your #ProblemSolving strategies here or on the post https://karendcampe.wordpress.com/2023/02/04/february-calendar-problems/

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& mental math Mondays from @howie_hua

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Here's another multiplication using the area model to show double distribution.
Same four partial products as above:
80•90 + 80•7 + 90•3 + 7•3
Total = 8051

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How about decompose with a target number?

83 • 97
83•(100 – 3)
83•100 – 83•3
8300 – 249 [bc 80•3 + 3•3]
8300 – (250 – 1)
8300 – 250 + 1
8050 + 1 = 8051

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Notice that I didn't say "FOIL" above... I chose to say repeated distribution since that more generally describes the math I am doing.
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How else might I do this problem?

Double & halve isn't a great strategy because neither number is even.
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Here is problem 1.
Reminder that for #TryMathLive I am sharing my thinking process... no need to jump in with suggestions (altho your own #ProblemSolving always welcome at the end of the thread).

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Explain how to multiply 83 x 97 using mental arithmetic.