As tweeted on 10-16-14...
Pattern #1
Explore on calculator...
352×11=3872
527×11=5797
365×11=4015
Keep going!
Discuss!
Explain!
Generalize!
Pattern #2
18=9×2,81=9×9
27=9×3,72=9×8
36=9×4,63=9×7
Keep going!
Describe, extend,generalize!
Is 407×9=3663 unrelated?
COREFLECTIONS...
(1) But these are just math curiosities, Dave. They don't really tie into the Common Core, do they? Well, doesn't multiplying by 11 connect nicely to the Distributive Property:
352×11=352×(10+1)=3520+352 etc.
How about 9?
(2) My goal has always been to expose our students to engaging and meaningful mathematics. But deeper conceptual understanding results from going beyond the "Oh, I get the pattern!" response. That's where the "describe, extend, generalize" and group dialog come into play. Not to mention our guidance!
(3) Students are always intrigued by the mystery and wonder of 9 and 11. How ironic that these 2 numbers put together will forever have a negative connotation for our society. It's important for our students to understand that many of the "tricks" involving these numbers are directly linked to their juxtaposition to 10, the base of our number system. In base 8, for example, 7 would display many of these properties!
(4) The more inquisitive students can research palindromes like 3663.
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