## Wednesday, September 24, 2014

### The sum of 2 pos int is 216, gcf=24 -- PUFM and Common Core

The sum of 2 positive integers is 216 and their gcf is 24. Find all possibilities.
Parents/Teachers/Students...
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REFLECTIONS
To solve the problem above without Guess-Test-Revise requires a more (P)rofound (U)nderstanding of (F)undamental (M)athematics - thus the acronym in the title. (Research Liping Ma for more info).
Students may find solutions by playing around with multiples of 24 on their calculator and that is a good thing. That's how we learn. But...
How many  will discover without our guidance a systematic approach to finding the 3 pairs of numbers. A method which makes sense to them and can be applied to more complex problems...
I believe there are BIG IDEAS, aka Fundamental Arithmetic Principles, embedded in this innocent question. I've said enough...