Today I saw an Nestle ad today targeting against Starbucks's instant coffee. The headline says something like "more taste for a fraction of the price of Starbucks".
Hmm, this is an negative ad, why you must say you are better than others? Ok, I have not tasted either products. Instant coffee just can't be better than real thing.
The word "fraction" is here is notable... so "at a fraction" usually mean "smaller". Well there is no indication of how much here. Is the fraction 99/100?
What if it is an improper fraction? Ok, improper fractions probably freak out some 5th graders. I wish all 5th graders can
tell me why they must use common denominators when adding and subtracting but not multiplying or dividing. Kids should be able to tell me why "cross-multiply" works.
Fraction is the elementary school student's term. High school students and beyond call them rational numbers.
Hmm, fractions seem to be able to represent any number. We can be as precise as we can be by tweaking the numerator and denominator.
But no! a little right triangle's hypotenuse simply can't be represented by a fraction! They... they are... irrational.
That freaks out of Pythagoras. OMG, the guy who discovered irrational numbers was killed because of that!
Even the roots are not enough to represent the circumference of a circle! Even more mysterious... they are transcendental. Ok, I know but I can't prove π and e are transcendental. Yes, you can find proofs on the web, if you can understand it that says a lot about your math ability: I am a small fraction of your ability.
Further study requires even more: the complex numbers originating from the square root of -1.
Most students stop here. (but not those who make a living as mathematicians)
1 comment:
Everybody wants a piece of Starbucks (McDonald's Dunkin's and now Nestle). Starbucks is more about being an "it" place, not about their coffee. The places without the giant sofas and hip decor will never beat Starbucks. Newer McD and Dunkin' constructions are a nice try, but where is the cozy fireplace? (answer: Panera's and Caribou's)
A fraction, in another way of thinking is "unsolved" division. You'd just write the expression up, and don't bother to solve it.
Too many kids memorize the algorithm the common denominator tricks without understanding.
Kids who study music will *snap* get fractions right away.
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