I mentioned this problem from one of my earliest blog posts with one of my students last week, so I thought I'd bring it back as this week's Math Journey. Enjoy!
The SAT messes with your head. Don't feel embarrassed, it messes with everyone's head. It's designed to. The SAT is a test of your critical reasoning skills, meaning it's actually far more about logic and figuring out the correct course of action than it is about actually knowing the material. This is nowhere more evident than on the Math section.
The SAT Math trips up so many students because they expect it to behave like a math test. The truth is, the SAT Math is about figuring out how to answer each problem using as little actual math as possible. It's all about working quickly, and the questions are structured such that they conceal the quick logic and context-based route behind the facade of a more complicated math question. They're trying to psych you out; to make you...
Since it's Thanksgiving week, let's think about pie for a second. No, not mathematical pi, just actual real edible pies. For Thanksgiving I'm in charge of making dessert, so I'll be bringing two pies, one pumpkin and one apple. Let's say that I sliced the apple pie into 12 pieces, and the pumpkin pie, since it held together better, into 18.
Fast forward to the end of the evening. My pies were a big hit, and I have almost none left. In fact, all I have is three pieces of apple and four pieces of pumpkin. I want to combine the remaining slices into a single pie pan, so that they take up less space in the fridge. How do I figure out if my remaining pie will fit in one pan?
Well, let's start by writing down the remaining amounts of pie in the form of fractions. Remember, one of the definitions of a fraction is parts of a whole, so let's apply that definition to figure out our starting fractions.
The apple pie was cut into 12 pieces, and we have three out...