Thursday, June 30, 2016

Why do math problems always involve pizza?

I feel for this woman. And yet... it's pretty damn funny, innit? 
This video should be played on the first day of every Grade 8 math class in schools,
just to show kids it's worth it to pay attention.

I've not been posting for a while because, well, I've been busy doing math (and a lot of other schoolwork). A few weeks ago I wrote the test for rate & ratio and got 95%, and on Thursday, I wrote the geometry test and got 90%. This is pretty amazing to me, considering I was the kid who froze at just the sight of numbers and failed both Math 11 and 12. Granted, the math I'm doing now covers Grades 8-10, but still, I'm doing a lot better at it then I ever did before. So what's the deal?

How does a math-phobic person go from not getting that a whole pizza is always a whole pizza no matter how many ways you slice it, to getting an A in geometry?

I have two hypotheses: 
  1. You need to have a purpose. I care to try now because I have a purpose behind understanding and getting a good grade in the subject. (If you want to do a psychology degree you have to take stats and research classes, both of which require a C- or better in Math 11), and... 
  2. You need to be an adult. I'm far less distracted outside a high school classroom, working at my own pace, on my own time, with the confidence that comes with being a grownup who figures, if a 13-year old can do this, why can't I? I've wanted to overcome what I feel must be dyscalculia since I failed math in Grade 12, and I don't want to go through the rest of my life thinking of myself as unable to deal with numbers. 

What's the secret to word problems?

Here's an example of a type of math problem that used to freak me out immediately: 
Dan works at a pizza shop. For every three cheese pizzas that Dan makes, he makes one mushroom pizza. If he made 12 mushrooms pizzas, how many cheese pizzas did he make?
The first step is to figure out what the question looks like without all those confusing words – what's the equation that we're being asked to solve? Well, in this case, it's these fractions:
What is x if 3/1 = x/12?  Well, x = (3x12)/1
So, if for every three cheese pizzas, Dan can make one mushroom pizza, then this should be expressed as a ratio of 3:1 (or a fraction of 3/1), and if the ratio we're looking to solve is x:12 (or x/12), then we need to cross multiply (the numerator of the first ratio and the denominator of the second ratio) to get a new numerator, and the denominator is the leftover denominator of the first fraction. Therefore, 3x12 (divided by 1) = 36. So the ratio we're looking for is 3:1 or 36:12, therefore...
Dan can make 36 cheese pizzas for every 12 mushroom pizzas that he makes. And somehow this makes sense to me now. Miracle of miracles. I can even convert fractions to percents, and percent to decimals. Here are a quick few rules of thumb:

  1. A percent (x%) expressed as a fraction is that number over 100 (x/100)
  2. A decimal (0.00) expressed as a percent (0%) requires the decimal move two to the right (so, 0.08 = 008. = 8%)
  3. A percent (x%) expressed as a decimal (0.00) requires the decimal move two to the left (so, 50% = 0.50)
  4. A fraction (x/1) expressed as a percent (x%) requires changing the fraction to a decimal, and then from a decimal to a percent, as above. 

And that's how you slice a pizza. Next up, algebra. Two units of that and I'll be ready for Math 11 in September. Hopefully it will be the last math course I ever take, but I have to say I'm actually kind of enjoying the work, and I'm determined to do well so I can cross this one off my list. 

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