Mathematical modelling (and how to prepare for exams!)
[PSLE Maths and up: Mathematics Modelling for Teachers]
Kept you waiting, huh?
You'll find this post to have a somewhat unusual approach compared to the sort of high-quality content you'd have expected from this blog. The following video might be a bit boring, but let me try to explain it:
What's important to understand, is that this happens pretty much every day in the staff room.
Basically, this is the preferred means of modelling that school teachers tend to use when designing real-world problems for kids in school. They take a pre-existing problem that happens in everyday society that requires them to make a choice ( drive further to buy cheaper rice, or drive less for more expensive rice? Assuming the goal is to spend less money, which helps me to save more? ) (another common example, at least for secondary schoolers, is trying to reach a kite on a tree, and trying to measure the height of the tree using the properties of triangles. (base x height) / 2 is a familiar formula, but (ab cos(C)) / 2 is the more appropriate trigonometric formula)
"Ah, but real prices of products tend to be complicated! Sometimes you get a discount for buying two, like the sale at Fairprice!" Correct, that's a very good observation! What the teachers effectively do, is to adjust the numbers on these problems to the point where it's comfortable enough for the students to work with. If they're primary 4 kids, they'll try to keep the decimals in tidy numbers, like having it end in 50 cents or keeping the calculations in whole numbers only. This is why they use algebra extensively; they only have to adjust a single variable for everything to change.
If you feel like studying for PSLE or your mid-year / end-of-year exams, I recommend changing your approach: Rather than solving the questions tidied up for you on practice papers and assessment books, try creating your own mathematics problems in your everyday life and use what you've learned to find the answers yourself. Join your parents when they go grocery shopping, train your mental mathematics while you're outside (or, don't. You have a phone, even if the phone's not yours, could be your mom's. You technically can do workings anywhere and everywhere.)
It's a scary process since there's no answer sheet prepared ahead of time to help you, but that's life - You don't really have an answer sheet for problems in life, you'll have to make your own. Do your very best, and hope your mathematics is enough to make your family's life easier.