Turn a real choice into maths.

A model, and the knobs that make it move.

Imagine you're choosing a phone plan. The real world is messy: adverts, fine print, shiny colours. Modelling asks you to ignore all of that and keep only the numbers that change the answer — the monthly fee, and the cost per minute you talk.

Here's the trick that makes it powerful: a good model isn't one answer, it's a machine for answers. Feed it any number of minutes and it tells you the cost. That's why you'll see it drawn as a line on a graph — every point on the line is one possible "what if."

The modelling cycle: there and back again.

Every model follows the same loop. Real life goes in; a decision comes out.

Real → maths → solve → translate back. The dotted arrow is the honest part: models are guesses you improve.

Notice step four. A pile of numbers isn't an answer to a human — "the lines cross at x = 300" means nothing until you say it out loud: "talk less than 300 minutes a month and Plan B is cheaper." Translating back is where maths becomes a decision you can actually make.

Drag the minutes. Watch the lines cross.

Two made-up plans, drawn as two cost lines. Move the slider to change how many minutes you use each month — the crossover point is where the cheaper plan changes.

That single crossing point is the whole answer. It splits every possible month into two worlds: "chatty months, pick A" and "quiet months, pick B." You didn't have to guess — the maths drew the border for you.

Where does 300 come from?

The graph found the crossover for you, but you can find it yourself with a tiny bit of arithmetic — no scary algebra. Watch the four moves happen in order.

See how gentle that was? The hardest step was noticing that "equal cost" is a question you can turn into one line of arithmetic. That noticing is the skill of modelling.

Cooking is modelling in disguise.

A recipe is already a model — it turns "a cake" into numbers. When you cook for a different number of people, you're solving that model. The key idea is proportion: everything grows by the same factor.

This recipe serves 4. Drag to feed a different crowd and watch every amount scale together.

Eggs are the honest snag. The maths might say "4.5 eggs," but you can't crack half an egg neatly — so you round to a whole number. Real life pushes back on tidy maths, and a good modeller expects it.

"Will we make it in time?"

Here's a model you can carry in your head forever. To turn a journey into maths, you only need one relationship:

That last bracket matters. The model assumed a steady 15 km/h with no red lights and no hills. Every model quietly makes assumptions like these — the skill isn't just solving, it's knowing which assumptions you snuck in, and whether you'd bet on them.

Build one model, in your head.

A taxi charges a $3 flag-fall (a fixed fee just for getting in) plus $2 per kilometre. That's a real situation begging to become maths.

Once you've built fare = 3 + 2d, every ride is just plugging in a number. One model, endless answers — that's the payoff for the work of setting it up.