PhET ratios and rates: building rate fluency Year 7-9 | No Drama Koala Maths

Most Year 7 students can tell you a ratio is "something to something." Ask them to use one in a problem and the wheels come off.

The gap isn't usually about not knowing the definition. It's about not having a stable mental picture of what a ratio does. PhET's Ratio and Proportion and Unit Rates simulations are built to install exactly that picture.

What the simulations do

Two free sims from PhET cover this space:

Ratio and Proportion — two coloured bars whose heights are locked in a chosen ratio. Move one, the other adjusts. Includes a challenge mode where you match a target ratio.
Unit Rates — buy fruit, paint, or candy at a given price per unit. Adjust quantity and see the cost. Built around the "per one" framing.

Both run in any browser, no login, work on a phone if you have to.

Three things they teach well

1. Ratios are coupled, not independent

The killer feature of Ratio and Proportion is that the two bars move together. Drag one up, the other moves up in proportion. Drag it down, same thing.

Students who think 3:5 and 6:10 are different ratios watch the picture stay the same as the numbers change. That's the proof. The visual coupling does what words don't.

2. Rate is the "per one" version of a ratio

Unit Rates asks the student to buy quantities at a given price. Buy 2 apples at 60c each, see $1.20. Buy 5 at 60c, see $3.00. The unit rate (60c per apple) is the thing that doesn't change.

That's the conceptual move at the heart of the topic: a ratio tells you the relationship; the unit rate extracts the "per one" version so you can scale to anything.

3. Scaling is the same operation, just bigger or smaller

Both sims hammer this: doubling one quantity in a ratio means doubling the other. Halving one means halving the other. By the time a student has tilted the bars a few times in Ratio and Proportion, the calculation rule "if you multiply one side by k, multiply the other side by k" is grounded, not just memorised.

Where they fall short

A few real limitations:

No rate problems out of context. Unit Rates is set in a shopping scenario. If your child is ready for "60 km in 1.5 hours" or "300 ml of solution in 4 minutes," the sim won't take them there. You'll need a different resource for non-money rates.
Limited challenge depth. Both sims max out somewhere around early Year 9. By Year 9-10, students need to work with ratios in algebraic form (k : 2k, x : 3x) and the sims don't go there.
No worked examples. The sims are exploration tools. They don't show step-by-step solutions. For students who want to see "how do I solve this on paper", you'll need a textbook or Khan Academy or Mathspace.

For a complete ratios and rates unit you'd combine these with adaptive practice (Mathspace handles the algebra well), worked examples for the calculation side, and a teacher reviewing where the student is actually getting stuck.

How we use them in the weekly review

In the No Drama Koala program, these sims tend to show up in two ways.

When a student's Mathspace data shows them treating ratios as two unrelated numbers (the classic "3:5 means three and five" mistake), I'll send a short Loom of myself in Ratio and Proportion dragging the bars while talking through what the coupling means. Five minutes there usually does what a textbook explanation can't.

When a student is comfortable with ratios but hasn't yet made the Unit Rates leap, the "anything else" section of the weekly review email gets a prompt like: "open this sim, set the price to your favourite, and figure out what one of those things would cost. Then what ten would cost. Tell me what stays the same." Open-ended enough to keep them thinking, structured enough that they don't drift.

Try this with your child

If your child is in Year 7 or 8 and you want a quick diagnostic on whether their ratio thinking is connected to anything real, try this:

Open Ratio and Proportion on their device.
Set the ratio to 1:2 and ask them to make the left bar twice as tall.
Then ask: what happened to the right bar, and why?

A student who has the right mental picture will say "it doubled too, because they're locked." A student who has the wrong mental picture will be surprised that the right bar moved at all. That's the gap. It's a normal one. Most secondary students need help connecting "ratio" the word to "ratio" the relationship at least once.

Want a qualified Australian teacher reviewing your child's actual ratios and rates work each week and setting next week's tasks calibrated to their specific gaps? That's exactly what the weekly review program does. Start with a free discovery check-in, I'll send back a personalised video diagnostic of where they're at.