Visualising fractions with PhET: a guide for Year 7-8 parents | No Drama Koala Maths

A common Year 7 mistake: deciding that 1/4 is bigger than 1/2 because 4 is bigger than 2.

It looks silly written down. In practice it shows up the moment a student is asked to compare unfamiliar fractions under time pressure. The mental model isn't "fractions are parts of a whole." It's "fractions are pairs of whole numbers."

PhET has four free fractions simulations designed to fix exactly this. They're worth knowing about, both as a parent helping at home and as background to what an adaptive platform like Mathspace is actually doing.

The four PhET fractions sims

PhET publishes these as a family:

Fractions: Intro — match numbers to shaded shapes, build fractions on a number line
Fractions: Equality — drag pieces between two representations to show equivalent fractions
Fractions: Mixed Numbers — convert between improper fractions and mixed numbers visually
Build a Fraction — game-style challenge mode

All are browser-based, free, and work on a phone (though a tablet or laptop is much better).

Three things they teach well

1. Fractions are quantities, not pairs of numbers

The Fractions: Intro sim is built around this. You drag pieces into a circle or bar to physically build a fraction, then watch the numerator and denominator update. Going the other direction works too: type 3/4 and the shape fills.

When a student who thinks 1/4 > 1/2 plays with this for ten minutes, the misconception tends to dissolve on its own. They can see that the half-circle is bigger than the quarter-circle. Words can't undo it; the picture can.

2. Equivalence as transformation, not memorisation

Fractions: Equality puts two representations side by side. You shade in 2/4, then drag pieces to the right-hand shape to make it equal. The platform highlights when the two are equivalent.

The mathematical move here, multiplying or dividing the top and bottom by the same number, gets grounded by the visual proof. Students stop reciting "multiply top and bottom by the same thing" and start seeing what that operation does to the picture.

3. Mixed numbers and improper fractions are the same quantity

Fractions: Mixed Numbers lets students slide between 7/4 and 1 3/4 with a single control. Watching the same shaded area get described two ways is the fastest fix for students who think these are separate types of fractions.

Where they fall short

I want to be specific about this because pretending PhET covers everything doesn't help anyone:

No operations. PhET fractions don't add, subtract, multiply, or divide. For arithmetic, Mathigon's Polypad has fraction tiles that combine, and Mathspace handles step-by-step working. PhET's job is concept formation, not calculation.
No word problems. Application questions (recipes, measurement, sharing) need to come from elsewhere.
Limited to standard shapes. Circles, rectangles, and number lines. If your child needs to reason about fractions of more complex shapes (area, irregular figures), the sims won't help directly.
Phone unfriendly. The drag mechanics work but the screen real estate is tight. A tablet or laptop is much better.

For a complete fractions unit you'd combine these sims with adaptive practice (Mathspace), worked examples (Khan Academy or your textbook), and ideally 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 show up at two specific moments.

The first is misconception fix-ups. When Mathspace data shows a student treating fractions like pairs of numbers (the 1/4 > 1/2 family of errors), I record a short Loom video using Fractions: Intro to walk through where their thinking went sideways. Five minutes with the sim usually beats a written explanation.

The second is the "anything else" section of the weekly review email. Something like: "open this sim and find three pairs of fractions that look different but are equal." Open-ended enough to keep them thinking, specific enough that they don't drift.

Both work because the sims are free, no login required, and work on any device.

Try it yourself, then talk to your child

If your child is in Year 7 or 8 and you want a quick diagnostic of where their fractions thinking actually is, try this:

Open Fractions: Intro on their device.
Ask them to build 2/3 and 3/4 side by side.
Then ask which is bigger.
Watch what they do.

If they reach for the sim and look at the shaded area, they have the right mental model. If they immediately say "3/4 because 3 is bigger than 2 in the top," that's the misconception worth fixing. It's normal. Most secondary students have a version of it at some point. But it leaks into algebra (rational expressions), measurement, and probability if left alone.

Want a qualified Australian teacher reviewing your child's actual fractions 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.