PhET decimals and the number line: place value made visual | No Drama Koala Maths

A common Year 7 question: which is bigger, 1.05 or 1.5?

About a third of students in my discovery check-ins get this wrong. Not because they're behind. Because they're treating "05" and "5" as numbers being compared, not as values in particular places.

This is the place-value problem hiding inside decimals. And it's the exact thing PhET's Number Line: Decimals simulation is designed to expose.

What the simulation does

Number Line: Decimals is a free, browser-based simulation from the University of Colorado Boulder. It opens to a horizontal number line with a draggable point. You can:

Zoom in to see tenths, hundredths, thousandths
Place points on the line and watch their decimal value update
Compare two values side by side
Switch between "explore" mode and "challenge" mode

No login, no download. Works on any browser, including a phone, though it's much better on a tablet or laptop where there's room to drag.

Three things it teaches well

1. Decimals are points on a line, not strings of digits

The biggest mental shift for students stuck on 1.05 vs 1.5 is realising decimals live in positions. Once they can zoom into the section between 1.0 and 2.0 and physically drag a point to 1.05, the comparison stops being abstract. It's here vs there.

I usually have students drag one point to 1.5, then a second to 1.05, then zoom in. The visible gap between them does the teaching.

2. Place value as scale, not memorised rules

Zooming the number line is the killer feature. Zoom into the gap between 0 and 1, the line subdivides into tenths. Zoom again, hundredths. Zoom again, thousandths.

This makes the decimal place value chart (units, tenths, hundredths, thousandths) feel like the same idea repeating at different scales, not four separate things to memorise.

3. Ordering and comparison

The compare mode shows two draggable points with the inequality between them updating live. Students who get tripped up by 0.6 vs 0.59 can see which one sits to the right, and therefore which is bigger.

This is where the well-meaning rule "if the digits are the same, the longer one is bigger" gets correctly unlearned. 0.6 is bigger than 0.59. The number line makes that immediate.

Where it falls short

Worth being honest about this, because pretending PhET covers everything doesn't help anyone:

No operations. There's no way to add, subtract, multiply, or divide decimals inside the sim. For arithmetic, you need something else. Mathigon's Polypad has a number line that supports operations. Mathspace handles it with step-by-step working.
No conversion to fractions or percentages. The bridge from 0.25 to 1/4 to 25% isn't shown. PhET's separate Fractions: Equality sim handles fractions to decimals, but not percentages.
No word problems. The sim is pure number sense. Application questions (money, measurement, recipe scaling) need to come from elsewhere.

For a complete decimals unit you'd combine this sim 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 it in the weekly review

In the No Drama Koala program, the Number Line: Decimals sim shows up in two ways.

When Mathspace data shows a student getting decimal comparison questions wrong, I'll often record a short Loom video of myself using the sim to walk through where their thinking went sideways. Showing the place values physically is much faster than explaining in words.

The other place it shows up is the "anything else" section of the weekly review email. When the student is ready for self-directed exploration, I'll drop a link to the sim with a specific prompt. Something like: "spend 10 minutes finding three pairs of decimals that look weird but follow the same rule." Open-ended enough to keep them thinking, specific enough that they don't drift.

Both work because the sim is free, no login, and renders cleanly on any device.

Try it yourself, then talk to your child

If your child is in Year 7 or 8 and you're not sure whether their decimal place value is solid, try this:

Open Number Line: Decimals on their device.
Ask them to drag a point to 0.7.
Then ask them to drag a second point to 0.65 and tell you which is bigger.
Watch what they do.

The wrong answer (0.65) is the diagnostic. If they hesitate or get it wrong, that's a real gap worth addressing. Not a "behind" gap. Most secondary students have this exact misconception at some point. But it leaks into algebra (rational expressions), measurement (converting units), and probability (decimal probabilities) if it's left alone.

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