Why does changing the parts keep the amount rather than the number on top?

Because that is the lesson. Shade a half, cut the circle into quarters, and the point is that the same amount is now two quarters. If the number on top stayed the same you would get a quarter instead, which is a different amount and shows nothing.

What happens if the new number of parts cannot show the same amount?

It goes to the nearest whole slice, in one step you can undo. A half cut into thirds is not a half however you draw it, and rounding is the honest thing to do rather than pretending.

How do I show an improper fraction?

Keep shading past the whole circle. A second one appears and fills, and the mixed number is written under the fraction: seven quarters, and under it one and three quarters.

Why is there no seventh or ninth?

No primary scheme of work uses them, and a slice that thin is hard to point at on a board. The eight offered cover everything from halves to twelfths that children are actually taught.

Fraction Circles

Fractions · Year 2–Year 6

Shade slices of a circle. Change the parts and the amount stays the same.

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About the fraction circles

Press a slice and the circle fills up to there. Press the last shaded one and it comes off again, so a mis-tap costs a tap rather than an Undo.

Changing the number of parts keeps the AMOUNT shaded, not the numerator. Shade a half, press 4, and the same picture is two quarters; press 6 and it is three sixths. That is equivalent fractions in one control, and it works because the shaded area never moves while the cuts do.

Go past a whole and a second circle appears. Seven quarters is one whole circle and three more quarters, and the mixed number is written under the fraction, so it is something a class can count rather than a rule to remember.

The fraction wall does the same maths in bars, and both are worth having: a wall is better for comparing two fractions side by side, a circle is better for a whole being cut up and for anything past one.

How to use it on your whiteboard

1Press a slice to shade up to it. Press the last shaded slice to take it off.
2Parts cuts the circle into 2, 3, 4, 5, 6, 8, 10 or 12. The shaded amount stays the same.
3The plus and minus buttons shade one more or one less part.
4Keep going past a whole circle and a second one appears, with the mixed number under the fraction.
5Fraction hides the numbers, so the class works out what is shaded.

Questions

Why does changing the parts keep the amount rather than the number on top?: Because that is the lesson. Shade a half, cut the circle into quarters, and the point is that the same amount is now two quarters. If the number on top stayed the same you would get a quarter instead, which is a different amount and shows nothing.
What happens if the new number of parts cannot show the same amount?: It goes to the nearest whole slice, in one step you can undo. A half cut into thirds is not a half however you draw it, and rounding is the honest thing to do rather than pretending.
How do I show an improper fraction?: Keep shading past the whole circle. A second one appears and fills, and the mixed number is written under the fraction: seven quarters, and under it one and three quarters.
Why is there no seventh or ninth?: No primary scheme of work uses them, and a slice that thin is hard to point at on a board. The eight offered cover everything from halves to twelfths that children are actually taught.