Angles as fractions of a turn

There are two ways to talk about an angle in Year 4: you can say its size in degrees, or you can say what fraction of a full turn it is. Both describe the same idea.

A full turn is 360°

A whole spin — back to where you started — is 360 degrees. Once you know that, every fraction of a turn is just dividing 360°.

You can build other angles by adding these up. For example, $\frac{1}{4}+\frac{1}{12}$ is $90°+30°=120°$.

Why this is useful

Thinking of an angle as a fraction makes some calculations easier than working in degrees alone.

"A clock's minute hand moves a full turn in one hour. How many degrees does it move in 15 minutes?"

15 minutes is $\frac{1}{4}$ of an hour, so the hand moves $\frac{1}{4}$ of 360° = 90°.

"I face north, turn 90° clockwise, then 90° more. Which direction am I facing?"

90° + 90° = 180°. That's a half turn from north, which means I now face south.

A sector of a circle is an angle

If you cut a circle into wedges, each wedge is an angle at the centre. A pie cut into 8 equal slices has 8 angles of $\frac{1}{8}$ of 360° = 45°. The bigger the wedge, the bigger the angle.

This is exactly the picture you see in the angle from a circle exercise.

Quick mental fractions

These come up a lot. Memorising them speeds up estimating.

• $\frac{1}{2}$ of 360° = 180°
• $\frac{1}{3}$ of 360° = 120°
• $\frac{1}{4}$ of 360° = 90°
• $\frac{1}{6}$ of 360° = 60°
• $\frac{1}{8}$ of 360° = 45°
• $\frac{1}{12}$ of 360° = 30°

What's next

• For parents
• Back to the introduction
• Using a protractor

Try it out

• 🎯 Angle from a shaded sector — read the angle from a circle
• 📐 Measure an angle with a protractor