Math · Stage 5
Clock-hand angle problems
A clock face is a circle — a full 360°. Once you know how fast each hand moves, the angle between them is never a guess: it's a calculation.
✦ Math📘 Stage 5 · S5⏱ ~14 min🧒 Ages 9–10★ Free to start
I can find the angle between the clock hands.
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Kavi and the Two Racing Hands 🕐
"The hands are racing around the dial," hoots Kavi, "and the minute hand is twelve times faster than the hour hand!" To find the angle between them, Kavi never guesses — she works out where each hand points, then measures the gap. ⏱️
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What your child will learn
1A clock is a circle of 360°A whole turn around the dial is 360°, split into 12 equal hour-marks. So between any two next-door numbers there are 360 ÷ 12 = 30°. At 3 o'clock the minute hand is on 12 and the hour hand is on 3 — that is 3 hour-marks = 3 × 30° = 90°, a perfect square corner. Tap +1 hour to watch the hands move.
2Walk the dial, 30° at a timeUnroll the clock face into a straight line of degrees, from 0° (at 12) all the way round to 360° (back to 12). Each hop of 30° lands on the next number. Tap Hop +30 → and count: 30, 60, 90 … — one hop per hour-mark.
3How fast each hand moves
4Half past 3 is 75°, not 90°At 3:30 the minute hand points at 6, so it is at 180°. The hour hand has slipped halfway from 3 to 4: 3 × 30 + 15 = 105°. The angle is the gap between them: 180 − 105. Tap Step → to subtract.
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A peek inside
Find the angle between the hands at 3:00.
minute hand on 12 = 0°; hour hand on 3 = 3 × 30° = 90°; angle = 90 − 0
Try this at home: 6 o'clock: the hands point exactly opposite. angle = __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.