Math · Stage 5

Rotational symmetry and order of symmetry

Spin a shape through one full turn and count how many times it looks exactly the same. That count is its order of rotational symmetry — and the smallest turn that matches is 360° ÷ order.

✦ Math📘 Stage 5 · S5⏱ ~12 min🧒 Ages 9–10★ Free to start

I can find the order of rotational symmetry of a 2D shape — the number of times it fits exactly onto itself in one full turn — and work out the smallest matching turn as 360° ÷ order.

Start the free lesson →⬇ Printable PDF

📖

Kavi's Spinning Star ✦

Kavi pins a paper star to the wall with a tack in the middle and gives it a slow spin. "Watch — it doesn't take a whole turn to look the same again!" Before one full turn is done, the star clicks into place looking exactly as it started — again and again. "The number of times a shape lands on itself in one full turn is its order of rotational symmetry. Let's learn to count it! ✦"

🎓

What your child will learn

1Rotational symmetry, and its orderA shape has rotational symmetry if it looks exactly the same after a turn of less than a full turn (less than 360°), spinning about its centre. The order of rotational symmetry is how many times it matches itself in one full 360° turn. Tap each card.

2A square matches 4 times → order 4Keep your eye on the top-right corner of the square as it spins about its centre. Each quarter turn (90°) the square lands looking exactly the same. Count the matches in one full turn.

3Order more than 1, or order 1 only?

4Shape → order → smallest matching turn

🔍

A peek inside

A rectangle (an oblong, not a square) is spun about its centre. What is its order of rotational symmetry, and what is the smallest turn that matches?

a half turn (180°) lands it on itself; a full turn lands it again → 2 matches

Try this at home: The order of rotational symmetry is the number of times a shape matches itself in one ___ turn.

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

Start the free lesson →⬇ Download PDF

Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.