Rotational Symmetry

What is rotational symmetry?

A shape has rotational symmetry when you can turn it partway and it looks exactly the same as it did before.

A square is the easy sketch. Turn it 90 degrees and it lands right back on itself.

The number of times a shape matches itself in a full turn is called the order. A square has order 4.

What is this module?

The module shows a shape with a symmetry number you can change. There are two copies. One sits still at the start. You turn the other one.

When the moving copy lands on the still copy, the module highlights it. That is a match.

What they're learning

• That a shape can look the same after a turn.
• That the match angles are spaced evenly. They are 360 divided by the order.
• That a higher order means more matches in a full turn.
• How to predict a match angle and then check it.

Aliases

• Turn symmetry
• Order of symmetry
• Rotational symmetry
• Match angle

Refresher

A shape has rotational symmetry if you can turn it partway and it looks exactly the same. The order is how many times it matches itself in one full turn. The match angles are evenly spaced, so each one is 360 divided by the order.

Try this together

You don't have to teach a whole lesson. A few minutes with the sliders is enough.

1. Set the symmetry to 4. Ask how many matches there will be in a full turn. Then count them in the table.
2. Ask what angle lines it up first. The table shows 90 degrees, which is 360 ÷ 4.
3. Set the symmetry to 5. The first match moves to 72 degrees. Ask why it changed.
4. Drag the shape slowly past a match angle and watch it highlight.

If you're stuck, remember the match angles are 360 divided by the symmetry number, then kept going around the circle.

Words you might hear

• Rotational symmetry: a shape looks the same after being turned.
• Order: how many matches happen in one full turn.
• Match angle: a turn that lands the shape on itself.
• Full turn: 360 degrees.

Deeper dive

A square matches itself every quarter turn. A full turn is 360 degrees, so 360 ÷ 4 is 90, and the square has order 4.

A shape with order 5 matches every 72 degrees, because 360 ÷ 5 is 72. Higher order means more matches going around. The module highlights a match whenever the moving copy lands on the still copy.