Stand up and face the front of the room. Without moving your feet, we will turn together and name each stop.

First we turn clockwise (to the right): one quarter turn, then another to make a half turn, then one more to make a three-quarter turn, then one last quarter to face the front again. Before each stop, say where you think you will be facing.

Now face the front again. This time we turn anticlockwise (to the left) the same way: quarter, half, three-quarter, then full turn back to the front. Notice that a half turn still leaves you facing the opposite wall, whichever way you turn.

Watch the arrow on the screen. It starts pointing up. Each time it turns a quarter, it moves the size of one square corner: first it points right, then down, then left, then back to the start.

Now watch a square turn. A square looks the same after every single quarter turn, because a quarter turn is exactly the size of a square corner.

A shape matches when it lands looking exactly the way it did at the start. Turning it never changes its size or its shape, only the way it faces, so a match is when the facing comes back too.

We turn this arrow a quarter at a time and check for a match after every turn:

1. A quarter turn clockwise. Where does it point now? Does it match how it started?
2. Turn again, so that is a half turn. Match or not?
3. Turn again, a three-quarter turn. Match or not?
4. One more turn brings it all the way round. Now it matches.

Key point The arrow matches itself once in a full turn, and only at the very end. A square is different: turn a square a quarter and it already looks the same, so a square matches four times. Say where you think the arrow will point before each turn.

Now let's name the turns together. The arrow starts pointing up. We turn it clockwise and stop, then say which turn moved it there: a quarter turn, a half turn, a three-quarter turn or a full turn. Say your answer before we look at where it ends up.