Everyone stand up in a clear space. Watch me turn on the spot, then copy each turn with me. First we turn all the way around, back to where we started. Now a half turn. Now just a quarter of the way. Each time we stop, notice which direction you are facing.

Watch the arrow turn around the dot in its corner. It spins a quarter of the way, then halfway, then three-quarters of the way. Each of those turns goes clockwise, which means the way a clock's hands go. Look carefully: the arrow stays exactly the same size the whole time. Only the direction it points keeps changing. Be ready to say which way it faces after the half turn.

Now watch a second shape make a single half turn. Be ready to say which way it points when it stops.

Take your cardboard arrow with the pencil through one corner. When I call a turn, spin it around that fixed pencil point and tell me which way the tip now points. We work through these four in order:

• Point it up — quarter turn clockwise.
• Point it right — half turn.
• Point it down — three-quarter turn clockwise.
• Point it left — three-quarter turn clockwise.

Now for the tricky ones with your arrow. Work these in order, each a little harder. Try to predict the new direction before you turn.

• Point it up — quarter turn clockwise. Which way now?
• Point it right — half turn. Which way?
• Point it down — three-quarter turn clockwise. Which way?
• Point it left — find the single turn that makes it point up.
• Start facing up. A full turn brings it straight back to up. Find a second, different turn that also brings your arrow back to facing up.