Here is a map of a schoolyard, and up in the corner is a compass rose. North points up the page.

On the map, the gate is on the bottom-left square. The hall is 2 squares to the right of the gate, then 2 squares up from there.

If north is up, which way is east? And if you stood at the gate, how would you walk to reach the hall?

A heading is a compass direction. There are four: north up the page, south down, east to the right and west to the left. A heading points the same way from anywhere on the map.

A turn is not like that. It depends on which way you were already facing. Watch the first two boards: Aoife and Cian stand on the same square and are both told to turn right, and they walk off in opposite directions.

Then look at the third board. That one is a heading route, east 3 then north 2, and it lands on the same square no matter who walks it.

Now we follow routes together on the grid. The three routes are separate: each one starts again from the marked square, so put the marker back there before you begin the next. North is up and east is to the right, so we slide the marker one square at a time.

We take these one at a time, and the class predicts each move before the marker goes:

1. North 2, then east 3.
2. West 1, then north 2.
3. South 1, then east 2, then north 3.

Key point — how to go home. Start on the marked square and go east 3, then north 2. To get home we do the opposite direction in the opposite order. North becomes south and east becomes west, and the last move we made is the first one we undo. So we come home south 2, then west 3.

We work through routes together on the grid map. Read each direction, move the marker one square at a time, then check where it finishes.

First the easy ones:

• North 2, then east 3.
• East 4, then north 1.
• North 3, then east 2, then south 1.

Now the reverse. Worked example on the board first: you went east 4, then north 1. We write the reverse set of directions together.

1. List the steps in reverse order: the last step becomes first, so north 1 comes before east 4.
2. Flip each heading to its opposite: north becomes south, east becomes west.
3. Write the full reverse: south 1, then west 4.

Check on the grid: start from the far square, follow south 1 then west 4, and plot the square you land back on. It should be the start square.

Your turn on the last challenge: reverse east 3, then north 2 the same way, write the directions, then plot the square you land back on.