Mathematics
Intermediate
50 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen

Directions and Routes: North, South, East, West

Learn to follow and write directions using cardinal compass headings (north, south, east, west) on a grid map of the schoolyard, and see how left and right turns depend on the way you face.

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    1 - Getting Started ~5 mins

    Illustration for Getting StartedHere 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?

    2 - Watch and Notice ~8 mins

    A heading is a compass direction — north, south, east or west — and it 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 two children get the same instruction and walk off in opposite directions, then watch the heading route on the grid stay the same for everyone.

    3 - Draw Your Compass Rose ~3 mins

    COPYBOOK MOMENT

    Illustration for Draw Your Compass RoseIn your maths copy, draw a compass rose and label the four arms N, S, E and W, with north pointing up the page.

    Check your rose against the board: north up, south down, east to the right, west to the left.

    4 - Try It Together ~10 mins

    Now we follow routes together on the grid map. North is up and east is to the right, so we slide the marker one square at a time. We are using headings today: north, south, east and west.

    We will work through these routes one at a time:

    • North 2, then east 3.
    • West 1, then north 2.
    • South 1, then east 2, then north 3.
    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. The last move we made is the first one we undo. So we come home south 2, then west 3.

    Move the marker by directions

    5 - Class Challenge ~8 mins

    Key point

    To reverse a route, write the opposite direction for each step and put the steps in the opposite order. Last out, first back.

    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.

    Follow the route to the finish

    Pupil practice
    Module 8 · Symmetry, Location and Transformation Algebra
    Lesson 97 · Directions and Routes: North, South, East, West
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