Find Your Way: Maps, Angles and Coordinates

You need: String or chalk · 8–12 cones · Tape measure · Cards with ordered pairs

1. Mark a horizontal line (x-axis) and a vertical line (y-axis) crossing in the middle of a court. The crossing point is (0, 0).
2. Mark every metre along each axis from −5 to 5.
3. The caller reads a card such as (3, −2). One student walks along the x-axis first, then up or down.
4. Try all four quadrants. Record which signs (+ or −) each quadrant has.
5. Make a shape by placing four students on points. Can the class name its corners?

How you'll know: You can stand on any point called and say which quadrant it is in and why.

Safety: Choose a flat area away from traffic and play equipment. Walk, don't run, on hard surfaces.

Go further: Reflect the shape in the y-axis. What happens to each coordinate?

You need: A straight stick about 1 m long · Small stones or pegs · A compass or phone compass · Chalk

1. On a sunny day around midday, push the stick upright into the ground.
2. Mark the tip of the shadow with a stone every 10 minutes for an hour.
3. Find the shortest shadow. In Aotearoa it points roughly south, so the opposite way is north.
4. Check with a compass. How close were you?
5. Draw a big chalk compass rose around the stick with eight points, labelled with degrees.

How you'll know: Your chalk rose matches the compass within a few degrees and you can explain why the shadow points south.

Safety: Never look directly at the Sun. Wear a hat and sunscreen.

Go further: Magnetic north and true north are not the same. Find out how many degrees apart they are in your town.

You need: Tape measure · Grid paper · Calculator · Clipboard

1. Measure out 20 m with a tape. Walk it normally and count your steps. Repeat ten times.
2. Find your average number of steps, then your pace length (20 m ÷ steps).
3. Pace the length and width of a court or building. Convert paces to metres.
4. Choose a scale (for example 1 cm = 5 m) and draw it on grid paper.
5. Check one distance with the tape. How far off was your pace estimate?

How you'll know: Your paced measurements are within about 5% of the tape measure and your drawing matches the scale.

Safety: Watch where you walk; keep off roads and car parks.

Go further: Write your scale as a ratio (1 cm = 5 m is 1:500). What would 1:50,000 mean?

You need: A clear plastic tub · Modelling clay or playdough · Water and a jug · Ruler · Clear plastic sheet or baking paper · Whiteboard marker

1. Build a lumpy hill of clay in the tub, lower than the tub's sides.
2. Pour in water to a depth of 1 cm.
3. Look straight down and trace the waterline onto the plastic sheet laid over the top.
4. Add another 1 cm of water and trace again. Repeat until the hill is covered.
5. Compare your drawing with a Topo50 map. Where are the lines close together? Where are they far apart?

How you'll know: You can point to the steepest side of your hill on the drawing and explain how the contour lines show it.

Safety: Wipe up spills straight away so nobody slips. Wash hands after using clay.

Go further: Draw arrows to show which way rain would flow off your hill. Water always crosses contour lines at right angles, heading downhill.

You need: A large paper circle · Protractor · Ruler · Coloured pencils · Science Learning Hub star compass diagram

1. Look at the kāpehu whetū diagram on the Science Learning Hub. Count the houses around the circle.
2. Work out the angle for each house (360° ÷ 32).
3. Use a protractor to divide your paper circle into equal houses. Mark the four main directions.
4. Lay an 8-point compass rose over it. Which houses line up with N, NE, E?
5. Write two sentences about why an ocean navigator might need more directions than eight.

How you'll know: Your circle has equal houses, and you can explain the calculation for their size.

Go further: The top and bottom stars of the Southern Cross point south when it stands upright. On a clear night, find it with your whānau and sketch where it sits over your house.

You need: Grid paper with four quadrants · Tracing paper · Coloured pens · Instruction cards

1. Draw a triangle-shaped 'waka' on the grid and write its three corner coordinates.
2. Follow three instruction cards, for example: translate 4 right and 2 down; reflect in the x-axis; rotate 90° clockwise about (0, 0).
3. Use tracing paper to check each move and record the new coordinates.
4. The final position shows where the treasure is buried.
5. Write your own three-step treasure trail for another group.

How you'll know: Another group can follow your instructions and land on exactly the treasure square you planned.

Go further: Find a single move that does the same job as two reflections. What do you notice?

You need: Class map and course cards · Checkpoint markers · Compasses · Tape measure · Results table · Stopwatch

1. Place a marker at each checkpoint.
2. Give a group of testers the map and course card only.
3. Follow them at a distance and record found, found after searching, or not found at each checkpoint.
4. Measure the real direction and distance for any checkpoint that failed.
5. Fix the clue and test again with new testers.

How you'll know: More checkpoints are found first time in the second test than in the first, and you can show the numbers.

Safety: Stay inside the agreed boundary. Walk near buildings and on hard surfaces. An adult supervises.

Go further: Time each tester and work out their average speed in metres per minute.