Pythag Mapping

Create a map. Design a route. Make every clue work.

Main unit task · Plan across several work sessions

Pythag Mapping

This longer task moves from field measurements to designing and solving a peer treasure route. Use the classroom instructions for the full requirements.

Five stages to plan

01 · Measure your landmarks

Choose at least five landmarks. Sketch their positions and identify horizontal and vertical legs that form right angles. Choose one consistent measurement unit and state your map scale. Keep a record of the actual measurements.

02 · Create five clues

Choose a treasure endpoint and build a route with at least five clues using five right triangles. Label the landmarks at the corners. Ask peers to find a hypotenuse, or add a leg, area or perimeter challenge where appropriate. Supply enough information for each clue to have a clear solution.

03 · Work and check your route

Create your own worked answer key, solved visual map and travel log. Show the equation, substitution, square root, units and rounding for each stage. Record individual and cumulative travel distances. Check that the mathematics and map lead to the same endpoint.

04 · Set up the hunt

Follow your teacher’s instructions to mark the landmarks with cones and place the treasure at the endpoint. Check that the route and physical setup agree before classmates begin.

05 · Exchange and solve

Use a peer’s clues, blank map and travel log. Show your calculations and record the route. Compare your result with the creator’s worked solution and discuss any unclear measurements or clues.

Try an invented route segment

Two perpendicular changes. One diagonal.

This is an original practice example, separate from the classroom hunt. A route moves 6 grid squares east and 8 north. Each grid square represents 5 m.

Predict first. Change one value, then explain the result. Diagrams show the entered dimensions; displayed decimals are rounded.

From grid distance to ground distance

  1. The diagonal is √(6² + 8²) = √100 = 10 grid squares.
  2. Apply the stated scale: 10 × 5 = 50 m.
  3. Travelling along the two perpendicular legs would be (6 + 8) × 5 = 70 m. That is a different route.
  4. Record the length of the route actually specified. Do not add a diagonal and its legs as though all were travelled.

Check before you exchange or submit

Route and reasoning checklist
  • At least five measured landmarks and a clearly stated unit and scale.
  • At least five clues using five right triangles, ending at the treasure.
  • A worked solution, solved map and travel log with cumulative distances.
  • A physical setup that agrees with the map and teacher instructions.
  • Work shown while solving a peer’s route.

Your teacher supplies deadlines, grouping, assessment criteria and classroom arrangements.

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