Goal:
Understand the concepts of position and path and mathematical ways of describing them.
Concepts:
- Position in one dimension
- Using a number to describe position
- Position in two dimensions
- Using two numbers to describe position
- Maps and scale
- Paths
Materials:
- Ruler
- Protractor
Preparation:
Nothing required
Procedure:
Follow along in class
Homework:
- Download this map of a Waiheke Island walking route:
- Determine the distance of each segment of the route, from the starting point and returning to the beginning. Use the scale on the map to determine these distances.
- Also record the turning angle, in degrees, each time the route changes direction. Let the angle be positive for a right-hand turn and negative for a left-hand turn. The turning angle is NOT the angle between the route segments. It’s the amount you have to TURN at each junction. Turning completely around would be 180 degrees.
- Also record a final turning angle between the last route segment and the first. This would be the amount you would need to turn in order to be pointed in same direction as you were in when you first started your trip.
- Add up all the turning angles, including the final turning angle. What do you get for this sum?