Learning On The Job

 The Pre

We’ve reviewed Cartesian coordinates, we’ve learned the distance formula, we’ve talked about transferring the Cartesian plane onto the surface of the Earth and coming up with latitude and longitude, we’ve studied SOH-CAH-TOA, we’ve talked about bearings, and we’ve found the distance between two points on the Earth using proportions and a bit of trig if necessary.

The Setup

I book two lessons in the computer lab. In that time, there are four tasks that need to get done:

1. We look at the idea of trilateration and how we can pinpoint an exact location using three circles. I’ve created a simple GSP activity to illustrate this.
2. With their new-found knowledge, the students get the chance to find a missing hiker, using page 2 of the same GSP file.
3. A simple WebQuest to learn about how GPS works.
4. Some problems for students to answer to reinforce.

   GSP – Trilateration – (For some reason, I can’t upload this file. If you want it, let me know and I’ll email it to you.)
   gps-and-mathematics.doc

Check-up and Learning the Tools

The next class is spent clarifying any questions and making sure they can answer the questions in task four. We then spend about 30 minutes getting to know our GPS receiver. I have the Garmin eTrex Vista, so I downloaded a .pdf version of the manual and snipped out the relevant screenshots. We go over how to create and name waypoints, how to find waypoints, how to measure the distance between two points, how to use the compass, and any other questions that might come up.

The Field Work

Armed with our knowledge of how our GPS receivers work (I normally borrow as many as I can from other teachers) and divided into small groups, it’s time to get outside and do some GPS-ing.

I’ve come up with four challenges that increase in difficulty. They use their GPS receivers to take measurements so that they can find the distances later.

1. Using a right triangle to measure the distance across a ‘river’. I do this with each group, step-by-step to ensure they
2. Using a similar technique to check the length of our soccer pitch.
3. Use the law of sines (which I introduce them to but do not go over in any detail other than to present the formula) and given points to estimate the distance to a building off-campus.
4. Use any method to estimate the distance from our flag pole to a different building off-campus.

   GPS and Triangulation

The groups can finish taking measurements for task 1 and 2 in a lesson. They then complete 3 and 4 during the next lesson.

Total time: 5 days (1 hour periods/day).

The students seem to enjoy the activity. Most of them have seen GPS systems (who hasn’t these days?) but have never actually used a handheld unit. None of them have ever used a compass to find direction. If you don’t have access to GPS receivers, you could probably get away with this activity using compasses and trundle wheels. But it won’t be nearly as cool…

Photos:
Dustboat Geocache