Mr. Hamada’s Universe

 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

• Starting with Learning Styles – An introduction to Sternberg’s Three Intelligences: Analytic, Practical, Creative (turns out I’m a mix of analytic and practical). We then looked at differentiating assignments by giving students a choice between three possibilities corresponding with these learning styles. It was an interesting alternative to Gardner’s Multiple Intelligences.
• Tiering Lessons – Differentiating lessons by readiness.
• RAFTs: A Differentiated Writing Across the Curriculum Strategy – This was the session I was least excited about going into the conference. However, there was some good stuff that came out of this. I like the RAFT format and am curious to see how I can use it in my classes. This is what I want to try to do before the end of the year in at least one of my classes.
• Applying Readiness Differentiation with Common Strategies – More hands-on example of readiness strategies. A bit repetitive of the second workshop, but good reinforcement of what I’d already learned.

Sandra also showed a graphic (of which I could not get a copy!) in her plenary from Grant Wiggins. It depicted the 3 Ps of assessment – Performance, Progress and Process – in equal proportions. If anybody knows where I can read more about this, I would appreciate a little Link-Love. I am thoroughly intrigued…

To be honest, I was a bit skeptical when this showed up on our school calendar. I certainly didn’t enjoy coming in on a Saturday, especially after a two day mid-week holiday. That said, I learned quite a bit and I hope to utilize some of these strategies into my class in the last 6 weeks of the year. And, as an added bonus, I’m in the process of setting up a school-based wiki to help share differentiation best practices.

Photo – “Be Different” by Vermin Inc