Teacher Notes

This activity uses technology to help students with the notoriously difficult idea of working with 2D planes within 3D situations and thus solve problems with trigonometry in 3 dimensions.Google sketchup is a simple and clear visual aid that encourages students to literally look at the problem from a different angle. The medium is both helpful and engaging and lends a dynamic reality to a 3 dimensional object that can't really be achieved with paper! This activity is best done with students at computers, but it can be done all together from the teachers computer if technology is not available.

How

The following is some practical advice about how the activity might be run.

Resources provided

The problems are given on the activity page along with a download link to a digital and printable word document. There are two 3D models made with Google sketchup that need to be opened with the same, free, program that students need for the activity. There is also a brief screencast to show 'orbiting' in action.

Resources needed

Obviously the lastest version of Google sketchup is required for this. it is free and very easy to use (especially if you are only orbiting). I recommend following some of Google's online tutorials and experimenting with this software for future reference, but for the purposes of this activity it is only orbiting that is really required.

Time needs

This activity takes at least an hour to do properly. It is important to allow time for acquiring and successfully using the files. It is equally important for students to have time to work carefully through the stages of the activity.

Starting and finishing

• The activity is fairly self explanatory and the most important thing, as I have said before, is that students have time to play with the files. 
• It is possible to do this activity together as a class if computers are not available.
• It may be an idea to do one or two of the problems together or to ask students to present what they have done at regular intervals throughout the activity.

Records

The activity encourages the use of different screenshots to help justify answers. Given that students need access to computers for the sketchup file, I suggest that answers are done on computer as well. Alternatively students make written notes and 2D diagrams on paper as they work.

What to expect

• The technology is only a visual aid. It is a powerful one, but the concept remains difficult and even if students have correctly identified a two dimensional plane, there is still a good chance that they will make a mistake applying trig ratios to those planes.
• I have found that students are reluctant to draw extra diagrams that only contain the section and the information they need to solve a particular problem. The task specifically asks them to do this in an attempt to establish a good strategy for solving the problems. As such, it may be necessary to add encouragement!