Teacher's Notes

When students simply use a calculator, the meaning behind trig ratios is quickly lost. In order to build the ‘cabri – calculator’ students are challenged to really understand the origins of the ratios. The plotting of these ratios as a function reinforces the patterns that exist in the relationship between 2 variables and gives a context for calculating a number of the ratios. In Part 3 students are asked to relate the patterns they find to the physical situation of the geometry and this is a critical link to make. These questions are all problems that can be solved with a variety of approaches and as such accessible to more students.

How

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

Resources provided

The activity page offers a video demonstration that defines the task along with a series of related tasks and questions for students to do. These are aimed at helping students construct the calculator and then to use it. In addition there are also a couple of videos that explain how the calculator can be made using Geogebra.

Resources needed

Students will obviously need access to computers for this activity. Previous exposure to dynamic geometry is really helpful.

Time needs

This can usually be done in 1 hour, but depends largely on previous experience and the amount of input the teacher decides to give.

Starting and finishing

Time and ambition are key here. Left to students alone, this activity represents a big challenge, perhaps the teacher might consider that for some students, whilst choosing to orchestrate a group input for others. Students could be provided with partially completed tables and axes. A teacher may even decide to provide the students with the 'calculator’ in advance. As such the depth to which this activity is taken is very flexible.

Records

Its great if students manage to create the calculator themselves and this then provides an excellent record of the activity.

What to Expect

• As mentioned already, much depends on previous experience students have of using dynamic geometry. If this is not very much then teachers will find themselves leading large parts of this activity.
• It is really important for students to get some experience of actually constructing the dynamic situation and watching what happens as the variables are changed. Giving students the pre-prepared file will not have the same effect.
• When students check that their calculator gives the same result they find it quite empowering and a real sense of understanding is given to the concept of trigonometry and this is invaluable.

More

This activity is a great start to the trigonometry element of the unit and can be nicely followed up with the activity  rearranging relations.