Sometimes you plan a lesson for days and sometimes you get a bright idea at the last minute. This trigonometry investigation is one of those in the second category that just worked. After completing the chapter on trigonometry, I wanted learners to draw the functions, to see the recurring pattern of the trig ratios. Using Google Sheets made it so much more real for them.
In the 90 minute lesson, we were able to play with the graphs, answer the questions, make some notes and draw the graphs in their books.
We just finished the chapter working with the trig ratios. In the previous lesson, I introduced them to the CAST diagram, which linked to this trigonometry investigation.
Each learner had their own device. Using Google Classroom I share the trigonometry investigation (click here to make a copy) so that each learner had their own copy.
If you are not yet in a 1-to-1 classroom, you can put the investigation on the projector and do it as a whole class activity.
I started the lesson by putting the investigation up on the board. I showed them that the sheet is pre-programmed to work out y = sinx, for each value of x you enter. I entered a few values, and they used their calculators to check that the answers are correct. As we entered more x-values, I asked them questions about what they notice on the graph, where they expect the next point to be. After everybody had been convinced that the sheet is actually working out the values of sinx, we used auto-fill to create more points. We tried using every degree, every 5 degrees, every 50 degrees (make them aware that you can not see the turning points) and every 90 degrees.
Using Google Classroom, I send them each a copy of the investigation to play with and answer the questions. I encouraged them to try different intervals, as well as some negative values of x.
The tan graph brought us to an interesting anomaly. The auto-scale on the y-axis was so big that it seemed all the points were in a straight line. When we inspected the table, we saw that the value of x=90 seemed out of the ordinary. I asked them to check the answer with their calculator, which lead to a brilliant discussion of asymptotes. Once we removed the incorrect values, we could see the graph. (BTW – the incorrect value is due to convert degrees to radians.)
Once they completed the investigation, I made them draw the graphs in their books as well as write some notes about it. Drawing the graphs electronically and on paper might seem like a waste of time, but I found they needed the time to wrap their heads around the concepts. Drawing them on paper made the graphs more concrete to them.
Something interesting I noticed, was that once they were working on their books, they all reverted to calculate each value manually with their calculator. I would just have copied the answers from the spreadsheet. This was just more proof that our learners are not yet used to using the power of spreadsheets to do their work.