Happy December!
It's my goal in precalc this year to have the kids apply knowledge whenever possible. We haven't been able to do that a whole lot (at all?!) so far in trig, so it was nice to get to graphing sine and cosine curves.
We've spent a couple of days graphing with periods, amplitudes, and horizontal and vertical shifts, so I'd assume that 90% of the kids could do that without a problem. Give 'em an equation and they can graph it.
Yesterday I gave each student a strip of paper with the name of a city and their average daily high temperatures for each month (found them here). I also gave them a full size piece of graph paper and a half-sheet of directions/questions for them to complete.
It was amazing the thinking they had to do. Everyone seemed comfortable with having 12 as the period of the graph, but how exactly do you fit that into the equation? (Some kids put 12... or 1/12...) What happens if you set January as month 1? Uh oh - a horizontal shift! And what trig function is it showing? Sine? Cosine? Has it been reflected?
Something that had become almost automatic for them turned back into a thinking game.
Nice.
Today I told the kids (after they'd turned in their results) that I didn't want to grade them all. After being accused of being lazy, I passed the graphs and equations out (making sure that no one got their own) and told them to grade it for me. (Had to give them some directions, too, of course.) They plotted the data points on their calculator, typed in the equation, and had to figure out what was wrong.
More thinking?! Oh my goodness.
First were the problems actually graphing the functions on the calculator. Check your mode. Did you remember to type the variable? Adjust your window?
Then the identifying of the equation errors. Graph isn't wide enough? So what's the problem? Could you fix it?
Graph isn't tall enough? Is in the wrong place? How could you fix it?
I also had the kids rate the equations on a scale of 1 - 5. I was pleasantly surprised to see that they were very generous with their scores. Someone who hadn't even included a sin or cos in their equation (or a variable...) was given a 4 out of 5. Wha?! And then one girl was given a 4.5/5 because (although her equation was virtually perfect).
I'm happy to say that I think most kids have a better understanding of the different transformations of a sine or cosine equation and what exactly they do to a graph. Hopefully.
4 comments:
Hey Again!
I printed out and am working on your Chapter 5 Pre-Calc sheet Solving Trig Eq's Legal Document. I have been working on #11 and #12 for a while, and I guess I am stumped. Can you tell me what to do? I love working identities and thought I was pretty good at them, but apparently not.
Thanks!
Christy
Hey Christy -
Are you talking about the one called verifying legal doc? If so, #11 uses angle addition formulas - the numerator is sin(x+y) and the denominator is cos(x+y). The right side of the equation is tan(x+y).
In #12 (the one with tans and cotans), you can change all of the cotans on the right to 1/tans and go through the fraction work - common denominators, multiply by reciprocal, etc.
Hope that helps! :) If you're looking at a different worksheet let me know and I'll see if i can figure those out too.
Kristen
That's it! Thanks. I didn't even consider the addition formulas.
This is awesome and so well-timed for me! We're just starting graphical transformations with trig functions and I'm planning a very similar project to what you have listed out here. Love that you had them grade everything.
One cool resource I found was over at wolfram alpha. You can tell it to 'play' a sine function, so yesterday in class I entered "play sin(880*pi*t)", which gives a sound with 440 frequency, which I think is a C. Nice audible interpretation of period.
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