When I went to meet with the consultants I brought them materials from my trigonometry unit. they provided me with a variety of suggestions and we had a good conversation. Now that I've taught the unit I have some thoughts on what worked and what didn't.
Make a template for kids to fill out for every trig problem they do.
It was really useful, but I neglected to consider how big kid handwriting in dry erase marker is.
Remake the template so it only has the triangle to label, ratios and cues to solve and check.
Version I used this year (print on paper, slide into a plastic sheet protector, instant dry erase template!)
Have kids write out all the ratios, then pick the one that's easiest to solve.
It takes forever for them to fill in six ratios. All my students struggled with understanding opposite vs. adjacent at the beginning (even when I had them place a finger over the angle in question) and switching between the two angles was rough.
Undecided. I wanted to believe that with more practice the ratios would come faster but with the number of interruptions we've had lately it hasn't happened yet for many kids. I do want to do all six a few times and have kids notice that sin/cos all have the same denominator (hypotenuse doesn't depend on angle), that sin(A)=cos(B) and that tan(A) is the reciprocal of tan(B). After that discussion I'm not sure it's worth the time. There's value in looking at the information given, looking at the possible equations and choosing which one to set up and solve. I may give kids the option to do that in the future.
Have kids solve for all three side lengths using trig, then hand the paper to a partner to check using the Pythagorean Theorem. Kids won't want to check their own work but they'll happily check each others.
Kids don't finish at the same time. Waiting and interrupting are both bad options.
Some kids wanted to check their own work, which was great. Other kids I directed toward any student who wasn't working (not necessarily their partner), this gave kids who were frustrated with the spacial or algebraic demands a chance to do some computations. A few kids I checked for them. I like checking with the Pythagorean Theorem because we get to talk about equal vs. close. Next time I'll start with kids checking their own work and if anyone is resistant I'll offer the other options.
Having a three day weekend and state testing during the middle of our unit on trig was a problem. There were a lot of interruptions and with a block schedule they only have me every other day to start. It was hard to build any sort of automaticity. Such is life.
I also updated the trig intro investigation. That went well. (Original post has more detail.)
Suggestion? Have kids develop the template themselves, then create it digitally for them to use. I envision the checkboxes like in your revision that could go next to each trig with labels "Have" and "Need" so that they focus on the ones they need. Maybe they would like arrows connecting the ratios that are either the same or closely related.ReplyDelete
Maybe also large, blank boxes (like you'd have in prealgebra before you learn to use variables) around the triangles where they can write in the numbers. Although, I guess the upper/lower case letters go with the LoS and LoC better. Maybe a = [ ]? I don't know.
Maybe they want the Pythagorean Theorem written on there for them to remember to use it?
Maybe it's useful, maybe not. That's why I'm sort of suggesting the students take charge of the template. I like the idea of a semi-standardized template, though. I'll try to incorporate it into my precal next year!
I like the idea of having kids help develop the template. I contemplated putting the definitions of sine/cosine/tangent on there as well. Tricky balance between providing too much info and making it workable. This year they had a notecard with the definitions that they referred to as they went (notecards for reference has been our system all year).ReplyDelete
The kids know to write the number over/next to the variables they have. I want the letters there because they need placeholders for the parts that don't have values. I'm also open to being convinced that at this age/level it's better to use all different letters so we don't have to attend to precision to the level of A vs. a. I probably should have been more explicit about "A is opposite from a." This might help with the kids struggling to identify the opposite side!
Yeah, angle A creates side a (or vice-versa). If you make one larger/longer, then the other also increases. I see what you mean about avoiding clutter on a thing like this, though.ReplyDelete