Apparently I just hate geometry. Algebra just comes so much more naturally to me. I have two different geometry classes and I've branched off and went two different ways with them. I think this may be causing more work for me but oh well. One class, I've been going by the book and following the order of topics. In the other class I jumped ahead two chapters to start using sine, cosine, and tangent in order to prepare for our state testing on April 28-29. We keep being pressured to prepare the students for state testing but no one is telling me how.
I don't think anything frustrates me more than to be told to do something and not told how. I can't work with nothing here. The only suggestion I've been given is to use ACT questions on my warm up. Which okay, I can do, but the point of the warm up is to review what we did yesterday and lead into what we're doing today. Finding ACT questions to fit that purpose is hard as heck. I use this site which gives an ACT question of the day, but of course that doesn't align with anything I'm doing. I went to a conference on ACT test-taking strategies and I've introduced a few of them in class but...that doesn't seem like enough. My teacher bestie teaches English and she gives her students short timed quizzes so they can get used to working under a time limit. I've tried that. Once. But I'm just not feeling prepared enough to prepare them. In my opinion, they need more content which is why I've skipped ahead to the back of the book to get more of the content covered by the ACT. That's my big nod to ACT prep.
Anyway, I don't know a good way to talk about my separate geometry classes except for separately. In one class, my students literally do not care at all about class or school, period. They don't do homework and copy as much as possible. I have totally failed this class. But, I digress. The way we do class now is that I lecture all period for one day and they take notes and then turn in their notes for a grade. By notes, I mean I print out Powerpoints as handouts and they fill in the blanks and work out practice problems on those. That is how I do notes in all of my classes. I grade the notes and then give them back the next day when they are quizzed and are allowed to use their notes. So lecture, quiz, lecture, quiz. This doesn't really work either. Only a few actually understand their own notes and the rest just blindly write down whatever I write with no sense of where the numbers came from or what to do with them. But I don't know what else to do and so this is where I'm at.
These Powerpoints were mostly copied and pasted directly from the textbook, so they aren't anything magnifical but I want to share everything I can to help as many people as possible. I am definitely a lesson-stealer. I steal everything I can get my mouse on for the classroom. There's really not a lot to discuss, so I will just link it up.
Convex and Concave Polygons, HW Quiz
Angles in Polygons
Area of Squares and Rectangles, HW Quiz
Area of Triangles
Area of Parallelograms/Rhombus, Notes, HW Quiz
Area of Trapezoids
Area and Circumference of Circles, Notes
Area and Circumference Part 2, HW Quiz
Polyhedra, Notes, Quiz
My other geometry class is the one where we have skipped ahead. We started with simplifying square roots which came with mixed reviews. I thought this was something easy to start with but they struggled a little with it. I think part of it comes from the fact that I let them off too easy one too many days and now they think the year is over and they should not have to do any work. But we press on. Next up was special triangles 45-45-90 and the cheat sheet I printed on colored card stock paper and allowed them to use on quizzes. Did the same for 30-60-90. Cheat. After begging for help on Twitter, Kate, directed me to her blog post on introducing right triangle trig. I stole this from her and modified a tiny bit. I gave them this and literally had them draw nested triangles directly on the protractor, using the black line on bottom as there bottom of the triangle. They had a LOT of trouble with measuring and writing the measurements in the right ratio. I put the answers in the chart so I would remember, so make sure you delete those if you use this. It took two class periods to accomplish this and they didn't come up with exact measurements, but they did realize they had the same answers as other classmates with the same angle. This Powerpoint demonstrates it pretty well I think.
From there we transitioned from bottom, vertical, hypotenuse to opposite, adjacent, hypotenuse and introduced sine and cosine. We practiced on this and I just lightly hit on tangent. I didn't even have a powerpoint, we just discussed if we had already used sine and cosine, the only other ratio left for tangent would have to be opposite over adjacent. From there we went to the inverse trig functions. Here's a worksheet. Then I totally stole this review golf game from ilovemath.org and edited a bit for my people. Last but not least, the assessment.. I first gave them a 10 question standardized quiz that they have 10 minutes to work on. Then they worked in a team to complete this quiz. I had quite a few students who did not finish and had to come in later to finish on their own. I even let them use notes and cheat sheets. I may have sucked it up but oh well now!
I know this is the linkiest post ever but I had to catch up and this is just how I roll.
Feel free to steal any and all of this, edit, ask questions, etc.
I teach Geometry too and I always do the trig section right after the section on similar triangles. I can build on the idea that two similar triangles will have matching corresponding angles and their sides ratis will be equal. I have them predict missing sides on triangles that are similar, using a few given sides. Then I expand the idea by saying "Well, that ratio should work for any 20-70-90 triangle, right?" I get them to predict a side on another 20-70-90 using just the ratio, without setting up the propotion of sides. I do that for a couple of different types of triangles. I get them to tell me what ratios would be useful -- there are only three combinations. THen I can say "Wouldn't it be great if someone had already figured all those ratios out for us?" And I whip out a trig chart for every one. It's worked pretty well for me. I still hem and haw over using the trig chart vs. using a calculator. I try to get them to keep the trig expression to the very end -- no decimal equivalents to throw off the accuracy. But then state testing comes around and they can't use a calculator and are given pieces of a trig chart to use... meh. Ideally, they'd be comfortable with both, but realistically I'd be happy if they can do the problem one way!ReplyDelete
I didn't even touch similar triangles because we were so sick of congruent triangles.ReplyDelete
I do see how that would be a great transition into trig ratios. Thanks for suggesting, I will have to incorporate that next year.