Day 23-24: Similarity Day 2 + Trig

Busy day yesterday and wasn’t able to post – I’ll combine yesterday with today:

We finished the similarity unit by talking about perimeter, area, and volume ratios. I started class with an investigation on area and perimeter of similar rectangles. The sheet is downloadable below. I first started with some students giving guesses for how the ratio of perimeters and areas changed with the similarity ratio and If students finished early, I asked extension questions like, “Will this work for all rectangles? Will this work for all shapes? How is the volume ratio affected?”  I liked that students were able to confirm or disprove their guess by this investigation.

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Then, after looking at similar solids we reviewed the similarity unit. I used another trail activity for this. I actually made this when I student taught for an honors geometry class. I still use it because, even though the questions might be more challenging than what’s going to be on the test, the students don’t know that and they still try their best to get through the trail. They all were able to complete it (some with some guidance) in about 45 minutes to an hour instead of the 30 minutes that I had given in student teaching. I still think it’s a great way to review, practice, and challenge the students. It is downloadable below.

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The class ended with a test.

Today, we started with an introduction to trigonometry. I feel like it’s really hard to just give an introduction, though. I got into the ratios and how these are really functions instead of multiplying by a “sin” or something like that. It’s hard to understand the inverse trig functions without having a firm grasp on the fact that these are functions, but then some of my students have never heard of a function before. I don’t remember running into this issue before but it definitely took a little longer to introduce it than normal. I had groups in the class trying to answer some questions about trig properties – Can sine ever be greater than 1? Can cosine ever be greater than 1? Can tangent ever be greater than 1? Can any of the trig functions be less than 0? What about the inverse trig functions? Some students just started by trying to plug in a ton of numbers in their calculator. Eventually, groups realized that they really had to look at the ratios.

When we got into angle of elevation I was so excited to try Kate Nowak’s “Measuring a Really Tall Thing” activity. I had the meter/yard sticks and the students had a member of each group with a clinometer app (the iPhone actually has it automatically in it within the compass app so most of my students were able to get it). I then took them outside and they got to measuring. I only had six meter/yard sticks so I had groups of 2 and 3 and about half the groups were able to do it correctly within half an hour. They then had to help the other groups figure out what was going on. I blame this on not giving enough time for the kids to really figure out what they were doing and also test how the clinometer works.  I was so excited that I just kind of said “go”. Next time, I actually should have them mess around with the clinometer maybe even before we leave the classroom. Overall, I think they saw how this could be applied to find the height of something very tall and were excited to be applying what they learned to something outside (even in the 90 degrees). It was fun and the students were excited, and next time it will be much better because I’ll know how to introduce it better. I really wish I had taken pictures…

Je suis trop occupée maintenant. C’est difficile quelquefois d’écrire le blog.

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Day 4: Bingo Review and First Test

Today started by continuing to look at basic composite area/perimeter problems. All that was used was circles, rectangles, and triangles. I gave students one of those Geo Joke worksheets with the corny jokes. The students loved it! I remember loving them too, even though the jokes are so bad. I feel like it has something to do with the answers being there so they can immediately check if their answer was correct or not.

We then started looking at special angle pairs – vertical, supplementary, complementary. We did our first proof to prove that angles supp to the same angles are congruent and I didn’t force a 2-column proof on them. I actually like the 2-column proof because it is very clear that every statement needs a reason, but I also went through four years of being a math major and if you did a two-column proof in a 400-level math class you would just get laughed at. So I accept paragraphs or bullets as long as each statement has a clear reason.

I also handed back their first quiz and didn’t have a score or any points on it a la Ashli Black. I saw this video last summer and was absolutely amazed at this concept of not putting down a grade for the student, but was way too scared to try it in my school. In summer school I have a little less stress from administration and parents. In this district they want it to be clear to students how many points each question is worth, so the students could figure out probably what their grade approximately was, but I just wrote a lot of feedback. Even with the quiz only being 2 pages, 6 questions and me only having 17 quizzes to grade, it still took me a solid hour to finish them all. I wish I had a stamp for the commonly used feedback items. I will admit, I was a little bummed by the lack of shock and response from my students. I know it’s summer school but they were still just silent getting them back. A kid asked if their grade was in the gradebook and I had to say that it would be. Maybe it won’t make such a positive shift away from grades. Maybe it was just because it was the first assessment. Maybe it was because it was 9am on a summer day. We will see how they react when they get their test back tomorrow with no grade. This time, I will not go over the answers to the test – that also could have been why there was little reaction.

We did our first review game – Math Bingo. I would share but it was pretty bad. I mean the kids were all over it – once again, it’s like an answer bank given to them. But I totally messed up their answer bank. I had made copies of an old bingo sheet I had from last year without remembering that I had changed it so only about half the answers were the same. I still had a few bingos but it stressed kids out that their answers weren’t showing up and ultimately might have hurt more than helped some of them. Oh well…I can’t beat myself up over it.

Quelquefois, ca ne va pas comme tu t’attends, mais tu apprends de ces moments.