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 11: Millionaire Review and Starting Quadrilaterals

Today was the most Monday-est of Mondays. The kids were zombies, I was probably a little zombieish, it was rainy all morning. I also didn’t have something with a lot of movement going today, which maybe would have helped. I had two things that were more interactive, but it was not enough…

So we started with a review of the chapter on special segments in triangles that we had finished before the weekend. My mistake was expecting them to be able to jump right in and remember everything. We did go over the homework, but kids were still rusty. Is that my fault for going too fast when teaching the stuff, or was it because it was 8am on a summer Monday? Probably some of both. But I tried to do a review game I’ve enjoyed before that I call Math Millionaire. It’s like Who Wants to Be a Millionaire. I have a bunch of multiple choice review questions that I will show one at a time to the class. The goal is for the class to get a certain amount in a row correct for a prize (I picked 6 in a row for today). They are in pairs and have to quietly work through the problem. I do pairs so that hopefully every student can feel some confidence in their answer after discussing with their partner. When an adequate amount of time has passed or all pencils are down, I call on a random student (using ClassTools.net or Triptico) and that student tells me their answer. If they’re right, they keep going for the prize. If they’re wrong, we talk about it and they start back at 0 in a row. I love this, also, because if they get it correct I now have an expert on that problem that can explain it to the class. Usually the class gets a prize once or twice. Today, not so much. It wasn’t really that the kids were always getting the wrong answers – it was more that it always got to the 5th or 6th student and that student just wasn’t trying with their partner and would just guess. The class got kind of angry. Looking back, maybe I shouldn’t have allowed those kids to participate, but I thought maybe they’d see the benefit in buying in at least so they didn’t get the whole class against them. I’ve never really had that happen. I’m blaming it on the Monday…

We then had the test on the unit and then started to look at quadrilaterals. This is the last unit of the semester and I’m a little more crunched for time on it than I usually am. I started with a discovery activity that took the students through properties of different quadrilaterals (download below). I had all students work for about 45 minutes in their measurements and would always keep pushing students to make more than one observation. I then had each group present one quadrilateral where they had to tell the class what they noticed and what made that one special. It was good, but always takes longer than I expect to do all the measurements. It helps students really see that the properties of different quadrilaterals are true. I wish there were even more examples to measure, but then it would take even more time. It does save time going over the different properties later like their textbook wants to do, so I guess that’s a tradeoff.

C’était vraiment un lundi…quelquefois, il n’y a rien d’autre à dire.