Day 26-27: Circles

Yesterday and today we looked at angle and arc measures in circles. I give a whole bunch of practice on these types of problems – central angles, inscribed angles, angles formed by secants and tangents and chords…It’s a lot for them to distinguish in two days but with all the practice most of them get it.

Yesterday didn’t really have too much excitement…today was the opposite because we played another awesome review game. It basically is Grudgeball but I do have a few adjustments. I introduce it with talking about Mario Kart’s battle mode – I talk about how I love Mario Kart but I hate playing the battle because my strategy is always to hide out because I hate getting my balloons popped. We talk about strategies of the game for a minute or so (further confirming to some students how nerdy I can be) and then I tell them they’ll be playing a version of this today. When I had an interactive white board, I would actually project balloons for each team and then students would slash or un-slash a balloon. This time, I just drew X’s and let groups erase or redraw an X. I gave everyone a pretty extensive review packet and said that for every two that the entire group shows me is correct, they could pop a balloon from another team, and for every three they show me correct they could blow up one of their own balloons. The students asked to do this for every review, but then thought of Mathketball and said we should split between the two. It really was engaging to all of them and I believe it helped them review as well. Some other notes:

  • I don’t let groups get multiple pops or blow-ups at a time – they either show me two or three and then I say “correct” and give the marker or eraser or “at least one part is incorrect” and then go away from the group. This keeps groups from just saving all of their problems for the end.
  • I had each group start with three balloons (X’s) and they could never have more than three. I wasn’t sure how the game would go over with high school students but next time I would give more balloons.
  • In the final five minutes, I tell groups that I will walk around to the groups one final time at the end to see if they can earn their last pops/blow ups. I take note of what they’ve earned then but don’t let the students go up to the board for this. When I’m done going to the groups, I then go randomly through the groups and tell the class how they want to use what they’ve earned. So it could be that there looks like a clear winner at the end, but in the final minute all groups wanted to pop that one groups remaining balloons and the game totally changes. I like this because it doesn’t allow groups to just slack off when they see they are winning or losing.
    All groups started with 3 “balloons”.

    Groups 3 and 4 were winners! It doesn’t look like much changed but there was so much change during the game…should have taken more pics.

I also had been given this clever cheat sheet for finding angles in a circle called “Dude Where’s My Vertex?” and I’m attaching that below.

La vengeance est amusante en classe!

Day 25: Finishing Trig

Today was the end of our tiny trig unit. Students worked on using trig to find areas of regular polygons that they hadn’t been able to find before (nonagons, pentagons, etc.) and did a group activity that I call a Roundtable. There are up to four members of each group and all start with a very similar problem. The first step is very simple and after everyone is done, they all pass their papers clockwise in the group. The next step will have something to do with what the person did before them, so they have to not only check the work from before, which could lead to great discussions, but they also have to continue with the problem. You will find two versions in the file below – one for a pentagon and one for an octagon. To challenge some groups that finished quickly, I asked them to check their answer using the similarity ratio before I check their final answers. They seemed to like being able to check themselves and I heard awesome discussions.

I am also attaching a picture of some students’ work on angle of elevation/depression problems that they did on the board. I introduce these with statements like “Guys, these are all gonna be word problems *listen to groans* but word problems are the best ones to show your creativity! We’re leaning a ladder against a house here – look at how nice my dream house is! *takes a little too much time to draw a nice house with a ladder leaning on it in front of class*” Now most of my students actually draw out what they’re seeing. It might waste some time but I feel it gets a little more investment out of the ones who would normally shut down to a word problem.


They also did a row game last class that I forgot to include. Basic trig stuff, but once again I think the students like being able to check their own answers and that’s what the row game gives you. Download below.

Download:

Les réponses données encouragent les étudiants à essayer plus.

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.

Day 22: Similarity

Today was the real start of similarity. Yesterday we got into it a bit at the end but there was too much excitement over the tin men. It wasn’t all that exciting of a day – lots of notes and then practice and then notes and then practice. The roughest part was similarity in right triangles. In the past, I’ve just told them the proportions to set up with the geometric mean like my teachers did with me and then went on with the unit. I thought it would be a good idea to prove this relationship this year…not the best idea. Or probably more likely I just didn’t do the best job of making it work. It just seemed like a bunch of random letters and redrawing and was kind of a mess…I still think proving it would be the best way for the students to truly understand why we have the geometric mean in right triangles with an altitude, but next year I will have to find a better way.

Il y a toujours l’année prochaine!

Day 21: Tin Man!

The Tin Men have arrived! This activity was awesome! I couldn’t believe how well it worked. It took a total of about 4 hours and 90% of the students were working that entire time. I used pretty much all of Elissa Miller’s Tin Man stuff. The reflection was homework so I will be reading that tomorrow. I only had six groups in summer school but 4/6 groups got the surface area right (I gave all groups a 5% error because I know the sphere and cone are difficult to wrap) and the other two got more aluminum foil after a point deduction on the project, but they weren’t that far off. One group also needed more time, but finished it after the end of class. It was tough to get to the start of similarity after this – next time I would try to have it all on one day.

J’ai dormi avant de publier ce message. Je me suis fatiguée, je suppose…

Day 20: Volume and Surface Area (and Tin Men)

Today was mostly review on Surface Area and Volume. We did Deal or No Deal review again and I got much better investment from the students than last time. I was just going to do it for an hour but it ended up going another half an hour because the kids just wanted to continue.

After their test, we got started on the Tin Man Project. So far they’re really into it. I was so surprised by how many cardboard objects we got! I meant to take a picture of them all before the students got to them. I was worried since I was really the only one that had brought anything in until today. I didn’t think to send out an all-staff email to see if other teachers could bring in stuff but it turned out fine! Here’s some of their work so far and they will hopefully finish tomorrow:

Il y a encore beaucoup de travail à faire pour ce projet.

Day 19: Volume and Spheres

I love the surface area and volume unit and like Lisa Bejarano, I just wish there was more time for all the cool projects out there! I already had a couple that I knew I would do, but coming across Lisa’s blog post opened up so many more that all seem so awesome. It was hard to choose what to pick. But I decided on doing many 3 Act Tasks – the File Cabinet yesterday, and then today I did Dan Meyer’s You Pour, I Choose and Meatballs. I worked them in the same way that I did the File Cabinet yesterday, so they take a long time, but students are engaged, curious, and working the whole time. I had a bunch of other activities cued up from Lisa’s list but I will have to see if there is maybe time at the end of the semester during final review. I will be doing Elissa Miller’s Tin Man Surface Area Project next class now that we’ve talked about surface area of spheres. I’m very excited to see how that goes!

Funny asides:

  • Apparently when I said “sphere”, a good chunk of the class thought I said “spear”. So they were preparing themselves for “working with spears tomorrow”…
  • I got comments from the class about how I know a lot of guy math teachers that are in my videos. I showed two male teachers, and not my videos. But high schoolers can think what they want…
  • Before doing the Meatballs task, I told them about how I was a terrible cook and always run into problems when I try to cook a real meal. I said that the next video is something I still haven’t learned from and run into this problem too often. Had them guess what kind of problems I could run into making spaghetti and meatballs with marinara sauce. The guesses were hilarious and the cooking stories that came from it were even better.

J’aime que mes étudiants ont un sens de l’humour, même avec un cours d’été.