Summer Geometry Reflection

Today was the last day of Summer Geometry. All of my students that were taking the class to replace a grade improved their previous grades by at least a letter (most did 2 or 3 letters). All but one student who were taking it for the first time got an A or a B and were pleased with that grade.

  
I did have one student who told me after the first day that he would fail. I tried to motivate him in class, tried talking to his mom to see what could help, and tried getting him to work with me one-on-one before or after school. Nothing worked. In class he would try to turn in tests after 10 minutes with most questions blank. I wouldn’t accept tests early that had blanks so sometimes he would just stare at his test for an hour. Sometimes he would write responses such as “cheeseburger/hamburger” or “x = 5 billion” on every question right away and try to turn it in. The crazy thing was, he was an out-of-district student and was taking this class because he had moved and the school he moved from didn’t teach geometry until junior year, but the school he moved to taught it sophomore year so he wasn’t going to be in class with his peers and apparently he had begged his mom to pay the extra money to take this class. I guess that’s what the Common Core is trying to prevent, right? I will admit, summer school math is not for everyone – it is a class where you have to learn quickly and/or be able to put in much more than the minimum effort outside of class to be successful. He told me he knew he could not understand the material and retain it quick enough after he saw what we did on the first day, and he was not prepared to work so much outside of class for one class. First semester, he earned a D- after I convinced his mom to bring him to school an hour early for the two days before the final exam so that he could retake tests. Second semester had many projects and, even though most students finished them in class, he refused to work. He told me he wished his mom would let him drop the class so that he could get a job and pay her back. It was second semester that he started doing anything he could to get out of class…started being disruptive to other students during work time, during a test he pulled out a newspaper and started reading it, blatantly held out his phone playing a game with the sound on while we were taking notes. Eventually, he figured out that attendance could get him kicked out of school, so, even when his mom dropped him off every day about 20 minutes before school started, he started walking into the classroom very late. On the day he was kicked out of class, he walked into my room 45 minutes late. He had a 12% in the class.

At first, I was beating myself up about how I could get this kid motivated to just try during class. I believed he could earn at least a C if he really tried in class and on the tests. Eventually, I started to feel bad for him – he understood that it was time to quit and move on, but his mom wouldn’t let him. I know it’s frowned upon to be a quitter, but sometimes it’s in your best interest (see Freakanomics Podcast Episode “The Upside of Quitting”). He could have even taken the class as an audit, but his mom wouldn’t let him. She wanted him to see the consequences of his actions. I asked my parents what they would have done if my brother or I did something like this in a summer school class. They said they couldn’t even think about it because they knew it would never happen like that – if either of us were struggling we would have done all that we could to pass. My parents couldn’t really imagine being in that situation with us. Near the end, I started to get angry at my student. He knew how to act respectful to his classmates and to me, but he was purposely acting out so that he could get out. I had so much stress from this one student for most of the six weeks, but when he eventually got kicked out I went back to feeling bad about the situation. I don’t know if there was anything more I could have done.

I liked blogging about what was going on in my summer school class. I think it helped me to have a place to reflect or even quickly jot down any interesting thing that I did. I don’t think I can do the 180 thing during the regular school year, though. I’ll have four new classes to plan for and will most likely just be trying to survive.  I do hope to keep up with the blog, though. I might set a day or two each week where I make sure I blog. We’ll see.

C’est fini! C’est l’été!

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Day 28: Final Review (2)

Today is the last day before the second semester final exam. I have a bunch of activities planned for final review days and then I also usually let the students have at least an hour of free review where they can work on their semester review packet as well as ask me any questions. All the activities I list are attached at the bottom of the page.

Activity 1 was Tic-Tac-Toe with similarity problems. I displayed a 3×3 board and split the class into 2 teams. Usually I can say girls against boys but I have only 3 girls and 14 boys this year…even so, the girls wanted to show the boys they could beat them. I then had a student from each team play rock paper scissors to decide who goes first and that group picked a box to start in. The goal was to win Tic-Tac-Toe, but you could only get the square if you answered the question correctly, and the other team could steal it if you got it incorrect. It’s always surprising to me how competitive a simple game like Tic-Tac-Toe can be (especially without it being Ultimate Tic Tac Toe). It ended up being 1 to 1 after two games, but still fun.

   
 Then, I had another trail (can you tell I like those?) for trig that was really just basic solving triangle stuff. There are two “tracks” in this one so I had to make sure the students were just staying on their track the whole time.

I also did another round of Last Man Standing for surface area, volume, and area review, but this time I added a box where they could see how much of each item there was. That way they couldn’t be surprised if something not-so-great was the last thing they revealed.

I then had another Roundtable review for circles, angles, and arcs.

I was planning on having some time for Mathketball or Grudgeball but we didn’t have time…I had promised an hour at the end to do their own review and ask me any questions and many used that time wisely. We’ll see how their final exams go tomorrow.

Downloads:

Il y a trop de choses de faire avant le début de l’école!

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…