# 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.

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 6: Polygons

Today didn’t feel all that exciting but we got a lot accomplished.

In summer school (and actually in regular school but we’ll see if I change it) I only assign about 6 homework problems a night. I have such different types of students and I want to make sure they all get proper practice of they want it. I do not grade it. It is purely for their practice. The last two years I have done homework quizzes randomly and I don’t know if I will continue it this year. I usually ask if there were any questions from the homework after showing the answers with no work. Usually I get one or two questions. Today we went over all 6 homework questions.  I had other students in the class answer them in multiple ways. I thought it was really beneficial for the class to see the multiple methods that all get the same answer. I did have some kids who clearly didn’t think this was a good use of time – luckily I was the only one who could see their eye rolls after yet another question was asked. How do I get these students to see that this could help them, even if they already got the right answers?

We looked at triangle angle sums and remote interior angles. Then we got into polygon angle sums with a little dabble in naming polygons. I saw what Dan Burfeind did with this and created my own. I gave each group a stack and said to put them in groups. That’s all. They asked how? I said just group them. They asked what words meant. I said just group them with what you know. There was some hesitation at first but after a minute or two they really got into it. Every group made a few different groups and we shared some of the ways to group them. Then I revealed the number of sides and asked if they wanted to regroup. Some did. Some (rightly) said that their categories were just fine. I love that the students were taking just what they noticed with little background knowledge to get things sorted. Great discussions too.

Students also took their second quiz and started looking at parallel and perpendicular lines in the coordinate plane.

Une journée un peu longue mais au moins j’ai des photos!

# 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.