Day 12: Finishing Quadrilaterals and Deal or No Deal Review

Today was the last day of learning new material before we kick into reviewing for the final and taking the final (no school July 3). It was kind of rushed. Next year I will do less algebra review at the beginning. Not sure why I decided to do that this year. Last year I did it because I had a sub the first two days (my school was still in session from emergency days) and didn’t really want her to start teaching the real geo stuff. This year I just didn’t want to think that far ahead…

Anyway, we started off with a quiz on what we learned yesterday and then got into properties of special parallelograms, trapezoids, and kites. I really like this unit because there’s a lot of fun work you can do, but I know it’s also one of the most difficult for the students because they have to memorize so many properties. I try to give them as much practice as possible. I start with giving them a ton of different practice worksheets. I let them choose three out of five that they need to complete, which gives a mix of quadrilaterals in the coordinate plane, proving different quadrilaterals, and using properties of the quadrilaterals. They can do the ones they want more practice with.

I then have a “Two Truths and a Lie” for quadrilaterals (download below). This activity consists of students coming up with three statements about a quadrilateral. Two must be true and the other must be false. The goal is to try to come up with two truths and a lie that will fool the rest of the class. I let them come up with some for a few minutes and then they can share with their classmates. I also let the students share a Two Truths and a Lie about themselves for some extra fun.

I also have a Rally Coach Activity (download below). Students are in pairs and have a Partner A and Partner B. The students take turns giving some properties and the other student has to figure out which one quadrilateral it is. Similar to Two Truths and a Lie and short and sweet, but it’s more practice.

I also did one of my favorite games that I call Deal or No Deal. I got the idea after student teaching from another teacher that graduated with me and it’s always made class fun with very little prep. All you need is a worksheet. You then have some sort of prize (candy, sticker, pride, extra credit, hw pass, etc.) or multiple prizes that is hidden behind a number – I say that they have 12 briefcases and they have to guess which one has the prize in it. Today I had a major and a minor prize. Then the students get to work in groups on their worksheet and try to get through as much as they can. You give students guesses at where the prize is based on how many problems or sections they get done as a group. I had a lengthy review packet that had many different sections. I told them that when the group has two sections done, they get a guess. I do this in groups so that students have more motivation to work (hopefully) and to reinforce group work. Students are not required, however, to all have the same guesses in the group. For instance, if Mary, John, and Jack have earned 3 guesses for their group, Mary can guess that the prize is in briefcase 1, 2, 3, John can guess 6, 8, 10, and Jack can guess, 3, 4, 5 if they want. What I love about this is that it transforms a worksheet into something fun, and students start to think about which problems/sections would be best for them to solve first. They do some reflecting about their own skills to help them get more guesses, and they also get a little probability in there to see that the more guesses they earn, the better chance they have of guessing correctly. I love that this also takes no prep besides the worksheet. I took post-its and cut them in half and under two of them (6 and 10) put stars for prizes. That’s it! And the class is engaged and begging you to get over to their group to check their sections the whole time. Somehow it also stays engaging every time.

Deal or No Deal  Deal or No Deal Prizes

Les activités les plus simples sont, quelquefois, les meilleures!

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 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.

Day 10: Special Segments and Triangle Inequality

We did an entire unit today. It started out with looking at midsegments and then we moved to perpendicular bisectors, angle bisectors, medians, altitudes, and all those fun centers that go along with the points of concurrency. I had done this awesome discovery activity when I student taught where it takes you through determining if the segments have a point of concurrency and all those equidistant things, but I couldn’t find it anymore. I searched for some ideas online but couldn’t find anything I liked that much. I didn’t think to email my old Geometry co-op until typing this out…maybe I can get it for next time. But we did go through what some of those relationships were and had fun drawing all the segments, using different colors and everything.

I also did a discovery activity for the inequalities in triangles. To see that the sum of two sides have to be better than the third, I had the kids use stick pretzels to test it. The only issue is that when they get to the one where the sum of two sides equals the third (which shouldn’t work) a lot of the kids don’t follow it close enough to make sure the two pretzels are really exactly the same size. Because of the error with that, a lot of times you have to go through that set again with students. I had some pasta sticks on hand for that purpose because it’s a little easier to see (but definitely not as fun to eat). Here’s the file:

I also had some kids turn in their Swan Challenge. It’s all about finding angle measured in this really complicated swan picture. Takes a lot of focus but it’s actually not too difficult once you get on a roll. Really more about perseverance. Here it is if anyone wants it:

Quelquefois, je pense de quelque chose un peu tard, mais c’est pas grave. Mes étudiants apprennent encore.

Day 9: More Triangle Proofs

Today was a continuation on proving triangles congruent and parts of triangles congruent. We did a ton of just practicing proofs. One way we reviewed for our test was to have pairs at the board. I forgot who I saw this idea from so I’m sorry I can’t give credit, but I definitely didn’t think of it myself. I wish I would have known about this strategy last year. Anyway, I gave each pair two out of 4 possible proofs and made it so that the group at the board next to them wasn’t doing the same two. The partners had to be using a different colored marker. Then they just had to redraw the figure and givens and then do their best to complete the proof. It was great group work and I loved that the students were happy with their successes. Groups kept erasing their work but I did get a picture of one group. While most groups switched off on who was writing on the board, this group chose to have one person always write out the statements and reasons and the other person mark everything in the figure. I liked how they talked about the different parts of their proof, especially when one started writing ASA and the other one showed why it was really AAS. Great discussions, happy students, happy teacher.

Un jour pour la pratique n’ait jamais fait de mal à personne.

Day 8: Triangle Congruence

Our main activity today consisted of discovering the triangle congruence theorems and postulates. I used an activity (download below) where students had to construct 6 different triangles. Four of them can only form one triangle, two of them (AAA and SSA) don’t. I have students construct these in groups and then at the end I let them tape up their triangles on the board with all Triangle A’s together, Triangle B’s together, and so on. Students then do a gallery walk where they are asked to give what they notice about certain triangles. In the end, they see that SSS, SAS, ASA, and AAS gives us congruent triangles. One thing to note is that this take a long time. Even with groups of three and only six triangles, it took my class an hour to get them all done. Groups that finished early were asked to try to make different triangles with the same given information. But I think the time pays off in the end because the students can really see that AAA and SSA really don’t work and are pretty surprised that the others do.

 We then practiced a lot of proofs and got into CPCTC before they took a quiz on it. The quizzes were ok…not great…but this quiz usually is. I leave a lot of feedback on what could help them in their proofs and usually this helps them a lot. Hopefully they actually look at my feedback. I usually get some comment like, “Well I knew we had to use CPCTC in the proof during class because we just talked about CPCTC but then in the quiz all I could think of was No Choice Theorem.” No Choice Theorem?! You mean the thing we literally did one example with and then never touched on again? Ok…I’m still searching for the best way to help students with proofs in such a small time frame. I feel like during the regular year when this unit spans weeks, it would be easier for students to build up to their reasonings.

Les étudiants pensent que les preuves sont trop difficiles, mais il n’est que le début!

Day 7: Place Your Bets Review and Congruency

I thought yesterday was a bit boring. Today was fun.

We started by practicing graphing and writing equations for parallel and perpendicular lines. Regular practice stuff. Nothing amazing. A student who missed class yesterday (which is a pretty big deal) was working with a volunteer tutor that just happened to be in the math wing that day so it was a good time for class practice while he could catch up.

We then reviewed the parallel lines and angle sum unit with a Place Your Bets game. I had a 10-question PowerPoint (download below) just with questions and answer choices. I was used to playing this game with a sheet where they would put their work and wager with numbers. I’ll put that below to download as well but it’s for sure not as fun as the way that Sarah Hagan does Place Your Bets. I of course forgot to take pictures but it looked similar to the ones Sarah has. Except I realized this morning that the room I am using for summer school is completely bare so I do not have chips or unit cubes or anything small and plentiful. So I improvised and used ripped up colored paper. That was a mistake but also smart…I first had the kids just rip the papers up into small pieces and didn’t specify how many they needed. I probably should have set a limit because the kids went kind of bonkers with this…I also remember seeing that Sarah set a limit for how much could be bet each round, and thought 25 was a good amount. That was a lot. I ended up getting different colors of paper and making green (what we started with) equal to 1, pink was 5, red was 10, and purple was 25. It was super fun but took also a lot longer than I expected. I actually only got through 6 questions in 45 minutes but then wanted to have the kids do some practice in their notes before our test. I know we didn’t get through a lot of review but the kids had great ideas and I learned something new about this game. Even though it was long, kids were all saying they wished they could do more, so I’m going to try to incorporate it without so much scrambling later.

We then had our second test. I gave back their quiz, which once again had no points marked. I think that since I gave them back when they were still doing group work, it brought out a little more discussion on their mistakes. I forgot to do the thing where they grade themselves like I said I would before, but I liked how they just were talking about how they did and maybe stopping that would have been bad.

I then went into our next unit and introduced congruent figures. I started them with this Illustrative Mathematics task that I found from Kate Nowak. We were able to have an awesome discussion about what it must mean for figures to be congruent, especially with Set C that has to be “flipped”. At first all groups were just eyeballing. I did a quick Plickers assessment for each set to see if the class thought that the shapes were congruent. All sets except A had a disagreement within the class. I said that we have to agree before we move on. The kids went back to discussing/arguing about the shapes in front of them, but then a student told me that it was hard for him to tell if some angles were really the same just from the looks. I asked him if there was anything that would help him make it easier to tell. He said a protractor, another student said she wanted scissors to see if they fit on top of each other. It’s funny how these ideas catch on like wildfire. Eventually all students had a tool – protractor, ruler, or scissors. Talk about Using Appropriate Tools Strategically (CCSS MP5)!!! We then did Plickers again and only had a disagreement on the flipping of C. So then I told them the definition of congruent figures and we had another discussion…at the end of the day everyone was agreeing on all sets! What a great way to end the day!


Nous sommes d’accord! Nous sommes d’accord! 🙂

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.

img_4230 img_4232

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!