What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was an opener problem I used the first day after I taught parallel lines.

What is it: This is a proof that practices using formal two column proof with parallels. It forces students to practice their reasons.

Why I like it: I like that students have to first practice the congruent complements theorem because even my honors students want to say substitution. Then, they have to prove the lines parallel using a converse to the original statements we learned the class before. Then, they end the proof using a straightforward statement. I think it is important that students have to practice and wrestle with knowing when to end their reasons with parallel or end it with an angle pair congruent.

Let me know if you used this and how it went!

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What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: Before I taught students what a polygon was, I just showed them some examples and some non-examples.

What is it: I used this in a powerpoint and had students, on their own, create their own definition of what an example was. As I revealed one example and then a non-example, I could see students constantly erasing and changing their definitions. Then, I had them work together and challenge each other’s definitions. Then, we moved on to practicing their definition. Only after, I told them that these were called polygons.

Why I like it: Instead of me telling my students what they need to know, they figured it out on their own. It appeared that everyone had the correct way to define a polygon before class was over and I did not have to do anything but guide them in the right direction and allow for discussion. So much more engagement than just telling them what the definition is and telling students to apply it.

Here is a link to the powerpoint if you want to try it out. Let me know if you used this and how it went!

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What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here.

How I used it: After students learned about the different types of angle pairs, they got to complete this challenge.

What is it: Students all went to the board with a partner and drew the diagram. With a marker and an eraser in hand, they had to try and put the numbered angles in the diagram so every statement was true.

Why I like it: So much discussion! Students were arguing (in the best way possible) over which angle goes where and why something was or was not a type. It was tricky because we had just learned the basics on a diagram with one transversal and now their were three! They learned that certain angles could be interior or exterior depending on what transversal they were looking at (or at least that is what they told me when we had a class discussion after the activity). I just acted as an answer key and when students asked me if it was right, I would just point out a counterexample and walk away. It was lots of fun and a nice way to get students up and engaging with the ideas.

Let me know if you used this and how it went!

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I have been slacking on this lately so here is hoping I can pick right up and keep going…

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here.

How I used it: This was a question we completed in class together as students were practicing proofs.

What is it: This involves students using the congruent complements theorem and angle bisector definition.

Why I like it: My students were tripped up about how to prove something is an angle bisector since they had to use the converse to the definition of an angle bisector (which I make my students write everything in if-then form at the moment). It was great discussion about how to use it and since it was our first problem that involved using a converse, now many are much more careful in checking.

Let me know if you used this and how it went!

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What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see my first post in this series here.

How I used it: This was a question on a review activity we were completing in preparation for our Chapter 1 Test.

What is it: This involves the idea of the segment addition postulate and ratios.

Why I like it: The idea of how students calculate lengths with the ratios always brings up interesting viewpoints like using 2x and 3x and some students doing it in their head and visualizing how to break it. The best part about this problem is how their can be more than one solution. Very few found that out at first glance.

Let me know if you used this and how it went!

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I could tell you why I love geometry but I think showing you is better. I am always on the lookout for great problems that can lead to some really interesting discussions. I have decided this would be a good year to share some of my favorites I have collected over the year in my segment called POTW = Problem Of The Whenever.

I was going to call it problem of the week but what if I do not have a problem I really like, what if we are testing, what if I just don’t feel blogging, what if…..this just works out better for me but still encourages me to share. I feel like finding good geometry problems can be difficult sometimes so hopefully this will give some people an extra problem or two as well as convince others to share!

In the future, I won’t bore you with all this text above so now lets get into a problem. Here are a couple of segment addition problems. Note: I teach honors geometry classes this year so these are geared towards them but I have had success using these with other geometry classes as well.

How I use it: I give this when students have just discovered what the segment addition postulate is and now need to practice a few. This is the first of 3 in a row I like to use.

What I like: Students usually approach it a couple of different ways and we get at what the midpoint is. Gets them to really describe to each other how they are convinced B is or is not a midpoint.

What I like: Students tend to assume the points always go in the order of A, B, and then C. This shakes it up a bit.

What I like: This allows students to practice their factoring skills and lets us discuss what occurs when you obtain two answers. The idea of a value being extraneous in the geometric world is always fun to have them debate over, especially in a problem like this where you can ask questions like: Does it matter if the variable is negative?

Hopefully, I will continue doing this throughout the year. Let me know if you use them and how it goes as well as any problems you would like to share!

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- Students need to see you care about them. I do not mean you should be telling them this verbally everyday but instead showing you value them. I try and find various ways to keep them engaged and practicing the material. They notice that I have put in effort to create a review activity or that I took time to give them feedback on something they wrote me. I believe students also see that I am fair. It does not matter if it is the student who is always making bad decisions or someone who has never gotten in trouble before but I am consistent in rules.
- When a student does something that I do not want to see in my classroom, I try and pull them aside to talk about rather than engaging in an argument in front of the whole class. I can always give a look or a quick verbal cue and then have the students start working on something so I have a chance to have a discussion about what just happened. It does not hurt to stand outside the classroom as students enter and talk to a kid this way as well.
- I like having both routines and chaos in my room; sometimes happening simultaneously. When students enter everyday, they know to go to the front of the room and grab whatever is out for an opener and begin work. They also know to have their homework out so I can check it and they can discuss. While this is happening, some students might be up at the board putting up homework questions they were stuck on while others are up answering them. At first glance it might seem a little bit crazy but students do a great job with this once I explain my expectations. This type of controlled chaos is what I enjoy having. I can hear conversations and discover misconceptions while looking on as others are trying their hand at a few practice problems. It seems to work for me and helps me decide right from the start of class where I need to proceed and anything I still need to wrap up from last class.
- One of the biggest things I have learned, especially being an early career teacher, is that having something for the students to engage with generally keeps issues down to a minimum. If they are actively working and participating on a task or a good problem, it is much more difficult for students to act out. It seems like when students finish something early or they already know how to complete a task, is when I tend to have most of my issues. I have learned to always have something extra to differentiate when needed and has helped out several times.
- My last, and probably most effective quality, is enthusiasm. When I get up in front of the room, I flip a switch and am really excited about whatever it is we are learning. I tend to flail around the room (as one student described it once) and constantly checking for understanding throughout the room while my students are working. Students can see I love this stuff and I believe it makes them want to like it a little bit more than they originally did. I get excited about students sharing methods. I get excited when they get something wrong that everyone can benefit from. I am just always excited to be in the room (even if I have to fake it a little on a particularly rough day). I may throw in an anecdote or a terrible joke for good measure too to get a laugh or raise the interest level.

I think that many of points go back to relationships. I believe this trumps everything else. Without that, I would have no buy-in and I feel like I would have a rough time managing any classroom. I am constantly working on making every student feel comfortable with me and with everyone else in the room. These are the things that have been vital to my success and I will continue working on them.

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I will be teaching geometry honors and algebra 2 studies (Learners who have struggled). In geometry I will be doing the same activity to build up a need for geometry vocab I have done before which you can read here. I will also be using my school fever activity that I have used before and you can read about that one here.

I have decided to try and get out of my comfort zone a little and instead of just reviewing how to plot coordinate points with my algebra 2 students, I thought it might be great to try and incorporate some sort of desmos activity instead. I am hoping that this will excite them instead of bore them to death on the first day of class. Students will be using the mini-golf coordinate activity with a few extra slides that I have added/modified at the beginning and at the end to lead some discussion about scatterplots. After being at #tmc17 and being involved in #desmoscamp I really love the idea of pausing and being able to restrict parts of the activity. This will be my first time trying all of this out on a new group of students day 1 but I am thinking it will lead to great success! If you want to see what it looks like and try it out then go here.

Regardless of what you are doing, I encourage you to think of ways to try and take a risk and go for something new. This has made me even more excited for the start of the year!

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Since this week is goals then I should talk about things I am looking forward to trying this school year:

- I am going to work on observing more. Observing my colleagues and having them observe me. We can all learn a lot from others we teach with and I want to try and do more of that this year. I also want to work on observing my students more. I want to have me do less of the talking and focus on listening to them and their conversations.
- I need to continue finding more hooks. More ways to get students pulled into a lesson. The morning session with the classroom chefs at #tmc17 talked a lot about adding small touches of humanizing aspects that students can engage with. I need to do this more often.
- I also want to work on discussion techniques. Even something as simple as having students stand up and talk to a partner about a strategy can make a huge difference. I need to capture more of those moments for students to talk with each other and share what they have learned.

I now see that the root of all my goals is on student perception in the classroom. I think these will be goals that are attainable. Now that it is August, it is time to start getting ready. What are your goals? Share them with me and lets keep each other accountable!

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- I learned nothing but friendly and amazing people attend this conference to make a first-timer feel welcomed
- I learned nothing but amazing things from Desmos and have inspired me to use the software even more
- I learned nothing can change how I feel about incorporating more student voice into my classroom
- I learned nothing will change in my classroom unless I take more risks
- I learned nothing but being vulnerable will help me grow even more
- I learned nothing will keep me away from the MTBoS and all the wonderful people involved in it
- I learned nothing was gained except an amazing new group of friends and an overload of ideas
- I learned nothing will stop me from attending as many TMC’s as possible

I learned a whole lot of nothing and I couldn’t be happier.

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