POTW: Segment Addition Postulate

If you had asked me before I started teaching, I would have told you their would be one subject I never want to teach: Geometry. I did not really get what it was all about doing an integrated curriculum in high school and I though proofs were annoying so I vowed to just stay away from it. Fast forward to now where I have taught some form of geometry every single year of my career…and I freaking love it!

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.

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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.

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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.

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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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Classroom Chaos – My take on management

Classroom Chaos – My take on management

This week’s topic for #SundayFunday is all about classroom management. While I do not view myself as a master of this YET, I do feel like I have certain strengths. The following are the things that lead me to be successful in the classroom:

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.

Fun Firsts? – First Day Of Classes 17-18

Fun Firsts? – First Day Of Classes 17-18

So a little behind here on #sundayfunday challenge but that is okay because the goal is just to #pushsend.

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!

Three Things – Goals For 17-18

Three Things – Goals For 17-18

Participating in a Sunday Funday post sounds a great way to jump on the blogging bandwagon momentum. More information here: https://ispeakmath.org/2017/07/31/lets-blog-together-sunday-funday-is-back/

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

  1. 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.
  2. 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.
  3. 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!

TMC17 Truths – I Learned Nothing

TMC17 Truths – I Learned Nothing

As I am back home and reflecting on Twitter Math Camp 2017, I feel like I have learned a whole lot of nothing.

  • 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.

Engaging Exhaustion – What to do after a quiz

I have always found that it can be tricky to re-engage my students after we take a quiz. With 90 minutes in class, I cannot just give a quiz and do nothing the rest of the block. Lately, I have found it really difficult to get students started up again. I have polled my students why it is so hard to get them working again when they can do such an amazing job at other times and here is what I learned:

  • Students feel mentally exhausted after a quiz
  • Students say it is hard to get started if it is a new topic
  • Students don’t want to do anything else
  • Students want to do something that is not “too hard”

I was trying to come up with different ways to get my students re-energized. While most were done and I was waiting for a few students to finish a quiz, I had students complete this little half-sheet below.

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Since others were still finishing the quiz they couldn’t talk to me or each other. The topic of logarithms was something I introduced last class. I did the first problem in each row as an example to show them. The result: Success. Almost every student actually completed it without any moans/groans and it was great to discuss any misconceptions about logs before we moved on with our next topic. Students told me afterward how much they liked that I did the first one since it acted as a reminder and took away the intimidation factor. I need to find other things like this that can engage them. I could even use this to recap something from a previous day.

Plain Practice – A last minute idea that was not half bad

The other day in my geometry honors class, I had to teach special right triangles. I knew that I just needed time for them to practice and didn’t have time to create some type of interesting way for them to practice. I grabbed a couple of worksheets to bring with to class. I decided at the last minute to make copies of the answer keys. As students worked on the practice problems, I placed my answer key copies up around the room. To my surprise, my students were working really well and only asked me a question when they critically needed it. My last block of the day would probably have kept going if I didn’t stop them to move onto something else.

One thing that made this more effective than I thought was also having two worksheets. One was simple practice with the special right triangles and the other was tougher with application problems. It was nice that students could use this and differentiate a little. Allowing them some movement didn’t hurt either. I think that I just need to give my students time to work and ask questions and I don’t always need something flashy and exciting to help them learn. I was feeling kind of bad about this and now I feel, even though I could still always update the worksheets for next year, that it was pretty solid and the students seemed pretty strong on the homework that I assigned. I needed to write this to remind myself of these things.