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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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!

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.

Dividing Daredevils

With my regular geometry class, I wanted to have an activity that they can get started with right way on the first day of school. I came up with them dividing shapes into similar figures using this worksheet below:

I think some students will divide into four congruent shapes while others will divide into four similar shapes. It can generate discussion about what the difference is and motivate some discussion on how these will be two huge concepts for the rest of the year.

Enjoy your remaining summer while it lasts!

Students Think I Am Weird + Lots Of Fun Problems = First Week Of School

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This week’s challenge is to talk about how the first week of school went so here we go!

This school year is different since we are on a Block Schedule but here is what happened on each day. My first week started the week of 8/25.

Monday: Prof. Development Day so I won’t bore you with those details.

Tuesday: More Prof. Development and then freshmen run through their schedule (literally running) and we get to meet them for a few minutes. They have 6 minute periods with no passing period time (so that makes sense right?). I feel so bad for freshmen who show up right when the bell rings to leave and they are huffing and puffing. To entertain them, I put a problem up for them to solve and discuss while we waited for more to show up. Then, I talked for one minute about what to expect the next day…”Expect to be learning and thinking. This will be your favorite class this year and you will have to wait and see why starting tomorrow.” I let them take guesses at the answer for the problem and then I tell them I will reveal the answer tomorrow. I love that in a short span of 6 minutes (even less since most arrive and then RUN away) I can sucker some of them in waiting for the next day. Since all my freshmen are in geometry and geometry honors, this square problem is perfect. Here is the problem below. Tweet me @jomalleyiv if you think you know the answer!

How many squares are in the figure below?

How Many Squares In The Figure

Wednesday: This is a gold day and I teach two sections of regular geometry and one section of honors geometry on this. (G for gold = geometry so I can remember when I am teaching stuff!!!!). When students walk in, they are instructed on the board to grab the worksheet at the front of the room. Everyday, they have an opener to grab so I like to start the routine immediately. It is an info sheet they fill out while I am waiting for stragglers. I let them go for about 5 minutes and then I put this problem back up on the board and I have them all take a guess and write it down. Then, I have some kids offer up answers and we discuss (usually someone counts all the rectangles). We talk about the answer and some other things that will reveal the answer so I won’t add anymore onto that. Then, we did the activity that I have posted about in the past here: https://functionsarefun.wordpress.com/2013/08/12/buliding-up-geometry-vocab/. After that, we used that motivation to talk about points, lines, planes, etc. Not the most exciting “lecture” but they were eager to learn from our “game” that we just played so I think it was okay. We even got to talking about the segment addition postulate. I let them try some problems and they figured it out by themselves!

Honors geometry was similar. I did the same geometry vocab game and the same square picture. After we talked about points, lines, and planes I gave them some t/f and always/sometimes/never questions for them to discuss in their groups. What is awesome about this group in particular, is when I say I want them to discuss they ask how and what they should say and then do it. With regular, they need more guidance on how to work in a group (I have all students in groups of four) but these students jump at the chance to discuss and debate. It is pretty awesome.

Thursday: Blue day so I teach two sections of Algebra II Studies (lower-level). I start with School Fever and it is a success as it has been in previous years. I blogged about it before here: https://functionsarefun.wordpress.com/2013/07/29/first-day-algebra-ii-will-you-catch-the-fever/. Then, I gave them a whole bunch of graphs that I hand-drew different models on and they had to highlight the model that would be appropriate for the situation (some examples were time vs. distance, time vs. height, days vs amount of water used). I like that I force them to use a highlighter because you can’t erase so it forces them to stick with something even if it turns out to be a mistake in the end. It was great and we had some awesome discussions. We then did a little algebra practice and the day was over…so fast!

Friday: See my geometry kiddos again. I am getting tired of typing at this point but we did more practice (in both classes) with points, lines, and planes. I had a lot of problems for them to try and practice/struggle with before I would jump in and help. We talked about unions and intersections with points, lines, segments, and rays. I gave them highlighters and had them color in the parts we were talking about and it seemed to really help make a big difference. Lots of practice this day but they seemed to enjoy the time to gain these skills and work together. I did not do much talking and I loved that.

This year will definitely be interesting and a lot of hard work but I really have amazing kids in all my classes and I am so excited to work with them this year!

Buliding Up Geometry Vocab

made4math_smallHere is an activity I made that I am going to use for geometry. I plan on using it the second day after we do some critical thinking the first day. I am totally fine with the students not knowing vocabulary at this point but it is interesting to see what they know as well as how they can communicate. What is great about this though is that you can use it as your first day geometry activity as well.

Here is how this works….

  • Each student pairs up with someone. One of the partners receives one of the two pictures from belowdrawing activity set 1. You are not allowed to show your partner the picture! (Note: I have two pictures so pairs sitting right next to each other cannot just listen to another pair’s discussions.
  • Students put up some sort of a divider in-between each other
  • When it is time to start one partner will draw the picture while the other student must only give directions and is not allowed to use hand gestures.
  • After some time I give the second set of pictures shown below and have the students switch roles. I usually pause before the students switch roles so they can talk about general strategy or things they thought were effective in at least getting them close to the pictures that were provided.

I think I read someone else doing this on a blog or something after they learned material so I made it my own. I actually like doing it before as it is fun to watch students squirm to explain how to draw something geometrical. I use this to springboard into the fact that we need a common language and it is hard for us to do something like this if we are only using words. Geometry, and math in general, has its own language and it can be really cool…but if we are all now speaking it the same way then it makes life difficult. Just like if you were in a language class and kept conjugating verbs incorrectly when you speak, it makes everyone kind of cringe. That same applies to this class as well. It makes sense for the kids as to why we need to then learn what a line or a point is and how to talk about them. I also hear students say things like “draw an equilateral triangle” and I ask where they have heard and how do they know it is equilateral. (Usually get something like “because it looks that way”) This helps me stress the importance of vocab and that they must precise on their definitions!

I also like to then do this a few weeks later (kids keep asking to do it all year because they think it is fun and probably don’t realize it lets me listen and focus on which students have mastered the vocabulary) and it really helps me assess my students in an informal way. Here is the second set that I give when the students switch…though this is much tougher mostly because one of them has a plane. The circle one seemed to be easier. I hope that if you use this, that your students will have as much as mine did. I am sure my honors kids this year will also enjoy it. Drawing Activity Set 2Of course, you can always make your own pictures and use whatever makes sense for you. It was easiest for me just to draw the two figures on a piece of paper, and then cut them in half and boom…easy instant lesson that hits a lot of things I want!

This can also be a great first day geometry activity that motivates learning the terms. SO MUCH FUN!