Dance Dance Transversal!

I really wanted to teach properties of parallel lines through investigation When I was working on my constructions unit using GeoGebra I found this great scaffolding worksheet for properties of parallel lines. I decided to try it so my students could discover and play around with parallel lines cut by any transversal. Some students figured out the sheet very quickly and others were extremely confused. I had students work on their own on GeoGebra but could work on the questions with a partner. This helped clear up a lot of confusion and created a lot of mathematical discussion.

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After they completed the geogebra investigation, all of my students got onto Pear Deck. I started my Pear Deck lesson with the question “what is a transversal? ” All students answered and I was able to scroll through their answers to see who understood the activity. We then came up with a definition together. Next I was able to discuss corresponding angles, alternate interior, alternate exterior, same side interior and exterior, and vertical angles. I wanted to see if my students understood where these angles were from the previous activity so I had them shade in their angles on Pear Deck. This lead to the discussion on why certain angles were there and which ones were congruent or supplementary. At the end of the Pear Deck I had students rank their understanding of the lesson and ask me a question. I did student takeaways so the entire Pear Deck lesson was sent to each of the students google drive, and I was able to go in and enter comments to answer their questions. SO COOL.

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Day two of this lesson was introduced to me by Julie Reulbach. She suggested that I do Dance Dance transversal. In order to this I had to make 10 dance floors around my classroom (two parallel lines cut by the transversal) using tape. I suggest using painters tape! SO much easier to take off!

I wanted to clear up any misconceptions before we danced so I had students work with a partner and find a dance floor. I gave them each scraps of paper and they had to use them to label each type of angle. This gave me a chance to walk around and help students who were struggling and to see who really had a firm grasp on the lesson.

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When they all finished we trashed the scraps and had 10 rounds of dance dance transversal!! We had 10 rounds and partners switched every other round. This made properties of parallel lines so much fun!! Check out my instagram for videos of my students dancing!!!

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Making Math Stations Easy By Using Folders!

In Geometry, we have been working on even/odd proofs. Some students were picking it up extremely quickly, but others were struggling (mostly over thinking everything)! I wanted to create an activity where students were able to work at their own pace to practice even/odd proofs. I decided that I would try out creating stations. I created 9 even/odd proofs ranging in levels of difficulty. I allowed my students to work with a partner and use their notes from our class before.

I started class by handing everyone proof #1 and a list of algebraic properties and explained the rules of the day.

  1. Work through proof #1with your partner. If you get stuck look at the examples in your notes. If you still don’t understand call me over for help.
  2. When you finish find the folder with the same color as your proof labeled “#1” Open the folder and check your answers. If it doesn’t match up where did your proof go wrong?
  3. Once proof #1 is perfected find the folder labeled #2. Paper clipped to this folder is your sheet for Proof #2. Go back to your seat to complete it.
  4. Repeat until finished Proof #9.
  5. When finished turn your proofs into a “proof book”
  6. ALL proofs must be completed before class tomorrow.

This activity was GREAT. It took a lot of prep, but students were able to check their proofs right away and work at their own place. Some students finished all of the proofs in class while others still had a few left. The ones who finished in class walked around and helped students who were struggling. For the students who did not finish had to complete the proofs for homework. I posted the answers to the proofs online, so my students could check their answers. Each proof was written in a different color, so it was easy to decipher which proof students were struggling with. It also made for a colorful booklet 🙂

These stations were great! They weren’t the typical stations where students rotated from table to table to switch problems, but I think they really enjoyed getting up to check their answers and grab the next problem. I liked having  them work with a partner because they wouldn’t move on to the next proof until both of them understood it.  Although this required a lot of prep, I had to do very little in class. Students were extremely very self-directed and only called me over to ask specific questions. These were questions that they were not able to figure out from their notes the day before. Once students started finishing up and started helping their peers this also decreased my involvement with my students.  By having the answers in the folders the question of “is this right?!” was completed eliminated. This gave me time to walk around and answer essential questions and figure out which students were struggling.

I LOVED using folders for stations. I’ve had students in Algebra 1 make their own stations with folders and worked beautifully. Having a problem on the front of the folder and the answers and work on the inside eliminate the teachers work of having to discuss every single problem. I also liked the folders for stations because it gave students instant feedback and a created a place to keep the papers for each problem.  If you do math stations of any kind I highly recommend using folders! The classroom felt so alive, students could work at their own pace, receive instant feedback, and ask questions!

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Points of Concurrency … two days of geogebra exploration

Coming to the end of our construction unit it was finally time to teach points of concurrency. I decided to break this lesson up into two days. The first day was an investigation day to discover the incenter and circumcenter. The second day consisted of a review of the incenter and circumcenter and as a class we discovered orthocenter and centroid.

Day 1: 

My students were given a paper copy of an investigation work sheet in which they had to use geogebra to discovery points of concurrency.  When I passed out the assignment I instructed my students to follow the directions on what to create on Geogebra and then answer the questions on the sheet of paper. They were to work on investigation 1 by themselves and investigation 2 with their partner. Investigation one discovered the incircle and investigation 2 discovered the circumcenter.

Step 1 – Construct three points and connect them to form a triangle: Easy enough. Students also realized that they could use the polygon tool to create a triangle.

Step 2 – Construct the angle bisectors of each angle: This is where things got exciting. For the past two weeks my students have been working on constructions using Geogebra. I know that they are able to bisect angles using the compass tools!!! I didn’t want them to have to go through the process3 of bisecting an angle every single time, so I allowed my students to use the angle bisector tool. This made constructing the incenter so much faster AND much more clear to see. I also told my students to change the color of the lines so they could see what they were trying to intersect. This activity was a clarity that using Geogebra for constructions was the right choice.

Day 2: 

Day two consisted of some note taking. I started out class by passing at a foldable (created by f(t) and modified by I Speak Math)  and having students open a Geogebra worksheet applet that consisted of all of the points of concurrency. I told them not to look at the applet until I said so.

I started out class with a simple question. What does concurrent mean? I had students write down their thoughts in their notebook before sharing with the class. I wanted to go over circumcenter and incenter before moving on, so my next slide started with the question What is a perpendicular bisector? This question helped lead into talking about circumcenter. As a class we were then able to fill in the foldable fill in the blanks about circumcenter. After we filled in the notes I had my students turn to the geogebra applet and only click on circumcenter. I told them to move around the vertices of the triangle and write down what they noticed  about the circumcenter when there were different types of triangles. We then came together as a class and discussed about happened to the circumcenter.

I repeated this same process for incenter, orthocenter, and centroid. It was great because we had structured notes, but students also got to explore the points of concurrency themselves, and share their ideas with the rest of the class.

Here is an attachment to my Smart notebook. 

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First Smartboard slide
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geogebra applet 🙂 SO AMAZING

With about 10 minutes left in class I had my students will out a google form. This form asked students to write down everything they knew about incenter, orthocenter, circumcenter, and centroid. It also had a spot for students to ask questions. This gave me great feedback on what they knew/ understood and gave them a chance to ask questions.

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Closed foldable
My foldable notes from class
My foldable notes from class

For homework I gave out a worksheet in which had students create all of the points of concurrency on one triangle (all the work for each point was in a different color) in order to explore Euler’s Line. Students had to complete this on geogebra. This was great because it had them practicing constructing points of concurrence and also exploring a new concept at the same time.

This is an example of a student exploring Euler's Line
This is an example of a student exploring Euler’s Line
Questions from the form I gave at the end of class
Questions from the form I gave at the end of class

Constructions Mini-Project

We are halfway through our construction until, so I’ve trying to figure out a way to accurately assess my Geometry students on Constructions. Being able to create a construction on Geogebra and actually understand the construction are two completely different things, so I decided to create a mini-project to practice the constructing we’ve done so far. Students were asked to create the following constructions on Geogebra, and provide an explanation on  how you created it, as well as some justification as to why it is an accurate demonstration.

  • Congruent Segments
  • Segment Bisector
  • Angle and 2x Angle
  • Angle Bisectors
  • Perpendicular Lines
  • Perpendicular Bisector
  • Midpoints

I provided a rubric for my students to reference, so they knew exactly what I was looking for. If I gave this project again (and probably will) I would be more specific about what I was looking for with perpendicular lines and would combine segment bisectors with perpendicular bisectors.

I felt like this was a great way to test my students construction knowledge with out giving them a traditional quiz or test. I also gave my students complete autonomy to how they wanted to submit the mini-project.  I told them to “print out their work and creatively submit it”. I did not penalize students for not being extremely creative, however, I gave a small extra credit point for students who went above and beyond (students didn’t know this when they submitted their project). Although some were more creative than others all of the projects submitted were AWESOME! I truly got to see what my students understood about constructions, and my students who strive creatively had a chance to express themselves in a math class. This project also had my students writing mathematically. Three-weeks ago I introduced my students to writing in a math class. It’s insane on how much their mathematical writing has improved in such a short time (complete sentences, vocabulary, accurately expressing concepts in words).

Overall this project was a great way to assess my students knowledge of the past three weeks. Students had a chance to create constructions, mathematically write how and why they are constructing, and creatively express themselves.

Here are directions and rubric for this project if anyone is interested! Below are also a few examples of some of my students projects

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