Tag: geometry

Scavenger Hunt Stations

Julia Finneyfrock1 Comment

I love using stations to review for a quiz or test. I have done many stations using folders and QR codes, but I found that my students like to work with the same people and tend to get the question from the station and go back to their usual seat. This time, I decided to change it up.

I created 7 stations and printed out two copies of each station. I laminated and then taped these stations all around the room. I also created a worksheet for my students that provided room for them to show their work for each. However, the worksheet did not provide any of the questions, so students had to stay at the stations to see and answer all of the questions.

Although there were only 7 sets of problems, I doubled them to create 14 stations. The maximum number of students I have in my classes is 20, so this ensured that there would be no more than 2 students at a particular station. I really liked this because it allowed my students to work with partners, but not in large groups. Students were also moving around the entire time! Some students did take pictures of the questions and went back to their seats… ugh… but most students stayed at their station. Because I had the stations taped to the walls (and one in the middle) I could see every student working. I could also see which students were struggling. It was also entertaining watching my students search for the stations they needed!

I used these stations to review for a quiz on special quadrilaterals and interior and exterior sums of polygons. Each station dealt with a different type of question that they would be assessed on. Overall, this was a pretty fun and successful review activity.

Here is the stations worksheet and stations that I used for this activity! Here is also my answer key.

Also, for station 1, I created a polygon and attached strings to one vertex and had students create the diagonals with the strings (you cant see what it is from my stations sheet) !

 

 

Grading made easy with Desmos Activity builder

Julia FinneyfrockLeave a comment

In my geometry class, I have been using Desmos Activity builder to teach finding points of concurrency algebraically. In order to assess my students on this unit, I decided to create a Desmos Activity. I also created a packet that had the same questions that were on my Desmos Activity for students to use to show their work. I like using Desmos because it allowed my students to check their answers easily by entering thier equations or coordinates. I can ask questions that don’t involve graphing, and it easily organizes students answers. It also made grading SUPER EASY.

When grading with Desmos you can either grade one student at a time by clicking on their name OR you can grade one  question at a time. I decided to grade one question at a time. Because each students answers showed up at once for each problem I could quickly see which students answered incorrectly. You can also overlay all of the graphs to check students anwers quickly. If no students answered incorrectly I can see that immedietly.

In order to grade most efficiently, I created a grading grid (I usually use this to record homwork) with every student in the class’ name. Instead of putting the date at the top like I usually do, I put the Desmos slide number, the packet question number, and the amount of points each question was worth. I used this grading grid to grade this assessment. If student got the question correct I put a check in the box, if the student made a small mistake (and I could tell what they did from the answer) I would put minus the amount of points they’d lose for that question in the box. If I couldn’t figure out their mistake from their answer then I would write “check” in the box. When I finished grading all of the questions I would go through each students test. I ONLY looked at the problems where I wrote “check”.  I use erasable pens when grading, so after I checked their work I could go back and change the grade in the box easily.

This was an extremely long assessment and took NO time to grade. Using Desmos  for a quick quiz would be even easier! This was my first time using desmos for an assessment, but I’m definetly going to use it again!

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Using Edpuzzle in the classroom

Julia FinneyfrockLeave a comment

I was missing class last week for a conference, and I didn’t want to lose a day with my Geometry class by giving them busy work. We’ve been working on parallel line indirect proofs by working through Parallel Line Land mazes.  While I was gone I wanted to introduce them to parallel line direct proofs. This was a long block day (1:30 class), so they had plenty of time to be productive. Our schedule rotates, and it happened that I would be in class for 2 sections of geometry on Tuesday, but miss one section on Wednesday. I decided to try out my plan with my Tuesday classes and then tweak my lesson so my students on Wednesday could do it without my help.

I was slightly familiar with using EDpuzzle but never used it in class before. Edpuzzle is a tool that is typically used in a flipped classroom. You can upload videos, add voice overs, comments, and questions for students to answer.

I didn’t make my own video, but found a one that walked students through a formal proof. During the video I created scaffolding questions. I wanted my students to be engaged in the video. Just like with flipped classroom videos, the length of the video should be 7 minutes tops! If you need the video to be longer you should split it up into multiple videos. I noticed that students zone off if it the video is too long.

At the end of the video, I added a comment with directions to practice proofs on different websites. The first site had a proof and then had students fill in the last “reason” of the proof. The second site was a little more difficult.  Students were given “the givens” and what they were trying to prove. They were also given a list of statements. They had to click on the statement that should come first and then a list of givens popped up and they had to pick which one went with the statement. This really confused my students when I wasn’t there to help them, but once I explained the concept they understood.

After they finished working through the links,  I  added a place for students to tell me how they felt about the video/websites and if what questions they had.

For homework students had 3 proofs they needed to work through. I created another edpuzzle for the next class (I was out two days) of me explaining the homework, so students could watch it and ask me questions while I was out.

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After seeing the questions by two classes had about the activities, I typed up a sheet answered all of the questions that I was asked.  I wanted to make the activity completely doable. I left a huge sub  folder with materials for my students. However, my sub somehow did not get my sub folder and my students were in a PANIC trying to figure out what to do. This activity also required students to try and really think about proofs, so students had a difficult time understanding that they could struggle. “Productive struggle” is a phrase we use daily in class, however, without my direction sheets and without me being there to help, students felt completely lost 😦 I would recommend not using this for a sub plan. It worked so much better when I was there!

However, I really do like edpuzzle. It was a great way to get feedback and give video lessons or just a review of homework. You can set due dates for the completions of the videos, but students can watch the video whenever and how many times they like!

Dance Dance Transversal!

Julia Finneyfrock3 Comments

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!!!

Intro to Logic… Reasoning and Conditional Statements

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Logic… OH BOY.  Teaching logic is like introducing an entire new languScreen Shot 2015-09-22 at 6.57.23 PMage to my students. The language of math. I started out this unit with a lesson on inductive and deductive reason that was created by Julie Reulbach.  This lesson consisted of a SMART notebook and a foldable handout. 

I had students discover the difference between inductive and deductive reasoning by using slips of paper with the following statements, pictures, and numbers on it. I told them to separate the slips into two piles. How are the piles the same? How are they different? Why did you group certain ones together? A common response I heard was “one pile is words and the other is shapes and numbers”. It wasn’t until i had them finish each statement that they started to see the pattern. At the end of the lesson we watched this clip from the Princess Bride. It was great to show them logic in a round about way and good wrap up for the lesson. IMG_5998

Next time I would give students inductive reasoning examples that did not have numbers or shapes. When they did their homework they had a difficult time deciding which type of reasoning was which. My students were also over thinking almost every statement.

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So now day two…. Conditional Statements.

So first off… I am OBSESSED with Don’t Panic, The Answer is 42. I’ve found amazing things for my geometry class from her blog.

I used her lesson on Conditional Statements and decided to recreate it by adding my own little touch. I turned the note section of her lesson into a foldable and a SMART Notebook. I started the lesson out with students reading misleading newspaper article headlines to make them see that words can be misleading. We talked about how in math we need to come up with a universal way to get across what we want to say. BScreen Shot 2015-09-22 at 7.25.46 PMefore even introducing Conditional statements I had my students write 3 if-then rules that they live by. I then had 3 students to come to the board to write their rules. When I finally did introduce conditional statements we usScreen Shot 2015-09-22 at 7.17.34 PMed my students rules to point out the hypothesis and conclusion of each statement. This was good because the students felt by looking at their own rules. I also had students come up to the board and underline and label the hypothesis and conclusion. This got my students up and moving around the room. During a class that is mostly lecture it can be hard to keep students engaged. I tried my best to keep students moving and involved in the notes.

After students became comfortable with labeling conditional statements we moved on to using p and q to represent statements. I told students that mathematicians are “lazy” and wanted a quick way to write conditional statements that made sense to everyone. We worked through a few statements, making them conditional and then writing it in p q form.

Next we moved onto truth values and negations. I introduced truth values the day before but now they were being applied to conditional statements. Students seemed to understand negations pretty quickly. Although taking it one step at a time seemed a little show students seemed to truly understand what was going. Screen Shot 2015-09-22 at 7.17.09 PM

Students were finally introduced to truth tables by given a p and q and then multiple case scenarios. Students were able to see and figure out themselves that the only time the conditional statement was negative was when the hypothesis was false. I thought that this lesson went pretty well even though “math felt like an english class today”. The intro into logic can be tough and confusing, so I hope that my students continue to go into it with a solid foundation!

Brain Dumping… Test Review

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It’s finally time for the first test! I wanted to create a review that was more than a practice test or worksheet . We had an long block today ((1hr30min), so I had plenty of time to do a good review. I started class with a 35 minute brain dump. I handed out large blank pieces of computer and told my students to dump their brains on to the paper with everything we’ve done in geometry. I told them to try and write everything down without their notes before turning to them. Some students used different colors and highlighting to organize their dump sheet.

After the 35 minutes I had my students turn to the person next to them. They were supposed to look and talk about their sheets. The purpose of this was to talk about what they wrote and see if their partner had something they may have forgetting. I gave them a quick 5 minutes break after they traded breaks and when they returned to class they had a new piece of paper on their desk.

This sheet was a graphic organizer that I put together. The first section of the sheet were vocabulary words that I expected them to know and recognize. Students then had to define each vocab word and represent it with a picture of symbol. The next section was a list of constructions they should know how to create on geoegebra. I had them create the constructions and explain to me what they did. The last section was all about points of concurrency. In words they had to explain to me how to create each point of concurrency and tell me what happens to the point in different types of triangles. I felt like this sheet was a guide to helps students study, but it wasn’t as direct as a practice test.

I think that I am going to use dump sheets as a review before every test. Not only does it help students organize their notes on to one page, but it also helps students see what they know and don’t know. Another bonus to our brain dumping is that students can save these sheets throughout the year and use them to study for midterms and finals.

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Points of Concurrency … two days of geogebra exploration

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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

Julia FinneyfrockLeave a comment

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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