Inquiry-Based Activity for Spherical Geometry

Spherical Geometry is a topic that I like to share with my Honors Geometry students, but it is very difficult to try to describe when we take notes on a two-dimensional piece of paper.  I found an activity on Twitter a while ago where people used balloons to talk about spherical Geometry.  This activity has quickly become one of my students' favorites.  

For this activity, I have each student blow up a balloon.  I also give each student a marker.  We talk about how lines in spherical geometry are "great circles" that have to pass through two opposite sides of the balloon.  We quickly discover that ALL lines in spherical geometry intersect.  We talk about Euclidean geometry where two points make one distinct line.  We draw out on our balloons how this isn't always the case in spherical geometry.  We also talk about how we can draw a triangle on our balloons that has three right angles.  

Since I had my students start drawing on balloons for this lesson, I can see that their level of understanding has greatly improved.  They also enjoy having a balloon for the rest of the day. 

Points of Concurrency Activity

In the past when we have studied points of concurrency in Honors Geometry, I have had my students construct these points with the basic construction tools: a compass and straight edge.  Many of my students run into issues with the compass and several other students don't bring the required materials with them to class.  This year, I had my students use the app "Geometry: Constructions Tutor (Lite)"  to construct an incenter, circumcenter and an orthocenter.  By using this app, students were able to construct accurate diagrams of each of these points of concurrency.  Additionally, they were able to focus more on the activity and got more out of it, rather than just worrying about whether or not they could draw a "perfect arc".

For our "centroid", I had my students construct this on a piece of cardboard.  This point of concurrency is the "balance point" of a triangle.  Students used a ruler to measure to draw in the three medians of their triangle.  They then were able to balance the triangle on the tip of a pencil.

Overall, students really enjoyed this activity and were more engaged than during the previous more "traditional" process that involved a compass and straight edge.

Class Expert Review Activity

For this activity, I wanted to create a resource for our class that students could refer to while preparing for our first unit summative assessment on the basics of Geometry.  Instead of just assigning a review packet for my students, I decided I would split it up and have different teams of students become our "class experts" on a particular problem.  I started by approaching some of the students that I knew were struggling a little bit and allowed them to choose a problem that was at their comfort level.  I approached some of my students who were ready for some more challenging problems, and I steered them in the appropriate direction.  Once the problems were assigned, I had the student teams create a video using the app "Explain Everything", where they walked through and explained the problem.

Here is an example of one problem:

I then had my students copy the link to their problem to a shared Google document and created a class library of how to solve each problem from the review.

If a student was struggling with a particular problem, all they would need to do is watch the video for a clear explanation.  Overall, this activity went pretty well.  There were some technical issues where some groups were unable to upload their video to YouTube.  However, the library of resources was fairly complete and could be used as a valuable resource.

Hands On Proof Practice with Google Slides: Angle Relationships & Proving Lines Parallel

When we first started working with proofs this year, I decided I would try to make a Google Slide document to share with my students.  For each slide, I put the proof problem with two column proof outline.  I also included some text boxes that had all the statements and reasons (and as students progressed, I included a few extra items) that they would need to complete the proof.  Students were able to drag and drop the statements and reasons into the chart in the correct corresponding place.  Students were able to work together and compare answers.

In the past, I have done this activity where I created the same activity but used strips of paper.  It ended up being very time consuming each year to do this activity since, inevitably, some of the strips of paper would get lost.

Overall, this activity went pretty well.  However, it was a little glitchy at times.  I will need to look into whether or not I can "lock" the proof table into place to prevent students from moving items that were not intended to move.

Hour of Code 2016

This year I hosted an Hour of Code event at my school.  I used some of the resources from code.org to get organized.  When I host this event, I always like to start with an "unplugged" activity.  This is an activity that allows students to think about computer programming instructions without having to know any actual language.  I chose to do "Color by Pixel" which allowed students to read and write programming instructions to color a grid to make a picture.  All of the students who attended this event had some sort of programming experiences, so we kind of flew through this activity.  

Once we finished with this, I introduced some different activity options and the students got to work.  Students could choose from Google's Blockly Maze activity, working with Scratch, creating a program using MIT App Inventor, or building an iPhone game with Swift.  Since many of the students who attended the event were enrolling in my second semester Swift programming class, most of the students chose the last option.  Students were having a great time with this and were cruising along with their apps. Unfortunately, we ran into some network issues which brought their progress to a halt.  Even with this difficulty, I think the students enjoyed the Hour of Code and were encouraged to learn more.

2016 Hour of Code Participants

Apple Teacher

Earlier this year, I attended the "Waukesha One" professional development day put on by my school district.  I attended one of the sessions led by an Apple professional.  During this session she talked about becoming an Apple Teacher.  After this professional development day, I looked into what it takes to gain this distinction.

I started viewing the training modules and was able to earn an "Apple Teacher" distinction.  Once I completed this, I was able to complete training on "Swift Playgrounds".  I have been teaching computer science for the past ten years or so and I have recently started to teach the Swift language.  I was really excited to see this as an option.  I was able to get a new iPad that was capable of running the Swift Playground app and was really impressed with its functionality.  I was able to earn the "Apple Teacher Swift Playgrounds" distinction.

Variables Gallery Walk

This semester I started to teach a new programming language, Swift.  Students seem to be able to create a basic app at the beginning of the semester, but I was worried that they didn't truly understand the fundamentals of variable creation.  To help students communicate and talk about variables, I had them break up into small groups and create a poster for their variable type (integers, doubles, boolean, String, how to check if two variables are equal, etc).  Each poster contained a description of the variable type and what this would look like with code.  The student then hung up their posters and the class participated in a gallery walk.   Many of my students decided to take pictures of these posters to keep as notes to use as a reference when they completed their next programming assignment.

Flash Cards Turned into a Game

I had my students try something a little different in preparation for our unit summative assessment on similarity.  At the end of each class period, I had students work in groups to write two problems based on the knowledge learned during the class period on the front of a notecard.  On the back of the notecard, students showed their work for how they solved their own problem.

At the end of the unit, I took the questions written by each group (and added a few more questions that I wrote) and turned it into a game.  I found a game board on Google Images that I modified and printed out on large paper, gave each student a token and provided dice for the group.  Students then played the game with their own questions.  If a group ran out of questions, I had them swap "question packs" with another group to continue.

Overall, the students really seemed to enjoy this activity and were very engaged in the activity.  Allowing students to write their own questions for this game caused them to be more engaged in thinking about the different types of problems we encountered throughout the unit.