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.

Similarity in Right Triangles Station Maze

Some of my colleagues have used station mazes in their classrooms to get students moving and to have them explore problem-solving activities.  My students needed some additional practice with similarity in right triangles, so I decided to try this out.

I created 15 problems related to this concept and listed four multiple-choice answers.  Based on the answer, students were then directed to a new station.  If the students were doing their math correctly, they should have visited five stations and then returned to their original starting point.

Within the stations, I embedded two paths with multiple entry points. I created a "yellow" path and a "pink" path.  Students could start at any point of the path and it would form a complete cycle.  Other distractor questions were thrown in to turn this activity into more of a problem-solving activity.

I tried this with two of my Honors Geometry classes and it went pretty well.  My students were having good conversations about math and were really trying to complete their paths.  Students were asking well-thought-out questions when they got stuck.  Instead of focusing on the answer, most of my students seemed to be focused on the problem solving behind it.  One of my students even asked if we could do it again!  Overall I think it went pretty well, but it was kind of time-consuming to create this.  I think with some additional practice, it will become faster to create.

You can view my entire maze station activity here.

Proof Puzzles

Proofs are one of the most dreaded things in my Honors Geometry classroom.  It is difficult to start thinking about justifying each step of what you are doing in order to "prove" something.  To get my students started thinking about proof, I use the "Peanut Butter and Jelly Activity".

I give my students pieces of paper in an envelope with the steps listed for making a peanut butter and jelly sandwich.  I then have them put the steps in order that would successfully create the sandwich.  Once we agree upon an order, we talk about how the ingredients are like the "given" information in a proof and how the sandwich is what we are trying to make, or what we are trying to "prove".  There is a logical order in which the steps get us from the ingredients to the sandwich, but sometimes we have some flexibility in this.  

In order to continue guiding my students along, I have put together "proof puzzles".  In order to create this, I write out a two-column proof.  I then cut apart the statements and reasons.  It is the students' job to reorganize the proof into a valid logical argument.  Once they get the hang of this, I start adding in some distractor statements that are not necessary to add to the proof or might lead to an invalid logical argument.  It gets the students thinking about the necessary steps and they start to evaluate their thinking.  I call these "proofs with training wheels" and I have found it helps students to start moving in the right direction.

Polygon and Quadrilateral Detectives in Training

Gaining Better Understanding of Quadrilateral Characteristics

I don't know what it is, but my students have always had trouble keeping the characteristics of quadrilaterals in order.  It could be that we usually go through this unit right before winter break and the students might be completing focused.  It gets even more difficult for students once we try to take our quadrilaterals to the coordinate plane and try to determine what our figure is based on its coordinates.

A colleague and I were searching for an activity to help increase student understanding of this topic.  We found a couple of cool-looking activities online, but nothing that totally fit our needs.  Based on what we found, we created our own activity called Polygon and Quadrilateral Detectives in Training.

In this activity, students had to graph a quadrilateral on the coordinate plane.  Students had to abide by some parameters in order to keep this from being too easy.  For example, students could not include more than one horizontal and one vertical line in their shape.  It would be too easy to just look at a shape to see those right angles that line up perfectly with the grid lines on the graph.

They had to use the properties that we had been learning about in class in order to correctly identify the coordinates for their shape.  Then, they listed a couple of ways that people could verify the name of the graphed shape.

The next day, groups switched figures.  The groups needed to use the slope formula, distance formula, and midpoint formula in order to discover the properties associated with their shape.  They were then able to appropriately give the figure a name.  Once this was done, students check with the answer key.  If there was a discrepancy, the two groups had a conversation to figure out the correct solution.

Overall, I think this activity helped increase understanding for most of my students.  When it was time for our summative assessment, students were better able to identify figures and were able to use the formulas to support their answers.  

ClassKick

Getting Feedback via ClassKick

One app I started using in my classroom this year is ClassKick.  I heard about this app a while back but I was reintroduced to it during some summer professional development training.  This program allows me to enter an assignment and then view my students' work.  The students can raise a virtual hand in order to get help or to ask the instructor to check an answer.  I have used this app before several of my summative assessments this year in order to give students more time to get help and receive feedback on their work.  Generally, I will run a "ClassKick" session on the night before a unit summative assessment for an hour or so.  These sessions haven't been as highly attended by students as I had initially hoped for, but I believe the students who attended got some much-needed one-on-one attention and were able to ask questions in order to gain a better understanding of the concepts we had been learning about in class.

With our most recent summative assessment, I tried to kick it up a notch.  Early in the week I had my students choose a problem to work on.  The students created a video using Explain Everything in order to walk us through the problem-solving process.  The students then uploaded these videos to YouTube and shared them in a Google Document.  I was able to take these videos and attach them to our summative review in ClassKick.  While students were working on the review and got stuck, they could view the video created by their classmates.  We had essentially created a class library of problem-solving strategies for the main concepts that we had talked about in class.  If students were still stuck on the problem, then they could raise their hand and get additional assistance.

I know there is also a feature in ClassKick that allows students to be able to work together and answer questions without solely relying on the teachers' expertise.  This is something that I would like to explore in future review sessions.