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.