Learning+Geometry+through+Billiards

**__Author:__** Aaron Brien

**__Class:__** I plan to implement this into my Geometry classes in the fall. My students in the class are primarily sophomores and juniors. A prerequisite to enrolling in the class is successful completion of Algebra 1.

**__Math Concepts to be taught:__** The math concepts in the lesson are: perpendicular lines, transformations (specifically reflections), and equations of lines.

**__Lesson:__** With this lesson, I will be giving my students a picture of a pool table with two balls on the table. The students will have the following tasks: 1) It will be their job to figure out how to send the yellow nine-ball into a pocket with one requirement. The requirement is that the cue ball must bounce off one of the rails before striking the yellow nine-ball. To do this, here is what you must do along the way:  a) First, you must make a video of yourself shooting the actual shot (do your best to approximate the location of the cue ball and the yellow nine-ball).  b) Then you must take a screenshot of the ball bouncing off the rail and explain mathematically through a picture and a written description why this location worked. 2. Next, predict another location (other than the one used above) on a rail that you could strike the cue ball into so that it would bound into the yellow nine-ball and send it in a pocket. 3. For some extra practice on finding equations of lines, take a screenshot of your initial cue ball and yellow-nine ball location and copy it into Geometer’s Sketchpad. Here you will place the graph over the top of the table with the origin in the middle of the lower left hand corner pocket. Find the equation of the line that your cue ball would follow if you were to strike the yellow nine-ball directly. 4. After you have done this, your task will be to upload this information to my blog.

**__Steps to set up the virtual manipulative:__** The only steps for the teacher to complete in order to be ready to receive student work is to set up a blog for their classroom. I have chosen to create a blog through edublogs.org as it is a free Web 2.0 tool for educators. The steps were as follows:
 * 1) Go to www.edublogs.org
 * 2) Click on the “Free” version button.
 * 3) Enter a username, password, email address, and agree to their terms.
 * 4) <span style="font-family: Tahoma,Geneva,sans-serif;">Name your blog and you are ready to begin customizing it.
 * 5) <span style="font-family: Tahoma,Geneva,sans-serif;">A teacher will need to add their students as users, so they have the ability to post to the blog.

<span style="font-family: Tahoma,Geneva,sans-serif;">**__Plan to assess student math performance:__** <span style="font-family: Tahoma,Geneva,sans-serif;">There are a few ways that I will assess my students math performance on this lesson. In order to answer the tasks that I have given my students they will be needing to perform some math. This work will be collected and I will look it over. Also, students will be able to assess themselves as they record themselves bouncing the cue ball off the rail at their calculated spot and hitting the desired ball into a pocket. Another form of assessment that is built into this lesson is for them to predict another location that the cue ball could be bounced off of in order to strike the yellow nine-ball and send it in a pocket. Having the students do this should really test to see if they can now put it all together and make an accurate prediction from what they have learned. I also plan to assess via a quiz on finding an equation of a line.

<span style="font-family: Tahoma,Geneva,sans-serif;">__**Reflection**__

<span style="font-family: Tahoma,Geneva,sans-serif;"> So the big question that begs to be answered from this action plan is: how will this bring relevance and rigor into my classroom? First, let me talk about the relevance. I wouldn’t say that the Web 2.0 tool (using a blog, and creating a video) necessarily makes the math content being taught more relevant, but it allows for students to do their work and represent it in a more culturally relevant way. In other words, using a blog is not aiding me, as the teacher, in teaching the concept of reflections, perpendicular lines, and equations of lines. However, using a blog and video camera, has allowed me to apply a technology that our students (the technology natives) are very familiar with and use it as an avenue for our students to represent their work. Doing this will inherently make the learning more relevant to the students. <span style="font-family: Tahoma,Geneva,sans-serif;"> On a secondary note, teaching these concepts through the context of billiards will make the learning more relevant. Traditional questions related to the concept of reflections will give students a line and ask them to reflect a point over it. Why? Why do they need to reflect this point over that line? In this context, understanding reflections are imperative to being able to hit a bank shot in the game of billiards. Also, by having my student’s video themselves hitting this shot puts the students in the math. It makes them see the need for the math in order to make the ball go in the pocket. <span style="font-family: Tahoma,Geneva,sans-serif;"> Very similarly to what I mentioned above, I don’t see much in how the Web 2.0 tools that I have incorporated into this lesson have increased the mathematical rigor. However, when we think about Bloom’s taxonomy and the levels of questioning. By putting the students in the math more we are asking them those higher levels of questions: the analysis, synthesis, and evaluation types. Again, in the traditional form of teaching reflections, students are asked to perform a reflection, but very seldom are asked why or to explain, and never asked to demonstrate experimentally why. One component that I made sure to add to this lesson was to ask my student to make a prediction of another location on a rail that they could bounce the cue ball off of before striking the yellow nine-ball and sending it into a pocket. This really forces them to synthesize, or apply what they learned mathematically to a slightly different problem. <span style="font-family: Tahoma,Geneva,sans-serif;"> As it pertains to rigor, if we think about ourselves as educators of students above just a math educator, by incorporating these Web 2.0 tools (blog and videoing) we are increasing the overall rigor of our lesson. Even though these students may be technology natives, I would think it would be easy to see that a lesson like I am proposing to do would be more rigorous than a traditional lesson on reflections. <span style="font-family: Tahoma,Geneva,sans-serif;"> In conclusion, after really reflecting on this lesson, I think that together the video camera and the blog will serve as great Web 2.0 tools to increase the mathematical and non-mathematical rigor and relevance of this lesson.