Radius+of+a+Pipe

__**Author:**__ Aaron Brien
 * Radius of a Pipe**


 * __Class:__** This lesson will work well in an Algebra 1, Geometry, or Algebra 2 class.


 * __Math Concepts to be taught:__** The math concepts in the lesson are: circles, radius, equations of lines, square roots, and much more.


 * __Lesson:__** With this lesson, I will give my students the following real-world problem:


 * To help my students answer this question, Geometer’s Sketchpad (GSP) will be used to help them visualize, gather data, and find a relationship between the distance //d// and the radius of the pipe //r//.


 * The students will need to open the file [|PipeProb.gsp] and follow the directions within the file.


 * Below I have included a few screenshots of what the students will get to do with this lesson


 * Students will have the ability to drab point B around to change the size of the pipe. After selecting “Go to Collecting and Plotting Data”, they will see the following:


 * Here, students will be able to select “Show Plotted Point (d,r)” and to the right, GSP will show the point and it will move as the user moves point B.
 * Students are then prompted how to have GSP show other data points at the same time for different locations of point B.
 * GSP will then plot the function that models the data collected and then calculate the equation that fits the line.
 * As you can see students are then left to make sense of the equation that GSP has generated.

This lesson requires the use of GSP. If your computer has GSP installed, all you need to do is download the [|PipeProb.gsp].
 * __Steps to set up the technology:__**

There are a few ways that I will assess my students math performance on this lesson. One of these ways would be to ask student to explain in words what their final answer means. In other words, now that you have an equation, how does this explain how we can find the radius of the pipe? If with this lesson I was trying to focus on the content on finding an equation of a line, it would be important for me to assess this skill. I say this, because GSP produces the equation for them, and it would important to assess if each student could do it as well. Other than these previously mentioned assessment ideas, I would want to make sure that I was walking around watching my students work on this problem and asking them some questions to gauge their understanding.
 * __Plan to assess student math performance:__**

For this assignment I chose to use a dynamic computer software called Geometer’s Sketchpad (GSP) to help visualize a real-world problem. This real-world problem was to find a radius of circle with only one other piece of information known to us. To make this question the most relevant would be to start with the physical problem in the classroom. What I mean by that is to bring in a circular object (pipe) and a carpenter’s square (as is used in the problem) and allow students to see in three dimensions the problem they are solving. This is the way I would introduce this problem to the class and then I would take my class to the computer lab for the students to discover the relationship between the measured distance and the radius. As mentioned above, this problem is very relevant. It may not be something that my students would ever be curious about, but it becomes a real problem when you take it out of the textbook. This becomes even more relevant when you have a three dimensional example in the class with you, because after the students have walked through the steps of discovering the relationship between the measured distance and the radius of the pipe, they can actually test their theory that they discovered. Continuing with this idea, if the resources allowed for a teacher to bring in different sizes of pipes, then the students could have multiple examples to test their theory. Honestly, rigor is the area that this lesson fails as it stands. One thing that I would do to make this lesson more rigorous would be to have my students work out by hand the equation of the line that shows the relationship between the two variables. Also, by asking my students at the end to explain what the equation that was generated means in terms of the distance //d// and the radius //r//. Lastly, this lesson could be made more rigorous by exploring other methods to arriving at this relationship between //d// and //r//, such as special right triangles, or using Pythagorean’s Theorem.
 * __Reflection:__**