Picture+Slopes

** Determining the Slope of a Line **
 * Action Plan for Incorporating Web 2.0 **

The action plan I chose to incorporate into my classroom deals with slopes. This lesson would be an ideal fit for my Algebra 1 classes. Algebra 1 is the lowest level of math that my district offers in the high school; therefore, there are a large number of freshmen in the class as well as some sophomores, juniors, and seniors who are repeating the course. Because of this spread of students, there tends to be a wide range of mathematical abilities, as well as occasional behavioral issues. This lesson plan is meant to be a follow up activity. Students should already have been introduced to the idea of slope and how to find a slope given 2 points. For this lesson students will need to be members of my wiki space. In order to make this process as easy as possible, I will get students e-mail addresses and send them invites to join my wiki space. Once students have received the e-mail they will need to complete the following steps. For this activity, students will need to find a picture to add to the Slope Pictures Page of my wiki. The only requirement of the picture is that it must contain an obvious line somewhere within it. There are several options to complete this task. One option is that students can look through any photos that they may already have on their computers and upload one of them. Another option is that students can take a picture with their cell phones, e-mail it to themselves, and then upload it. The last option is that students can search the internet for a picture and paste the link for the picture onto the wiki page. I will show students how to find the page on the wiki and how to edit it so that they may upload their picture. Example Picture:
 * 1) Click on the link to go to the wiki space
 * 2) Click the link to create an account
 * 3) Come up with a username
 * 4) Come up with a password
 * 5) Write your username and password down in a safe place so that you do not forget them
 * 6) When it asks if you want to make a wiki you can say no
 * 7) Click the option for the Wiki to be public
 * 8) Under the Wiki Type dropdown menu choose the option for K-12 Education
 * 9) Click Join
 * 10) (If the username you selected has already been chosen, you may have to repeat steps 3-9 again.



The next part of this activity will take place in the classroom. I will provide a large coordinate plane on the whiteboard and we will project the pictures, one at a time, onto the coordinate plane. We will then choose two points from the photos that we can use to determine the slope of the line in the photo. I will upload 3 photos to use as an example before getting to photos added by students. These first 3 photos we will complete together so that students understand how to accomplish the task. After these examples, I will rotate through the student’s photos giving them enough time to determine each slope. Students will be assessed for this activity three different ways. One is participation, whether they uploaded a photo or not. The second is completion, whether they have slopes for all of the photos or not. And the last piece is sharing; they will each have to share the correct answer to the slope of the photo they submitted. One extension to this activity is we could try to estimate the slope in each photo visually, and then use the coordinate plane to check to see how close our estimate is. After we talk about parallel and perpendicular lines, another extension is that we could compare the slopes in the photos to see if any have slopes that are parallel, or perpendicular to each other.

** Reflection on Action Plan for Web 2.0 **

It has been my experience that several Algebra 1 students lack motivation when it comes to homework and school work in general. I believe this is in large part due to the fact that Algebra 1 is the lowest level class that my school district offers. Some of these students are taking this class for the 2nd, 3rd, or even the 4th time. The goal of this activity is to give them some freedom so that they may find a picture that is of interest to them. If they understand that they are helping to make their assignment, they may be more inclined to participate. Furthermore, it may be intriguing for them to see what pictures others have posted. In general, I think the appeal to this activity, is that the skill seems more relevant because we are using items that may be around students in their everyday life. Also, it gives students a break from the textbook, while still getting a great deal of practice. We possibly may even get to learn a few things about each other once we see what pictures others have chosen.

The rigor of this lesson is not necessarily hard if you just follow the basic outline of the lesson. However, it can be made more rigorous with the extensions that were noted in the action plan. One extension was that students could first be asked to estimate what the slope of the line is before they are given the projection of the picture onto the coordinate plane. This is more rigorous because students are being asked to use their knowledge of slopes to first give an estimate. They have to know what makes a slope steep vs. shallow, positive vs. negative, no slope, and even undefined slope. Another extension that can add rigor would be to revisit these photos after covering the concept of parallel and perpendicular lines and how their slopes are related. We could look through the photos again and determine if there are any photos that we believe may be parallel or perpendicular, and then look through the completed solutions to see if we are correct.

This lesson serves many purposes. One is that student are given the freedom to choose their own problem (photo). A second purpose is students are introduced to the wiki, which can be used for several future lessons. Lastly, students are able to get a great deal of practice determining slopes in a way that may not seem as boring as working out of the book, and they may even have some fun while they are completing it!