Patterning and Algebra

          This week's session focused around the concept of patterning and algebra; and the various resources educators can use to help students improve their skills in this concept. Throughout my years learning math, I've always enjoyed learning the basic fundamentals of patterning and algebra. By high school, when the concepts became more difficult, the positive feeling started to dissipate. However, in general, I believe I have a strong basis of this concept.

          Firstly, one of the teacher candidates gave a sample lesson for students. This activity involved practicing to identify various patterns based on images and a table. The handout provided a great way for students to develop a basis of identifying the pattern; what is the operation and number by which the pattern is increasing or decreasing? Overall, a great way for students to develop a foundation of the basic skills needed for the concept of patterning.

          As a class, we continued this development of skills by practicing various problems about pattering and developing an algebraic expression. This was modelled by output # = input # x __. This algebraic expression will help students to predict what the pattern will look like for a higher term, such as 100. A sample problem is found below.

Pagliaro, T. © 2016.

           The next step our class took was to demonstrate these patterns with the use of manipulatives; instead of just a regular table. Each table was given a bag with various patterns indicated  Each member of the table chose a pattern and had to construct this pattern with square coloured chips (math manipulatives). After each table was done making their patterns come to life, the class did a gallery walk to see the different ways in which people represented the pattern. As a class, we noticed that most individuals represented the pattern flat on the surface of the table. However, there were some individuals who chose to build the pattern by expending upwards; stacking the math chips on top of one another. I enjoyed this method a great deal since it would allow students to visually represent each of these patterns and hopefully make more sense of this math concept. Below are some images of this activity; the pattern with the rule beneath it.

                                             Pagliaro, T. © 2016.                                                                                       Pagliaro, T. © 2016.

          We continued to build on this manipulative method by expanding on the original pattern. The algebraic expression that was used no longer just contained a number that is multiplied by the term number, but rather adding an operation; such as output # = 2 + 4. The representation of the constant number added a bit of an extra challenge. The same process occurred for these questions. Each member picked a pattern from the bag, then displayed this pattern on the table using the math chips. Once all tables were complete, the class completed another gallery walk. Here are some images of the representations of these patterns.

                           Pagliaro, T. © 2016.                                                                                         Pagliaro, T. © 2016.

            Lastly, the class was able to explore the innovative app called "Dragon Box." Our instructor described this game as an opportunity for students to practice algebra without viewing algebra in a traditional form. She also disclosed that she uses this app all the time with her students. Therefore, I thought this app must be a great source for students. At first, I found the game was a bit confusing. However, after playing around and figuring out the elements of the game, I could see how this would be a great game to help students develop their algebraic skills. Instead of solving for "x", students must try to isolate for the dragon. Through trial and error, students will become familiar with the process of eliminating various boxes to get the dragon by itself. As students progress, the levels will get harder and harder; which will help them develop their skills for the algebra concept. Despite having to pay for this app,  I believe this would be a great app to use with students in the classroom.

          To sum up, this week has proven to be very informative for the concept of patterning and algebra. Through the use of manipulatives and various technological resources, such as the app "Dragon Box," I believe I would use any of these resources in my classroom.