Patterning and Algebraic Thinking, Week 7

Hello Everyone,

Katic, K (2015) ©. Patterning Worksheet.

This past week was the week that I was looking forward to since the beginning of the term...that's right presentation week! Every week throughout this course, a select few students are responsible for presenting a 10-minute lesson based off of one of the chapters in the Small textbook. It's great as it allows everyone to teach the class about a topic they have become an expert in, and it's so interesting to see what kind of creative solutions my peers come up with when presenting math. The section I was responsible for was the patterning strand for Grades 5s and 6s; it was actually a lot of fun seeing as this week was Halloween and I was able to create an engaging, fun presentation and worksheet using Halloween graphics!

Within the textbook, it gave quite a good background on patterning and algebra. Small discussed the importance of teaching students about patterns and pattern rules before students can be able to expand and create their own. As stated in the textbook, "A pattern rule is an unambiguous, unarguable description of the pattern; every element, including the first element in the pattern, must be described" (Small, 2013: 610). This is a critical element to understand with patterning as this is the foundation upon which students build and expand their mathematical knowledge off of. As such, this directly relates to pages 77 and 87 within the Ontario curriculum, where problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, and representing and communicating are all key processes and expectations that students are expected to utilize.

Teaching Treasures (2014). Triangles Puzzle 1. 

After doing extensive research about this topic to ensure my lesson went off without a hitch, I began to realize that, given more time during my presentation, I would have discussed tools and useful games that teachers can use to engage their kids. While it is admittedly difficult to make algebra fun, I found this great online resource that can aid kids with thinking algebraically. It's called Triangles Puzzle 1 located on the gamequarium website. This game meets the patterning and algebra expectations for Grade 6s (specifically on p. 95 under the variables, expressions and equations specific expectations). It is not as action packed as some of the other math games I have discovered, but it certainly contributes to algebraic understanding. Very simply, students are expected to find a pattern illustrated in the top two triangles (it is the same pattern rule), and then apply it to the bottom triangle. The answer is inputted into an answer box at the bottom, answer correctly and another puzzle will be generated.

Teaching Treasures (2014). Triangles Puzzle 2.

Expanding off of this game is Triangles Puzzle 2 located on the same website! It meets the exact same curriculum expectations as the Triangles Puzzle 1, however instead of trying to compete the bottom right triangle within the larger triangle, in this game students are expected to answer the middle portion of the triangle. In this game, it's great that there's a help button available for students if they really are stuck with trying to solve the pattern and determine the pattern rule. I believe that both of these puzzles are great resources for students to access in order to get them thinking about patterns and algebra.  By utilizing all of the above resources, I am hoping that I will become an effective math teacher one day who will be able to show my students that in fact, yes, math can be fun! I hope these expectations and games I have discussed above will help all of those who read my post. Feel free to post any questions or comments below! Have a safe and happy Halloween.

References 
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Small, M. (2013). Chapter 22 In Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada. 
Teaching Treasures (2014). Triangles Puzzle 1 and Triangles Puzzle 2. Retrieved from http://www.teachingtreasures.com.au/maths/yr7-puzzle1.htm