Week 7- Patterning and Algebra

I find it quite ironic. I really enjoy patterns but in the past I’ve never been fond of algebra. Even though, they are two strands of math that essentially complement each other, the thought of algebra always scared me because I was not very comfortable with algebraic equations. I also never realized the relationship between patterning and algebra and I cannot recall if both strands were taught together when I was in elementary school. Therefore, as I read the assigned chapter for this week, it was interesting to see the relationships between the two.

One of the most important things about Patterning and Algebra is learning to find and understand patterns. Patters can appear in many different forms such as, colours, shapes, and numbers and in math we have to possess the ability to find and determine the relationships within these patterns so that we can progress into a deeper knowledge into algebraic thinking. In class, we worked on an excellent algebraic matching exercise, which got our minds thinking about the relationships between patterns and algebra. We were given a set of cards and were asked to match cards that fit specific algebraic equations. For every equation, there had to be a matching graph card, t-chart card, and pattern block card. This exercise was a great way for students to recognize the relationships between the patterns and the algebraic equations. It also gave students the opportunity to visualize the many different ways that these patterns and equations could be solved. I think that providing students with activities and manipulatives such as these are great because they stimulate the student’s minds into thinking outside of the box to recognize that math problems can be solved in many different ways.

The textbook suggests that teachers sometimes overemphasize growing patterns over shrinking patterns. It extremely important for teachers to provide practice using all different types of patterning because down the line when students are asked to solve difficult algebraic equations, some students will not be able to recognize and determine the patterns because their teachers rushed through patterning in their early grade and did not give students the practice that they needed to develop their patterning and algebra skills in the future.

In class we also had the opportunity to use blocks as psychical manipulatives to see what increasing and decreasing patterns can look like in their different stages.  To do this, Pat had us use two different block colours to help us recognize the change in our patterns. For example, the picture shown below has a constant of 2 red blocks and an increase of 2 each time. Therefore, our equation for this growing pattern is (2s+2).  I really enjoyed using the coloured blocks as a physical manipulative. It really helped me to visualize everything that was involved throughout the pattern and the equation. I think that it is extremely important for teachers to use physical manipulatives because it allows students to construct their own ideas for mathematical processes and equations and it gives them the opportunity to explore different ways to communicate their understanding.