WEEK [square root of 49]

Dear Math Friends,

I am excited to share that last week, we started one of my favourite units in math class: patterning and algebra! In her book "Making Math Meaningful to Canadian Students K-8, 3rd Edition", Marian Small states that, "algebraic reasoning is the process students use when they generalize numerical situations using equations, variables, and when they study how quantities are related". Additionally, she states that algebraic reasoning can help you focus on the specifics of a problem while looking more generally at patterns and structure.

In this post I will be exploring these concepts and relating them to a unit that I really like in the Grade 9 math curriculum!

Patterning and Algebra in the Ontario Curriculum 

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What might one experience when doing patterning and algebra activities you ask? Here, the Ontario Curriculum breaks down patterning and states, "one of the central themes in mathematics is the study of patterns and relationships. This study requires students to recognize, describe, and generalize patterns and to build mathematical models to simulate the behaviour of real-world phenomena that exhibit observable patterns".

In the junior and intermediate grades, patterning requires a lot of visualizations strategies because students must see how a pattern may continue before necessarily computing an equation for it. Examples of  how students may approach patterning is by using shapes that make a pattern and also use numbers. Specifically, the curriculum states that students need to engage their representational learning strategies, "...students represent mathematical ideas and relationships and model situations using concrete materials, pictures, diagrams, graphs, tables, numbers, words, and symbols". Oftentimes, students struggle with the particular strand because they cannot visualize the connections between math and the shapes, symbols and numbers. Luckily, many students are diagnosed as visual learners and teachers can help easily scaffold their class into understanding patterning.

Another part of the strand is linked with the term "equality". This is my favourite part of the strand! The concept of equality is described as undestanding how equations come from and what makes an equation equal. See that pattern? The root word equal is part of all those words. To put this into math context, students may manipulate equations based on the fundamental principal that the left side and right side of the equal sign should always be equal to each other! With this basic algebra fact, students can solve the most complicated equations!

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Sample Problems

An excellent Ontario Curriculum website is edugains.ca. From one of their documents titled "Continuum and Connections", I found a great sample problem on patterning and algebra for Grade 9 math. This particular example ties into linear equations, where numbers will increase or decrease on a graph at the same rate, creating a pattern. You can find the first differences between points on the graphs and see if you get a pattern! Check out the Grades 9 and 10 math curriculum for more information.

I personally love linear functions as I have tutored this for Grades 8, 9 and 10. Students are usually introduced to linear functions in Grade 8 because once they enter Grade 9, they explore this unit in detail. In Grade 10, students expand on linear functions and start exploring how to solve algebraic equations with substitution and elimination methods. It is really fun, I believe, because you re using your patterning and algebra skills to the max, in addition to other skills like data management!

Check out this example and see if you can follow it. ↡

It is also explained in more detail below:
http://www.edugains.ca/resources/LearningMaterials/ContinuumConnection/PatternsAndAlgebraicModelling.pdf.

Here's an additional video resource on linear function patterns.

I hope you explored these resources and learned something new about patterning and algebra, friends!


See you next week!

Teddy