{"id":19,"date":"2026-01-25T00:23:53","date_gmt":"2026-01-25T00:23:53","guid":{"rendered":"https:\/\/learnx.ca\/um\/?page_id=19"},"modified":"2026-02-16T20:11:27","modified_gmt":"2026-02-16T20:11:27","slug":"algebra","status":"publish","type":"page","link":"https:\/\/imaginethis.ca\/u\/algebra\/","title":{"rendered":"Algebra"},"content":{"rendered":"\n

“One person’s constant is another person’s variable.”
\u2015Susan Gerhart<\/p>\n\n\n\n

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What is Algebra?<\/h2>\n\n\n\n

When we ask adults what variables and algebra are about, the most common response is something like: Algebra is when you solve an equation like x\u202f+\u202f5\u202f=\u202f12, and x is the variable whose value you have to find.<\/em><\/p>\n\n\n\n

But in x + 5 = 12, x<\/em> is not actually a variable at all.
It is a<\/em> constant<\/em><\/strong>\u2014specifically, x<\/em>\u202f<\/em>=<\/em>\u202f<\/em>7<\/em>. Nothing in the situation varies.<\/p>\n\n\n\n

And algebra is not fundamentally about finding the value of a constant.<\/p>\n\n\n\n

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Real Algebra<\/h2>\n\n\n\n

Algebra is about relationships between quantities that change<\/em><\/strong>.
A genuine variable is something that varies<\/em>\u2014like in the spiral\u2011walking code, where both the repeat count and the step length change together in a coordinated way. Their values shift in relation to one another. That relationship is the algebra.<\/p>\n\n\n\n

Real algebra is dynamic, not static.
It\u2019s about expressing, exploring, and understanding how quantities co\u2011vary\u2014not about uncovering a single hidden number.<\/p>\n\n\n\n

For example, in the pattern below we have used in grades 1-3 classrooms, the number of blocks increases as the train car number changes. how many blocks are in the 10th car?<\/p>\n\n\n\n

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This pattern can be represented in a table.<\/p>\n\n\n\n

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And as a bar graph.<\/p>\n\n\n\n

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In Grade 9, patterns like this can be expressed using the linear equation
y = 3x + 3<\/strong>.<\/p>\n\n\n\n

This is the foundational algebra students need to understand\u2014how the growing pattern can be described using a rule that connects x<\/strong> and y<\/strong>.<\/p>\n\n\n\n

Growing patterns<\/h2>\n\n\n\n

Take a look at the image below.
What do you notice? What is changing, and what stays the same as the patterns grow?<\/strong><\/p>\n\n\n\n

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Comparing growing patterns<\/h3>\n\n\n\n

Explain the ways these three growing patterns are alike and how they differ from one another.<\/p>\n\n\n\n

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Screenshot<\/figcaption><\/figure>\n\n\n\n