Linear functions are major work in middle school mathematics, but before students can graph slope or write equations, they must understand what a function truly represents.
In this episode, we trace the vertical development of functional thinking from 6th grade ratio reasoning to 7th grade proportional relationships and into 8th grade functions. You’ll hear how unit rates and the constant of proportionality evolve into slope, and why understanding how two quantities vary in tandem is the foundation for mastering functional reasoning.
We unpack the language of the standards and clarify the distinction between proportional reasoning and functional reasoning. While proportional relationships focus on quantities changing together, functional reasoning introduces variables, abstraction, and a broader structure that includes domain, range, and representation.
This episode emphasizes geometry, number sense, and multiplicative reasoning as essential preparation for modeling with functions. You’ll walk away with clarity about what a function is, how it builds over time, and what to listen for in student thinking.
Because functions are not just formulas.
They are relationships made visible.
Build multiplication fluency through understanding with the Seeing Patterns, Building Power series. Two books now available on Amazon—plus check out my son’s new adventure novel, Anansi: Shadows of Myth and Mystery!
Thanks for tuning in to this episode of the Make Math Happen podcast! If you enjoyed today’s conversation, subscribe on your favorite listening platform, leave a review, and share this episode with your fellow educators.
You can also join the discussion and connect with me directly by clicking the link to join the Math Collective. Together, we’ll keep exploring practical strategies to transform classrooms and inspire students.
Remember, new episodes drop every Sunday at 9:00 am, so mark your calendars! Until next time, keep making math happen, and I’ll catch you in the next episode.
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