Modeling Math: What is a Function
Description
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.
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