The language and features of functions get careful treatment in a complex but doable lesson. Learners get a lot of practice really figuring out what a graph means in context, and also identifying key features of graphs. Key ideas like domain, continuity, and increasing or decreasing are common threads throughout the lessons. Students end the unit much more comfortable and capable in their algebraic graphing skills than when they began.

Concepts

functions, graphing, domain, range, continuous function, slope

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Additional Tags

math

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Instructional Ideas

• A natural next lesson or extension is a formal introduction of piecewise-defined functions (used informally throughout the lesson)
• Advanced students might have interest in smoothness of a function, in addition to continuity concerns

Classroom Considerations

• Weaknesses in identifying domain/range or in using function notation will quickly show up, so have remediation handy
• Common confusions in graphing distance vs. time instead of position vs. time will require careful treatment
• Building of lessons throughout the unit might require individual remediation in the case of absences
• Teaching reference available separately, under Included Materials

Pros

• Careful and accessible treatment of high-concept math concepts without losing rigor
• Natural progression of difficulty throughout lessons introduces new ideas in a non-intimidating fashion
• Focus on interpreting math concepts and terminology in context emphasizes higher-level analysis and synthesis

Cons

• No summative assessment
• No answer key available

Common Core

HSA-CED.A.3 HSA-REI.D.11 HSF-IF.A.1 HSF-IF.A.2 HSF-IF.A.3 HSF-IF.B.4 HSF-IF.B.5 HSF-IF.C.7.a HSF-BF.A.1.a HSF-BF.A.1.b