Learners tackle a wide range of intimidating topics in this comprehensive unit that spans piecewise functions, absolute value of functions, and inverse functions (among other topics). Investigative group work alternates with more teacher-led discussions to seamlessly integrate discovered concepts and their more theoretical explanations/representations. Each component spirals in concepts from previous work (inverse functions related to piecewise notation, absolute value related to transformations and reflections, etc.), keeping all of the material fresh in student memory throughout the extensive unit.

Concepts

functions, algebraic properties, inverse functions, absolute value, piecewise functions, domain, range

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Additional Tags

math

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Instructional Ideas

• Could be readily integrated into a physics or physical science unit on motion and velocity/acceleration
• Could be used in pieces for review/remediation in an introductory calculus class

Classroom Considerations

• Components are highly dependent on material learned in previous sections, a consideration for student absences
• Student facility in and access to graphing calculator use assumed

Pros

• Careful treatment of inputs/outputs (domain/range) in piecewise functions, a key sticking point for many learners
• Heavy emphasis on exploring distance-time relationships provides a solid grounding for future work in derivatives and other slope investigations
• Exceptionally thorough and detailed activities, teacher notes and worksheets
• Students are led to consider underlying concepts, not just memorize patterns

Cons

• No teacher keys for student worksheets
• Final summative assessment provided is for this and several previous lessons, not focused on this unit alone

Common Core

HSF-IF.B.4 HSF-IF.C.7.b HSF-BF.B.4.a