Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents feature prominently in an approachable and engaging lesson. More thought provoking explain- and discover-style questions and activities are interwoven with nuts-and-bolts calculations and practice, developing and extending the young mathematician at a myriad of levels.

Concepts

quadratic equations, rational exponents, properties of exponents, irrational numbers, properties of real numbers, imaginary numbers, complex numbers, complex roots, fundamental theorem of calculus

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Additional Tags

math

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Instructional Ideas

• Cross-curricular possibilities between physics / physical science situations (projectile motion) and business (maximizing revenue and profit)

Classroom Considerations

• Activities are highly dependent on one another, referencing notes and conclusions from previous work (considerations for absences)
• Dense reading passages on student worksheets might require greater instructional support
• Learners might need to be encouraged to show more calculations than the space provided allows

Pros

• 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
• No final summative assessment provided

Common Core

HSN-RN.A.1 HSN-RN.A.2 HSN-CN.A.1 HSN-CN.A.2 HSN-CN.C.7 HSN-CN.C.8 HSN-CN.C.9 HSA-SSE.B.3.c HSA-APR.A.1 HSA-CED.A.4 HSA-REI.B.4.a HSA-REI.C.7 HSF-IF.C.8.a