Through a variety of hands-on activities and physical scenarios, this far-reaching unit leads learners through an exceptionally thorough exploration of circles and parabolas as conic sections. Geometric construction techniques are used as manipulatives for the development of coordinate plane equations, and then these equations are linked to the properties of quadratic forms. Learners also work to manipulate given quadratic forms to tease out hidden features and patterns of circles and parabolas.

Concepts

circles, conic sections, distance formula, pythagorean theorem, parabolas, quadratic formula

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Additional Tags

math

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Instructional Ideas

• Sprinkler activity (8.2) could be completed as a class or small group activity in a field or gymnasium 

Classroom Considerations

• Geometric construction and experimentation lead to development of parabolic and circle properties, but ellipses and hyperbolas are not included

Pros

• Exceptionally thorough and detailed activities, teacher notes, and worksheets
• Students are led to consider underlying concepts, not just memorize patterns
• Traditionally complicated concepts of conic features are broken into manageable and intuitive discovery lessons
• Relevant concepts (specifically completing the square and manipulating quadratics) reviewed in activities before being used

Cons

• No teacher keys for student worksheets
• No final summative assessment provided

Common Core

HSG-GPE.A.1 HSG-GPE.A.2