Equation of a Circle (General Form)
Students will derive and apply the general equation of a circle (x-h)^2 + (y-k)^2 = r^2, including completing the square.
Key Questions
- Explain how completing the square transforms the general form of a circle's equation into standard form.
- Analyze the impact of the center (h,k) on the position of a circle in the coordinate plane.
- Design a method to find the center and radius of a circle given its equation in expanded form.
Ontario Curriculum Expectations
Suggested Methodologies
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Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
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Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
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Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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