MPM2D Unit 2: Analytic Geometry

Students develop the midpoint and length formulas, then use the length formula to develop the equation of a circle centred at the origin, x² + y² = r². They find radii, sketch circles and test whether points lie inside, on or outside them. Combining these with Unit 1 skills, they write equations of right bisectors and medians, and find the shortest distance from a point to a line. They investigate properties of triangles and quadrilaterals by folding and in GeoGebra, classify figures using lengths and slopes, and plan and carry out multi-step verifications such as midsegment and diagonal properties. A design lesson applies every tool to a park plan.

Assessment of learning: Town Planner, placing a library equidistant from three neighbourhoods, checking cell coverage, planning a driveway and verifying a park is a rectangle, with a rubric. A unit test with full solutions is also included.

Lessons

1. Midpoints
2. Length of a Line Segment
3. Circles Centred at the Origin
4. Right Bisectors and Medians
5. Shortest Distance to a Line
6. Investigating Properties of Figures
7. Classifying Triangles and Quadrilaterals
8. Verifying Properties: Multi-Step Proofs
9. Analytic Geometry in Design
10. Analytic Geometry Review

Plus a unit test class.

What you get

• A teacher lesson plan for every lesson: curriculum expectations, learning goals and success criteria, a timed sequence, differentiation, look-fors and worked answer keys
• Detailed slideshows (15 to 18 slides per lesson) with speaker notes on every slide: what to say, what to ask, what to look for and how long to spend, plus warm-ups, worked examples, guided practice, quick checks and answer-key slides
• Student handouts (usually two pages) and exit tickets, with every problem worked out in the answer key
• Editable Word and PowerPoint files, plus PDFs
• A unit overview, the summative task with a four-level Growing Success rubric, a unit test, and teacher solutions for both

Built for the Ontario Grade 10 Principles of Mathematics curriculum (MPM2D, 2005, with the 2022 Addendum), and easy to adapt for any Grade 10 academic math class.