MPM2D Unit 5: Quadratic Equations

Students solve quadratic equations by factoring and by graphing, and see that an equation can have two, one or no real roots. They complete the square with algebra tiles and diagrams, rewrite y = ax² + bx + c in vertex form, and sketch quadratics using intercepts, completing the square, partial factoring and technology. A history lesson follows quadratic problem solving from Babylonian tablets and al-Khwarizmi's completed squares to the quadratic formula, connecting each step of its development to a numerical example. Students use the formula, interpret the discriminant, and solve maximum and minimum, projectile, area and revenue problems. An optional coding lesson reads and alters a Python program that applies the formula.

Assessment of learning: Launch It, modelling a water-bottle rocket launch and finding its maximum height, landing time and time above 8 m in more than one way, with a rubric. A unit test with full solutions is also included.

Lessons

1. Solving by Factoring
2. Solving by Graphing
3. Completing the Square
4. From Standard Form to Vertex Form
5. Sketching y = ax² + bx + c
6. The Story of the Quadratic Formula
7. Using the Quadratic Formula
8. Real and Non-Real Roots
9. Maximum and Minimum Problems
10. Projectile Problems
11. Area and Revenue Problems
12. Coding Quadratics
13. Quadratics 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.