MPM2D Unit 3: Quadratic Relations

Students collect quadratic data from a string-loop experiment and from secondary sources, and fit curves of best fit with technology. They discover that quadratic relations have constant second differences and parabolic graphs, and they name the key features of a parabola. They compare y = x² with y = 2ˣ and use patterns and exponent rules to explain zero and negative exponents. In Desmos, they investigate the effects of k, h and a separately, then combine them in vertex form, y = a(x − h)² + k. They sketch parabolas by hand with the step pattern and determine equations from graphs, vertices and points. Applications include kicks, dives, arches and fountains.

Assessment of learning: Parabola Hunt, modelling drawn and real parabolas in vertex form, checking a model with differences and contrasting parabolas with exponential curves, with a rubric. A unit test with full solutions is also included.

Lessons

1. Collecting Quadratic Data
2. Second Differences
3. Key Features of a Parabola
4. Comparing y = x² and y = 2ˣ
5. Zero and Negative Exponents
6. Translations of y = x²
7. Stretches, Compressions and Reflections
8. Vertex Form
9. Sketching from Vertex Form
10. Finding the Equation of a Parabola
11. Parabolas in Our World and 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.