MPM2D Unit 7: Acute Triangles

Students see why the primary ratios need a right angle, label acute triangles, and investigate the ratio of each side to the sine of its opposite angle. They follow the development of the sine law from two right triangles that share an altitude (connecting it to solving a system), then the development of the cosine law from the cosine ratio and the Pythagorean theorem. They use both laws to find sides and angles, choose the right tool with a decision chart, and solve problems in navigation, surveying, roof framing and sports. A review lesson connects Units 6 and 7.

Assessment of learning: Trail Mapper, planning a hike-and-paddle route through a park with both laws, a time estimate and a route card, with a rubric. A unit test with full solutions is also included.

Lessons

1. Beyond Right Triangles
2. The Sine Law
3. Using the Sine Law
4. The Cosine Law
5. Using the Cosine Law
6. Choosing the Right Tool
7. Acute Triangle Problems
8. Trigonometry 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.