MPM2D Unit 6: Similar and Right Triangles

Students tell similar figures from congruent ones, investigate the properties of similar triangles, and use proportions to solve real problems with shadows, mirrors, maps and models. In an outdoor lab they measure heights indirectly. Similar right triangles then lead to the primary trigonometric ratios, which students use to find side lengths and angles, build a clinometer, solve angle of elevation and depression problems, combine two right triangles, and model jobs in navigation, roofing, surveying and accessible design.

Assessment of learning: Measure the Unreachable, measuring something tall around the school with similar triangles and a clinometer, then comparing the two results and explaining the error, with a rubric. A unit test with full solutions is also included.

Lessons

1. Similar or Congruent?
2. Properties of Similar Triangles
3. Similar Triangles in the Real World
4. Indirect Measurement Lab
5. The Primary Trigonometric Ratios
6. Finding Side Lengths
7. Finding Angles
8. Angles of Elevation and Depression
9. Two-Triangle Problems
10. Trigonometry at Work
11. Right Triangle 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.