I have just read through student reflections for our unit on Right Triangles.
Unit 7 – Right Triangles
Level 1: I can use the Pythagorean Theorem to solve right triangles in applied problems. G-SRT 8
Level 2: I can solve special right triangles. G-SRT 6
Level 3: I can use trigonometric ratios to solve right triangles. G-SRT 6, G-SRT 7
Level 4: I can use trigonometric ratios and special right triangle ratios to solve right triangles in applied problems. G-SRT 8
Define trigonometric ratios and solve problems involving right triangles
G-SRT 6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
G-SRT 7. Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT 8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
7A – 45-45-90 Triangles
7B – 30-60-90 Triangles
7C – Trigonometric Ratios
7D – Solving Right Triangles
7E – Performance Assessment (Hopewell Triangles)
7F – Mastering Right Triangles
7G – Assessing Right Triangles
Most students felt like the Math Practices they used most in this unit were Construct viable arguments and critique the reasoning of others and Attend to precision.
Think back through the lessons. Did you feel that any were repeats of material that you already knew? If so, which parts?
- Trigonometry is a completely new subject for me, so no, none of the lessons were repeats to me. I had no idea about anything except for the Pythagorean Theorem honestly.
- A student from Iran: yes, I leaned part 7A,7B and 7D in middle school, but the difference was that in middle school we just taught how to use Pythagorean theorem and that the side of triangle opposite to 30 angle is half of h, … which were formula but i didn’t know about sin and cos.
- The only part of this lesson that I knew how to do before was the Pythagorean Theorem.
Think back through the lessons. Was there a lesson or activity that was particularly helpful for you to meet the learning targets for this unit? If so, how?
- Trigonometric ratios and solving right triangles were the most helpful lessons because we learned the most new information in these lessons. What we learned in these lessons also applies to all triangles, not just a special type of right triangle.
- The self-check bell ringer that we did a few days ago was very helpful to me. When I know that one of my answers are wrong, I persevere in solving it correctly.
- When we finally put it all together and we were solving right triangles really helped me to finally grasp the whole idea. I had slowly learned and built a solid base and the solving right triangles lesson put it all together for me.
- I believe that the Trigonometric Ratios helped me the most because they allow me to solve a triangle with a different set of information.
Our Trigonometric Ratios lesson came from Geometry Nspired. I’ll write a post about it some day.
What have you learned during this unit?
- I have learned how to use sine, cosine, and tangent, and also the purpose of these formulas. Before I was taught what the formulas were used for, I was always curious as to what they meant on the calculator. Now not only do I know, but I also know how to work problems using sine, cosine, and tangent with accurate results.
- I have learned that there are “special” right triangles, and that there are quicker ways to solve these triangles. I also learned about trigonometry, which is something completely new to me. It was definitely new, and a little hard since it was the first time I saw it.
- I have learned how to solve right triangles, how to do trigonometry, and how to think about the problem before I try to draw it out.
What I have learned during this unit?
I have learned that the “I can” statements are really important for students. We reviewed them daily so that they could see where we were and where we were going. We are slowly making progress towards having students recognize what they are learning (I can …) and how they are learning it (Standards for Mathematical Practice). And so the journey continues …