I’ve been asking my students to reflect on each unit as we finish so that I can have some feedback on what changes to make for next year. I collect their responses through an assignment in Canvas.

- I can use inductive and deductive reasoning to make conclusions about statements, converses, inverses, and contrapositives.
- I can use and prove theorems about special pairs of angles.
- I can solve problems using parallel lines.
- I can prove theorems about parallel lines.

Which Standard of Mathematical Practice did you use most often in this unit?

The top 3 responses:

Make sense of problems and persevere in solving them.

Construct viable arguments and critique the reasoning of others.

Look for and make use of structure.

Think back through the lessons. Did you feel that any were repeats of material that you already knew? If so, which parts?

Many students recognized vertical angles, parallel lines, and the triangle sum theorem as something they had used before. However, they also recognized that we were learning why those relationships worked – and not just that they worked.

One student replied: None of these were repeats so to speak. I already knew what parallel lines and the different types of angles were, but I had no idea why or how or how you use them so much in math. I never sat there and thought, “Oh, we learned this last year, I don’t have to pay attention.”

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?

- I really like 3A Logic for this lesson. It allowed me to think through things and use “logic” to solve problems.
- Interactive activities were particularly helpful as they visually showed the justification of postulates and theorems such as the Angle Addition Postulate, the Definition of Vertical Angles, etc
- Logic in the beginning helped out with the whole unit because that’s mainly what everything linked to.
- All of the lessons were helpful, but I found that the logic lesson was particularly helpful. It helped me to understand what a proof is and get introduced to them. Proofs were very important to meeting the learning targets for this unit.
- The symbolic logic was helpful in the case that if I could figure out one part, it could lead me to unlocking other parts, kind of like a puzzle.

What have you learned in this unit?

- I have learned how to prove things that I already knew were true.
- I have learned all the objectives. I am also better at solving proofs and proving theorems. I learned about triangles and theorems about those as well as the way I can draw in Auxiliary Lines to find angles in problems.
- Do not procrastinate on homework.
- I’ve learned that math isn’t always numbers and equations; it can be proving things through logic and reasoning and postulates and many other things that I really didn’t know existed before this. I learned WHY parallel lines are parallel and WHY the alternate exterior and alternate interior and corresponding angles are the same and WHY all of the angles of a triangle added together equal 180 degrees. I also learned how to apply this knowledge in geometry and how it can help us in real life.
- I have learned that I cannot give up when problems are complicated. I also learned that my way isn’t always the only way.

I think these reflections are good news as the journey continues ….