A final look at quadrilaterals in the coordinate plane

The common unit assessment we're using includes a couple of coordinate proof problems. Since we hadn't worked in the coordinate plane for a week or so, I decided it would be helpful to revisit this work before moving to similarity.

A colleague had put together four problems that covered this material. Each problem gave coordinates for a different quadrilateral. In the first problem, they had to calculate the slopes of the sides to show opposite sides were parallel. In the second, students had to calculate the length of the sides to show that opposite sides were congruent. In the third, students had to show that diagonals bisected each other. In the fourth, they used protractors to show that opposite angles were congruent.

This work went fairly well. Some students stilled had questions about calculating side lengths or slopes. For the most part they seemed comfortable with the tasks. For a couple of students, they really just wanted a formula to use.

I pointed out that they should try to work with what they know. If a problem didn't have pieces they know, think about how they could break the problem down into pieces that they knew. For example, the distance formula is essentially the Pythagorean theorem used for a specific purpose. However, problems often don't provide the right triangle dimensions needed. Students need to ask themselves how they could create a right triangle to use the Pythagorean theorem, since they typically know this theorem well. The idea started to click for some of these students and they were able to proceed ahead on their own.

I did pass out a quiz and told students it was a take-home quiz. The quiz emphasized concepts as opposed to solving problems for x. I allow notes to be used on quizzes and tests, so I felt there wouldn't be much difference in results by having the quiz completed at home. This also saved me a class period for investigation and instruction versus assessment.

Tomorrow we start similarity. Today, another colleague worked through the first lesson I am using tomorrow. She was really pleased with the engagement and learning that took place. I'm excited to see how the lesson goes in my class.