Tri-Mind: Perpendiculars and Squares
Lesson 3 of 11
Objective: Students will be able to construct perpendicular bisectors and squares.
As we begin to move on to more complicated constructions, I want to reiterate the features of high quality explanations with my students.
High Quality Explanations...
- Provide clear explanations on what to do
- Provide directions that answer the question, “How do I perform this construction?”
- Provide a clear explanation on why a “step” must be completed.
- Enable the user to answer the question “Why did I have to perform these steps?"
For this Pair Check for Understanding, I use the document camera to show my work for constructing a perpendicular through a point given on a line, with each "step" numbered. I ask students to write step-by-step directions for how to perform the construction and require them to use the words "equidistant" and "endpoints" in their explanations.
I remind students of the features of high-quality explanations we discussed at the beginning of the lesson, telling them that they need to make sure their explanations answer the questions, “How do I perform this construction?" and “Why did I have to perform these steps?"
I ask for at least two different pairs to read out their explanations so that everyone can hear them and check their explanations.
I want to assess individual student's understanding, particularly at this point in the unit when we have performed several constructions. I introduce the Constructions Tri-Mind to students, explaining to students that they can choose one of three options for demonstrating their understanding of the constructions we have done so far--the Tri-Mind gives me a way to differentiate the product students create to show the level at which they can meet this lesson's learning objectives.
Before having students work, I make my expectations explicit, telling students they need to incorporate clear constructions markings (arcs, rays, lines), precise geometry vocabulary (point, ray, endpoint, adjacent, bisect, perpendicular, etc.), and step-by-step explanations of all constructions, even the most basic ones. I tell students they should check their explanations by asking if anyone can follow their directions and perform the construction successfully.