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# 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?"

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**How far away am I from the wall?**

**How would you construct a perpendicular to a line through a point using a compass and straightedge? How can you connect this question to our construction in the last lesson, which was to construct perpendicular bisectors?**

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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.

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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.

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Introducing Constructions: Copy a Segment and Angle
- LESSON 2: Bisect Segments and Construct Perpendiculars
- LESSON 3: Tri-Mind: Perpendiculars and Squares
- LESSON 4: Bisect Angles
- LESSON 5: Construct Parallel Lines Through a Point Not on the Line
- LESSON 6: Use Constructions to Show Slope Criteria for Parallel and Perpendicular Lines
- LESSON 7: Construct Points of Concurrency
- LESSON 8: Constructions Teaching Project: Day 1 of 3
- LESSON 9: Constructions Teaching Project: Day 2 of 3
- LESSON 10: Constructions Teaching Project: Day 3 of 3
- LESSON 11: Constructions Unit Assessment