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# Developing Transversal Intuition

Lesson 5 of 16

## Objective: SWBAT connect the concepts of vertical and supplementary angles to interpret the relationships between angles formed by a transversal.

## Big Idea: Students get a change to make informal arguments about angles and explain why and when angles will be equal when they are cut by a transversal.

*65 minutes*

#### Lesson Beginning

*15 min*

Today I want to keep it simple. I present a simple diagram of a transversal:

Teach_Students_to_Decompose_a_Transversal

I ask students to measure all of the angles in the diagram. When I feel the class is ready, I ask them “how did I (or a student) solve this by only measuring *one *angle.” I use this as a launching point to discuss many different features of angles and transversals.

Many students are able to reason with the help of the transitive property, vertical angles and supplementary angles that alternate interior and exterior angles must be equal. Although you will certainly spend some time *defining* math vocabulary, don’t force the conversation around these angles being equal. If students aren’t able to articulate why alternate interior and exterior angles are equal, you can get back to in later in the lesson.

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#### Lesson Middle

*30 min*

Next, I ask my students to practice mild, medium and spicy problems from the Transversal Spice Rack. As they work I circulate with a purpose. I want to gather information for a summary discussions. I am on the lookout for particularly interesting examples of student work.

**Extensions and Scaffolds:** If necessary, I make the discussion at the end of this section more accessible to my students by providing handout with diagrams of transversals that accompany my introductory presentation. I do not want students spending a tremendous amount of time setting up and labeling the points and angles of a diagram. Check the video, Teach_Students_to_Decompose_a_Transversal, for some helpful themes around this lesson.

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#### Lesson End

*20 min*

To end the lesson, I have students present their solutions to the problems they solved. As they do, we discuss ideas around angles and transversal lines. I pay attention to whether students use vocabulary appropriately and make valid inferences (MP2, MP6). I am on the lookout for students who are using the idea that the corresponding angles will also be equal. In order to ground the discussion, I may return to the question of when and why angles cut by a transversal are equal or not equal.

#### Resources

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##### Similar Lessons

###### PTA (Parallel Lines, Transversals and Angles)

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- UNIT 1: Starting Right
- UNIT 2: Scale of the Universe: Making Sense of Numbers
- UNIT 3: Scale of the Universe: Fluency and Applications
- UNIT 4: Chrome in the Classroom
- UNIT 5: Lines, Angles, and Algebraic Reasoning
- UNIT 6: Math Exploratorium
- UNIT 7: A Year in Review
- UNIT 8: Linear Regression
- UNIT 9: Sets, Subsets and the Universe
- UNIT 10: Probability
- UNIT 11: Law and Order: Special Exponents Unit
- UNIT 12: Gimme the Base: More with Exponents
- UNIT 13: Statistical Spirals
- UNIT 14: Algebra Spirals

- LESSON 1: Developing Right and Straight Angle Intuition
- LESSON 2: Create Problems with Right and Straight angles
- LESSON 3: Why Are Vertical Angles Equal?
- LESSON 4: Create Vertical Angle Problems
- LESSON 5: Developing Transversal Intuition
- LESSON 6: Create Transversal Problems
- LESSON 7: Why Do Triangles Have 180 Degrees?
- LESSON 8: Walking Around a Triangle
- LESSON 9: Defining Key Angle Relationships
- LESSON 10: Triangle Sum Theorem Proof
- LESSON 11: Angles and Algebra
- LESSON 12: Super Practice with Angle Values
- LESSON 13: Super Practice with Angle Values - Feedback session
- LESSON 14: Super Practice with Angles and Algebra
- LESSON 15: Super Practice with Angles and Algebra - Feedback Session
- LESSON 16: My Little Transversal: A multi-day project lesson