Exploring Angle Relationships Along Parallel Lines

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Objective

Students will be able to understand and prove angle relationships along parallel lines cut by a transversal through the application of transformations

Big Idea

I Like to Move it Move it, Move Angle Measures Along a Transversal to Map Relationships

Lesson Author

Christa Lemily

Bowling Green, KY

Grade Level

Eighth grade

Subjects

Math

translation (Geom Transformations)

Geometry

reflection (Geometry)

dilation (stretches and shrinks)

Standards

8.G.A

Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

8.G.A.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

MP1

Make sense of problems and persevere in solving them.

MP3

Construct viable arguments and critique the reasoning of others.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Bellringer - Lesson Opening

15 minutes

Begin the Angles Activity

40 minutes

Watch a short video explaining the rational for this lesson and why I have chosen to apply transformations to parallel lines cut by a transversal.

Clarifying and Sharing Learning Goals

Always begin by clarifying for the students what it is they will be learning from the activity today. Click here to watch a short video on what it means to clarify and share learning intentions and criteria for success with students:

Clarifying and Sharing Learning Intentions and Criteria for Success

The learning goals for today are to continue to focus on graphing linear equations with the purpose of using those lines to see angle relationships. Tell students that they will be graphing two different intersections which will create eight angles for this activity. The goals are the same as on the angles activity prior to this: move angles through transformations to map relationships between certain pairs of angles. Let students know that there will be a lot of vocabulary throughout the activity and it is important to know these angle pair names. An organizer to help with the vocabulary will be used on the last day of the activity.

Working in Cooperative Groups to Graph

Allow students time to graph the three given equations and number the angles as the directions indicate. Students should work within their partnership or small group to correctly graph and label. While students are graphing, move about the room formatively assessing progress and providing feedback that will move your students’ learning forward. To better understand how I group students into cooperative teams and how I provide feedback to students, click on the links below to watch a short video on each strategy.

Cooperative Grouping Explained

Providing feedback that moves learning forward

After allowing time for groups to correctly graph and label ask one group to place their papers under the document camera and share how they created the linear graphs. Choose this group as you are providing feedback and let them know you would like for them to present their correct work. I sometimes allow more than one presentation if multiple graphing strategies were used and each is a viable method of graphing. I call this time of students presenting their work a “mini wrap-up” because I do not spend long periods of time closing a lesson at the end of the class period. We use small lesson closers after a small chunk of material has been completed. Click below to watch a short video on how I use the mini wrap-up strategy.

Cooperative Grouping Explained

Once all students have correct graphs, it is time to begin answering the angle relationship questions. These questions are challenging and ask students to think about and prove angle relationships. This is a key time to provide feedback to students both yourself and through partners within small groups. Students need to be able to discuss ideas and questions. I often had to remind students to use their tracing paper in order to compare angles and find their relationship first (congruent or supplementary) and then begin to think through the transformations that would move and map angles together. Click below to watch a short video on how students provide feedback to one another within small groups.

Students as resources for one another

Where to End the Lesson

The goal for the first day is to reach at least question 4 and discuss the answers to these questions in a mini wrap-up before the end of class. Of course students will work at their own pace and that is encouraged. You just want to at least get everyone through question 4 by the end of the first class period. Some of the key ideas to focus on throughout the lesson today include: graphing linear equations (fluency), understanding algebraically why two lines are parallel (same slope different y-intercepts), and the definition of a transversal. The math standards of focus in this lesson today include: 8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Through the use of partners to provide feedback and work to graph linear equations with efficiency and fluency the following math practice standards will also be used: MP3MP7.