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# Exploring Rotations in the Plane Extension Activity Continued

Lesson 9 of 23

## Objective: To begin conceptual development of how rotations are the basis for many other geometry concepts.

## Big Idea: Use compound rotations to develop a conceptual understanding of regular polygons, rotational symmetry, interior angle sums, and area.

*50 minutes*

Begin today by reminding students of the purpose of this extension activity.

Here is a link to a short video about opening each lesson by first "**Clarifying and Sharing Learning Intentions and Criteria for Success." **

The purpose is to apply compound rotations in order to see why and how other concepts in geometry fit together. Some examples of other concepts include understanding what it means to be a regular polygon and then all the extra features regular polygons have because of rotations. Part of the concepts will focus around the usefulness of triangles as they compose other polygons. Today, the activity will focus on special properties regular polygons have because they can be created through compound rotations. Students will be looking for patterns as well among angle measures so they can use their skills at creating function rules to generalize patterns into a rule.

Start the activity today by reviewing the last rotation, triangle PIG, under the document camera as this rotation was probably homework. Discuss with the students all the major concepts that were learned yesterday: what happens to a point when it is on the point of rotation, what it means to be a regular polygon and how they know, and how regular polygons can be broken into isosceles triangles.

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#### Beginning the New Work

*30 min*

Allow students to work in their groups to completed questions 19 through 24. As students complete this work, walk about the room assessing learning and providing feedback to groups that will move their learning forward. Here are a few short videos links to help you with these strategies.

**Activating Students as Resources for One Another**

**Providing Feedback that Moves Learning Forward**

After allowing about 10 minutes working, or until you feel most or all of the class has put thoughtful answers on paper about these questions, then pull the classroom together for a mini-wrap up. The wrap up should focus on these questions and pull it all together by question 24 when the consolidated ideas can be put into a table. It is always best to allow student groups to present their thinking to each of the questions. This presentation time really helps with student engagement and making students owners of their own learning.

Here are a few short videos on mini wrap ups and helping students take ownership of learning.

**Activating Students as Owners of Their Own Learning**

**Mini Wrap Ups**

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After a full wrap up of all questions 19-24 and especially a good discussion of question 24 and the generalized rule of 360/n for the central angle measure of rotational symmetry, allow students to complete the chart in questions 25 and then assign the rotational symmetry homework page.

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- LESSON 1: Introduction to Transformations using Play-dough
- LESSON 2: Hands-on Exploring Translations in the Plane
- LESSON 3: Hands-on Exploring Translations in the Plane Continued
- LESSON 4: Hands-on Exploring the Movement of Reflections in the Plane
- LESSON 5: Hands on Exploring Reflections in the Plane Continued
- LESSON 6: Reflections in the Coordinate Plane Continued Again - finishing it up
- LESSON 7: Exploring Rotations in the Plane
- LESSON 8: Exploring Rotations in the Plane Extension Activity
- LESSON 9: Exploring Rotations in the Plane Extension Activity Continued
- LESSON 10: Exploring Rotations in the Plane Extension Activity Completed
- LESSON 11: Rotations in the Coordinate Plane
- LESSON 12: Combining Transformations Formative Assessment Lesson
- LESSON 13: Combining Transformations Formative Assessment Lesson Continued
- LESSON 14: Combining Transformations Formative Assessment Lesson Completed
- LESSON 15: Exploring Angle Relationships Through Transformations
- LESSON 16: Exploring Angle Relationships Through Transformaitons Continued
- LESSON 17: Exploring Angle Relationships Along Parallel Lines
- LESSON 18: Angle Relationships Along Parallel Lines Continued
- LESSON 19: Angle Relationships Along Parallel Lines Completed
- LESSON 20: Optional Parallel Lines Unit Project Day 1 of 2
- LESSON 21: Optional Parallel Lines Unit Project Day 2 of 2
- LESSON 22: Transformations Unit Exam
- LESSON 23: Parallel Lines Challenge Problem