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* *Reflection: Shared Expectations
Introduction to Transformations using Play-dough - Section 2: Collaborative Hands- on Activity

This one lesson has been the most beneficial lesson I ever created for correcting a very common misconception - corresponding parts. In years past, my high school geometry students really struggled to understand corresponding parts and this one concept runs throughout so many skills in geometry such as: congruent figures (corresponding parts are congruent), similar figures (corresponding sides are proportional and corresponding angels are congruent), transformations (labeling of corresponding parts), and parallel lines cut by a transversal (corresponding angles). This one lesson has greatly improved my students' conceptual understanding of what it means in geometry to correspond. However, as awesome as this lesson is, if it is your student's first experience with hands-on materials in your room it might not be a productive experience. The classroom management aspect of this lesson is hectic. I set very clear expectations at the start of the year and then remind students of these before each hands-on lesson. The play dough is of course an attractive means of modeling very inappropriate images so be explicit about this in your instructions. Allowing time at the start of the lesson to play with the dough will help reduce the number of incidents during the actual lesson time.

*Classroom Management - Shared Expectations*

*Shared Expectations: Classroom Management - Shared Expectations*

# Introduction to Transformations using Play-dough

Lesson 1 of 23

## Objective: Students will be able to understand the definition of congruence and corresponding parts as they relate to transformations.

## Big Idea: Engaging students to concretely understand the definition of congruence and identify corresponding parts.

*53 minutes*

#### Setting Expectations

*10 min*

Tell students that class today will explore what it means to be congruent and how to prove figures are congruent. Let the students know that the exploration will involve using cookie cutters and play-dough. Students will have the first two to three minutes to play with the play-dough and get all the creating out of their system. Now is also when you set your expectations about behavior with the play-dough and school appropriate creations. Once you have established your expectations, pass out the dough giving each student their own portion and allow them to play and create.

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This is the hands-on part of the lesson and having a document camera and projector will really help with this demonstration. Let your students know that they will be using cookie cutters to cut out designs and therefore should begin to flatten out the play-dough. Also warn students that they will need their cookie cut out for the rest of the class period so do not smash the dough until told to at the end of class. I have had issues with students smashing their figures before the end of class and needing to recut the figure and waste time. As you pass out the the cookie cutters, tell students you only have enough for about half the room, so they are to use what they are given, no trading, and then give them back to you. If you allow students to trade cutters or pass them over to the other students you will create problems for yourself. What you want to do is get at least two of each cookie design somewhere in the room but not sitting anywhere near each other. After all the students have used a cookie cutter and you are certain you have at least two of each design present in the room, then say, “Get up and move about the room until you find the figure that is congruent to yours. Whoever has the congruent figure to yours is now your partner and the two of you should sit together and show me proof that your cookie figures are actually congruent.

Allow students to move about the room and find their congruent figure. Visit each group and check for congruence, make students prove to you their figures are actually congruent. In order to prove congruence, you really want students to stack their cookie cut outs on top of each other and explain to you how this proves congruence. After visiting all the groups, ask one partnership to take their figures up to the document camera and show everyone how they proved their figures are congruent. This is a great time to discuss the definition of congruence: two figures are congruent if through series of transformations one figure can map directly on top of the other. Ask students what type of transformation the two students just demonstrated - a translation. This is a good time to begin scripting important information on the board for students to write as notes and keep as a resource throughout class. Send the students back to their desks at the end of the whole class discussion over the definition of congruence and translations as a mapping transformation.

Next, tell the class that the partner sitting on the left is to pick a feature on their figure and point to it. After the left partner picks a feature, tell all partners sitting on the right to begin pointing to their corresponding part. Again visit all the groups and ask groups to confirm how they knew which part was corresponding to the first partner’s choice. You may want to reenforce the corresponding parts concept by asking students to switch roles and the partner on the right points to a feature while the partner on the left pints to his/her corresponding part. After visiting the groups pull one partnership up to the document camera and ask them to point to corresponding parts under the camera. As a class, develop a definition for corresponding parts based on the examples just completed. Understanding the concept of corresponding parts is vital to proving congruence and similarity and using corresponding angle relationships along parallel lines.

If time allows, you may want to begin discussing different types of transformations that would preserve congruence and script student thinking about translations, rotations, and reflections on the board. I usually ask students to explain what it means to translate and they use the elementary word slide. I ask students what it means to reflect and they use the elementary work flip. I also ask about how to rotate and most students mention turning. This introduction is the only time I allow students to use the elementary words slide, flip, and turn but it is a good link to past material.

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#### Wrapping Up the Lesson

*3 min*

To end this introduction, I simply summarize the goals of this unit. I tell students this unit is about studying and proving figures congruent and similar. Congruence is proven through rigid motions that do not change the size or shape of the preimage and we have brainstormed about rigid motions we all remember from elementary school. Tomorrow, we will take a closer look at the details of translations.

Homework: No Homework on this night

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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