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.
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.
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