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# Reviewing Congruence

Lesson 8 of 17

## Objective: SWBAT use transformations to identify congruent figures and to describe the transformations which superimpose a polygon or pattern onto itself. Students will understand the properties of bisectors and the precise meanings of congruence and symmetry in terms of rigid motions.

*53 minutes*

#### Lesson Opener

*5 min*

The warm-up prompt for the lesson asks students to think of the homework problems that gave them trouble. Each team must agree on ONE problem, which the team scribe will write on the board. I display the prompt using the slide show for the lesson. The lesson opener follows our Team Warm-up routine.

**Goal-Setting**

Following the warm-up, I display the lesson agenda and learning targets. Today we will review Homework Set 2, and students will complete thier learning portfolios for the unit.

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Today, we will conduct homework review as a team activity, using the Team Review variation of our Homework Review routine. I display the instructions and get the class started.

The solutions to some of the problems were provided with the homework set. Most of the problems are constructions, so students' solutions are not expected to be exactly like the model solutions. This is another opportunity to have a discussion about what can vary in the construction of a figure and which properties are constant (**MP7**). I remind students to leave construction marks so that I can see whether constructions were performed properly and to label their figures correctly (**MP6**).

I am particularly interested in seeing how students are describing the reflections, rotations, and translations that carry a polygon or a tiling onto itself: Are their descriptions complete? Are they accurate? (**MP6**)

As students are checking their work, I circulate.

Next, I remind students how they are to complete the Progress Check** **in their Learning Portfolio. The purpose of this assignment is show students how to use homework to assess their own progress toward unit learning goals.

Students will be turning in their portfolio problems for me to review. Students should have answered Congruence & RigidMotions Portfolio Problem 1 - Tricky Tiling completely. They should have revised their original answers to provide more complete, precise descriptions of the rigid motions, following the examples in their notes (**MP6**). I do not expect students to have made a complete answer to CR Portfolio Problem 2 - Lost Rover at this time. They should have made a good start, however, and that is what I will be evaluating (**MP1**).

I also return students' Unit Pre-Tests, if I have not already done so. Students are responsible for correcting any incorrect answers and turning in a perfect product as part of their learning portolio at the end of the unit.

##### Resources (7)

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#### Extra Practice

*20 min*

I plan time in this lesson for students to get Extra Practice. Ideally, students will identify the areas they want to work on themselves, but I generally know which skills the class needs extra time on.

I make a few extra copies of the practice activities from earlier lessons on constructions and have them on hand. There are problems in Homework Set 2 that review material from the first half of the unit. I use these problems to meet individual needs.

Students may also use this time to work together to correct thier unit pre-tests. They are responsible for turning in a near-perfect product as part of their learning portfolios.

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The lesson close follows our Team Size-Up routine. The Lesson Close prompt asks students to give a precise definition of congruence.

**Homework**

For homework, I assign problems #23-25 of Homework Set 2. Problems #23 and 24 review constructions: perpendiculars and parallels, a hexagon inscribed in a circle, and angle bisectors. Problem #25 asks students to describe the rotations and reflections which superimpose an equilateral triangle onto itself.

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- UNIT 1: Models and Constructions
- UNIT 2: Dimension and Structure
- UNIT 3: Congruence and Rigid Motions
- UNIT 4: Triangles and Congruence
- UNIT 5: Area Relationships
- UNIT 6: Scaling Up- Dilations, Similarity and Proportional Relationships
- UNIT 7: Introduction to Trigonometry
- UNIT 8: Volume of Cones, Pyramids, and Spheres

- LESSON 1: Previewing Congruence and Rigid Motions
- LESSON 2: Congruence and Coincidence
- LESSON 3: Re-Discovering Symmetry
- LESSON 4: Perfect Polygons
- LESSON 5: Bisector Bonanza
- LESSON 6: The Shortest Segment
- LESSON 7: From Perpendiculars to Parallels
- LESSON 8: Reviewing Congruence
- LESSON 9: Re-Examining Reflections
- LESSON 10: Reconsidering Rotations
- LESSON 11: Taking Apart Translations
- LESSON 12: Visualizing Transformations
- LESSON 13: Reasoning About Rigid Motions
- LESSON 14: Analyzing the Symmetry of a Polygon
- LESSON 15: Reviewing Rigid Motions
- LESSON 16: Rigid Motion and Congruence Unit Quiz
- LESSON 17: Describing Precise Transformations