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# Introducing Geometry Quiz: Four Triangles

Lesson 6 of 6

## Objective: Students will be able to demonstrate their understanding of the Four-Triangles problem to determine line symmetry and rotational symmetry for a set of pentominoes.

#### Warm-Up

*25 min*

I use this warm-up because it gives students the opportunity to brush up on some of the Algebra 1 skills necessary for a Geometry classroom. This is a longer warm-up than I typically use because of the rich discussion I facilitate when having students share out the answers. Two of the warm-up problems (#1 and #3) have given me rich opportunities to facilitate student discourse because these problems focus on reasoning while giving students the chance to construct their own arguments and critique the reasoning of others (**MP3**).

In the first problem, students will ideally grapple with –(-1)^{27 }without expanding (-1)^{27} and then explain why their answer makes sense. I like the third problem because students tend to use multiple approaches when solving. When circulating the room and looking at student work, I note several different students who I want to present their work, which will allow for rich discussion as audience members make connections between the ideas presented.

#### Resources

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#### Quiz

*30 min*

In this quiz, I ask students to apply what they learned from the Four Triangles problem by making sense of a new situation: pentominoes (**MP1**). Students will analyze the symmetries for a set of pentominoes and explain whether any of the pentominoes are congruent. Students will also have the opportunity to classify a given four-triangle figure by its polygon name as well as use foundational geometry vocabulary like rotational symmetry, line symmetry, convex, concave to describe the figure.

I always have tracing paper in my classroom readily available to accommodate students who may have difficulties seeing line symmetry or rotational symmetry.

*Resource Citation: I want to acknowledge Cathy Humphreys, a colleague and mentor, who shared this task with me.*

#### Resources

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review