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* *Reflection: Unit Exams
Transformations Individual Assessment - Section 1: Transformations Individual Quiz

My favorite questions on the Transformations Test are #5 and #6. When assessing students’ understanding on the test, I saw that #5 provided students with opportunities to explore transformations in multiple representations (graphically and symbolically) while giving them a chance to explain the transformation using academic and mathematical vocabulary in their writing. Throughout the transformations unit, I pushed students to use the “ingredients” for high quality explanations. I saw the majority of my students were able to clearly explain how they knew a pre-image and image were reflections of each other; for example, students wrote that a triangle was a reflection of its pre-image over the x-axis, for example, because the x-axis perpendicularly bisects every segment connecting corresponding points of the pre-image and image.

I really liked question #6 (is the reflection of the given isosceles triangle a translation of the pre-image?) because it was so open-ended that students could answer the question in different ways, both of which show deep understanding of transformations. One, students could argue that the pre-image and image were translations of each other (if they were allowed to ignore vertices). Two, students could argue that the pre-image and image were not translations of each other if they pointed out that the orientation had changed.

Some of the best arguments involved students talking about the fact that the isosceles triangle itself has a line of symmetry, so reflecting it over any line parallel to its line of symmetry would result in an image that is a translation of the pre-image.

*I would like to thank the Geometry teachers at Fremont High School for sharing some of these assessment items with me.*

*Unit Exams: Updated Transformations Unit Test*

# Transformations Individual Assessment

Lesson 4 of 4

## Objective: Students will be able to apply the characteristics of translation, reflection, and rotation and make connections between the coordinates, graphs, written descriptions, and ordered pair rules of figures that have been transformed.

## Big Idea: Students demonstrate their proficiency with translations, reflections, and rotations as operations and rigid motions.

*55 minutes*

As they complete Transformations Quiz, students will demonstrate their understanding of translation, reflection, and rotation by performing these transformations and answering questions that require them to justify their reasoning.

#### Resources

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Students often have difficulty organizing their old notes, papers, and work; typically, most students do not have a strong sense of what it means to put in *effective* effort when preparing for cumulative assessments. By showing sample student work, I can give students an idea of what they can do to study in a practical and efficient way. Instead of telling my students what I want them to do, I ask, “what do you notice?” as they look at the work, forcing them to point out the characteristics that make the plan of action high quality and useful.

I hope my students will notice how the work is organized, the specificity of the notes/reminders/tips listed, the specific math examples and diagrams that will make the big ideas concrete, specific, and meaningful. By asking students to publicly name these qualities for the class, I hope they will gain a better understanding of what effective studying can look like and how their studying should address their particular needs.

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Since the upcoming midterm exam will feature two proofs, I make sure to build in time to discuss the more challenging problems and proofs from the last unit test on triangle properties, triangle congruence, and proof. I want to address any confusion or misunderstanding so that my students continue improving their written justifications as well as write high quality proofs.

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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