##
* *Reflection: Positive Reinforcement
Transformations Overview: Focus on Reflections - Section 2: Launch Reflections

In launching this lesson in the past, students sometimes did something really interesting: they would hold the slip of paper up to the light so they could easily read the backwards-printed definition of "reflection." This year, I noticed several students holding the slip of paper up to the screen of their cell phone, essentially using their phone's screen as a mirror to reflect the backwards printing.

These instances are worth pointing out because they show students thinking strategically and using a variety of resources to make sense of their work. My students intuitively found clever ways to solve their problem, which is interesting and worth noting. However, the reason I bring up these instances is this: as my understanding of transformations continues to deepen, so does my ability to recognize moments to push students further in their conceptual understanding. I now see that when students held the piece of paper up to the light, they hadn't just found a shortcut; they were demonstrating their understanding that the paper itself served as a line of reflection for the pre-image (the backwards printed definition) and its image (the definition students could now easily read). Similarly, when students held the piece of paper against their cell phone screen, they were showing that they saw the screen as a line of reflection. By highlighting these strategies for the whole class, I was able to help my students see connections between their intuition and the concept of reflection.

*Encouraging Resourcefulness*

*Positive Reinforcement: Encouraging Resourcefulness*

# Transformations Overview: Focus on Reflections

Lesson 1 of 4

## Objective: Students will be able to discover and apply the characteristics of reflection and explain (using words and symbols) the position and orientation of 2-D shapes after transforming them.

## Big Idea: Remind students of the meaning of transformation and motivate students to learn more about rigid motions in the plane.

*45 minutes*

#### Overview of Transformations

*15 min*

To introduce the idea of transformations to my students, I briefly review the definition of transformation and give examples of **translation**, **reflection**, and **rotation** in a whole-class discussion. **Since students have a strong association with all of these words in their everyday life, it is important to give them opportunities to tinker around with their newfound understanding of what these terms mean mathematically. ** I ask students to work through several examples in their groups before we debrief answers as a whole class and discuss confusions, misunderstandings, and insights. In particular, I find that #6 provides an opportunity to have a rich discussion on the importance of flexible thinking when working with transformations.

#### Resources

*expand content*

#### Launch Reflections

*10 min*

I find it challenging to get students to really grasp the precise definitions of all of our transformation vocabulary because they use these words all the time in their everyday lives. “Reflection,” for example, can be tricky for students to wrap their heads around because they have a strong, intuitive sense of the term already. ** I print a description of the term “reflection” backwards to engage students in digging deeply into the definition of the term**—students must use a mirror in order to decipher the description correctly and, then, as a group, define “reflection” in twelve words or less. We then debrief groups’ definitions as a whole class and transition into the next task.

#### Resources

*expand content*

In this task, students are given various sets of points that they must first reflect over the x-axis, then reflect over the y-axis. My goal is for groups of students to notice patterns for themselves, which they can describe with words and express symbolically as an **ordered pair rule**. A great extension for groups who may finish early is to ask them to come up with a rule for reflecting over the line y=x or the line y=-x.

As in many group tasks in math, there is a risk for one or two students to “take over” in a group—perhaps they see patterns quickly, perhaps their teammates perceive them as having high academic or social status. For this reason, it is important to have a structure that will support equitable participation and respect for others’ thinking within the group, which is why I run the task as a **Participation Quiz**.

#### Resources

*expand content*

#### Debrief

*5 min*

As the Participation Quiz nears its end for all groups, I make sure to debrief the key points with the whole class on our Transformations Notes. While every group should have discovered patterns in the coordinates as they were reflected over the x- and y-axes, I make sure to have at least one group share out their discoveries with the rest of the class so they have a mathematical voice in the classroom and an opportunity to test their understandings and receive feedback from their peers.

#### Resources

*expand content*

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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