##
* *Reflection: Performance Tasks
Mapping with Reflections - Section 4: Independent Practice

In this reflection, I am sharing something that is still an unsolved problem for me. I really like going to the computer lab to have students get practice working with Geogebra or Geometer's Sketchpad but three things have me feeling less than fully satisfied with the experience of doing so.

First, some students simply play when they have a chance to use dynamic geometry software. They use it more as a doodling tool than as a geometry platform. It is easy to get these students to stop doodling, but what I haven't figured out yet is how to get them to really buy into the value of the software as a tool that allows them to explore geometry.

My second challenge is that students are simply not experienced enough with the software to engage in the kind of inquiry that I want them to do. I find myself feeling like I need the entire period just to train students in the basics of the software before even getting into the lesson. The next time I teach Geometry, I will definitely want to do some training early in the year and create/locate some training modules that students can complete at home to get their Geogebra and Sketchpad skills up (MP5)

Finally, I have not found a way for students to document their work on Geogebra or in Sketchpad. So far it's just been an experience for the students and informal observation for me. I think this is probably contributing to my first problem of students not taking it as seriously as I would like. I wish there was a way for them to document their work in a way that would show me what they've done , but not be so cumbersome that it's unmanageable for me. I've considered having them create a document with screenshots and narrative, but I haven't tried that yet. I think that will be my first attempt at it next time I teach the course.

*How to check work from Sketchpad*

*Performance Tasks: How to check work from Sketchpad*

# Mapping with Reflections

Lesson 7 of 7

## Objective: SWBAT identify a series of at most three reflections that maps a figure onto a congruent figure.

#### Activating Prior Knowledge

*20 min*

**Where We've Been:** We've just finished a lesson on Mapping and Congruence in which we defined congruent figures as figures that can be mapped onto one another through a series of rigid transformations.

**Where We're Going:** We'll soon be looking at congruent triangles using the rigid transformation definition to establish triangle congruence criteria.

So in this section, I will develop the concept of mapping a point onto another point using reflection. Students have had experience with reflecting points across lines in previous lessons, so the goal here is just to have them realize what they already know.

The resource for this section is Activating Prior Knowledge: Mapping with Reflections. The students will have to determine the reflection line that maps one point onto another using construction and using coordinate algebra.

Students may be a little rusty on the rules for performing the perpendicular bisector construction, but that doesn't mean they can't at least figure out that they need to construct the perpendicular bisector. So I keep copies of the instructions for basic constructions (perpendicular bisector, angle bisector, copying a segment, copying an angle) handy so that I can hand students whichever one they think they need.

If students are stuck on the coordinate algebra, which we've done before several times, I assist by suggesting that they draw a diagram first. Then I make sure they know the relevant formulas. Past that, they are left to collaborate with their classmates.

After 15 minutes or so, I review the correct results.

*expand content*

#### Concept Development

*15 min*

In the last lesson, students have just started working on mapping one figure onto another through a series of transformations. In this lesson, we will develop the idea that no matter what, we can use a series of reflections to map a figure onto a figure to which it is congruent.

To develop this idea, I perform a demonstration, the basic essence of which is captured in the following screencast.

*expand content*

#### Guided Practice

*40 min*

Once we've illustrated that the end state of any series of rigid transformations can be replicated by a series of at most three reflections, I model for students how to document that series of reflections.

The following screencast** **will give you an idea of what the demonstration is like:

The item in the video is the first item from the GP_Reflection Mapping resource. I model the first item using Sketchpad on the projector, as shown in the video. For the second item, I call on students to give me explicit non-ambiguous directions regarding what step I should take next. I require them to speak in complete sentences using correct vocabulary (MP 6). By the time we reach the third item, I start to select random non-volunteers and we pass the wireless mouse to that person so that they, themselves, can execute the next step. As they execute the step, they must explain what they are doing, again in non-ambiguous terms using complete sentences. See the Pass the Mouse Video Description for more information.

*expand content*

#### Independent Practice

*40 min*

For this section, we travel to the computer lab so that every student can have extensive practice executing the steps on Sketchpad. Each student receives the Independent Practice_Reflection Mapping resource. There are various correct answers to each item depending on which corresponding vertices students decide to map, and in which order they choose to map them. This is a good way to make sure that the whole class is not copying from one another.

My job during this phase of the lesson is to be a constant presence as students are working at their workstations. By going around to each student and asking them to explain what they are doing, I get a good sense for how well each student is working, who the overachievers are, and who the loafers are.

#### Resources

*expand content*

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- UNIT 1: Community Building, Norms, and Expectations
- UNIT 2: Geometry Foundations
- UNIT 3: Developing Logic and Proof
- UNIT 4: Defining Transformations
- UNIT 5: Quadrilaterals
- UNIT 6: Similarity
- UNIT 7: Right Triangles and Trigonometry
- UNIT 8: Circles
- UNIT 9: Analytic Geometry
- UNIT 10: Areas of Plane Figures
- UNIT 11: Measurement and Dimension
- UNIT 12: Unit Circle Trigonmetry
- UNIT 13: Extras