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# Exploring Reflections 2

Lesson 6 of 16

## Objective: SWBAT Find coordinates of reflection images of points in a plane.

## Big Idea: Students see that the image of a figure can be found by locating the images of enough points to determine the figure.

*55 minutes*

#### Launch

*15 min*

I begin today's lesson by projecting the image Golf clubs on the SmartBoard and telling the class that many object pairs come in different or opposite orientations like the set of clubs on the board. One is a right handed club, the other a left handed one. I then ask the class as a whole to name all the objects they can think of that have opposite orientation, like the golf clubs.

As I call on the students to respond I write their answers on the board. I emphasize to the class that there should be no objections to any answer until we are through. I quickly write the responses, right or wrong, and stop when I have at least 8 or 10 answers. Some of the responses I've gotten are:

- baseball gloves
- mittens
- guitar

I then ask the students to state if they object to any responses and to explain why. Students may object to objects that are identical like tennis or ping pong rackets, and state that their orientation doesn't change when flipped horizontally. I instigate a debate by asking other students for their opinion. A student may say that flipping the racket vertically changes orientation. "But does a horizontal flip really preserve orientation," I ask.

I then project the image objects pairs showing sets of objects that visibly show orientation change, except for the ping pong rackets. I ask a student to go to the board and write numbers 1 through 6 on one racket in clockwise rotation, just like the numbers on a clock. I than ask this student to try and write the numbers on the other racket after a vertical flip. If done correctly, the student, and the class will see that counting from 1 towards 6 in the image is counter-clockwise. I end the section by stating that as we learned in the previous lesson, reflections do not preserve orientation.

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#### Activity

*25 min*

To begin the second day of our Reflection lessons, I project the resource Copy Town on the SmartBoard and hand each student a GSP slip. I tell the class that **Copy Town** is a neighborhood that was designed using reflections. The north side of town (north of X Road) is an image of the south side. The east side of town (east of Y Road) is an image of the west side. There are things students should know before asking to complete the GSP slip so I stand at the board and indicate:

- The main roads are the x rd. and y rd. which are the x and y axis of the plane
- The streets in Copy Town run North - South. The avenues run East - West
- Only the main public buildings are shown on this map.
- Each address is written using street first (x) followed by avenue (y).

**Example**: The library on the north-east part of town is located at 1st street, Ave B.

After students understand this, I ask that they pair up with an elbow partner and answer the questions on the GSP slip.

Once students complete the GSP slip, I ask volunteers to share their answers with the whole class. Students usually do well with the addresses, yet may differ on the questions where they give conjectures (questions 4 and 8). Most of the time they will word their responses differently like "the x coordinate changes sign" or "the x coordinate becomes negative", when reflecting a point over the y axis. This is not a problem as long as the students see that reflecting a pre-image over the y axis yields an opposite x coordinate for each point of the pre-image, and the same happens for the y coordinate in a reflection over the x axis.

I then write or project Reflections 2 new info on the board and ask students to find the reflection rule for a reflection over the x-axis and the y-axis.

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#### Closure

*15 min*

To close the lesson and assess students progress, I hand each learner a Closure Activity sheet. I have them work independently here and collect each sheet at the end of the class. I make sure I go through them before our next encounter so I can guide my planning accordingly.

#### Resources

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- UNIT 1: Number Sense
- UNIT 2: Solving Linear Equations
- UNIT 3: Relationships between Quantities/Reasoning with Equations
- UNIT 4: Powers and Exponents
- UNIT 5: Congruence and Similarity
- UNIT 6: Systems of Linear Equations
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- LESSON 1: Exploring Dilations 1
- LESSON 2: Exploring Dilations 2
- LESSON 3: Translations (Day 1 of 2)
- LESSON 4: Translations (Day 2 of 2)
- LESSON 5: Exploring Reflections 1
- LESSON 6: Exploring Reflections 2
- LESSON 7: Exploring Rotations 1
- LESSON 8: Exploring Rotations 2: On the plane
- LESSON 9: Reflections over parallel or intersecting lines (Day 1)
- LESSON 10: Reflections over parallel or intersecting lines (Day 2 of 2)
- LESSON 11: Angles and Parallel Lines (Day 1 of 2)
- LESSON 12: Angles and Parallel Lines (Day 2 of 2)
- LESSON 13: Vertical angles and Linear Pairs
- LESSON 14: The Triangle Sum Setup
- LESSON 15: Kaleidoscope Eyes
- LESSON 16: Where's The Math? Analyzing our Kaleidoscope Images