Exploring Transformations

Introduction

Geometric figures can be described by their position in space. Changes in their position are defined as Transformations. In this investigation, you will be exploring four of the most common types of transformations: Reflections, rotations, translations and dilations.

Task

To demonstrate mastery of the concepts involved in transformations, you must be able to:

1. Define the terms: transformation, reflection, rotation, translation, and dilation.

2. Identify the transformation that has occurred when given a figure and its image 

3. Perform transformations (reflection, rotation, translation, dilation) on a coordinate plane when given instructions in algebraic form

4. Write an algebraic description of each transformation when given a figure and its image

You will create an Explain Everything presentation to show that you have met each objective above.

Process

Step 1:  Define the terms: transformation, reflection, rotation, translation, and dilation.

Watch the video "What is a Transformation"

http://www.virtualnerd.com/pre-algebra/geometry/transformations-symmetr…

Complete the interactive module below:

http://www.jogtheweb.com/run/GXzVc7HKZ0NP/Online-Geoboard-Practice-Tran…

http://www.jogtheweb.com/run/GXzVc7HKZ0NP/Online-Geoboard-Practice-Tran…

Record on Explain Everything ***

Page 1: Transformations title page with a picture, definition of the term "transformation" and your names

Page 2: definition of reflection, picture of reflection

Page 3: definition of rotation, picture of rotation

Page 4: definition of translation, picture of translation

Page 5: definition of dilation, picture of dilation

Step 2: Identify the transformation that has occurred when given a figure and its image.

Play the game "ShapeShoot" that challenges you to identify transformations:

https://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/Translat…

Record on Explain Everything ***

Page 6: record your score from the game "ShapeShoot". If you made any mistakes, tell what they were

Step 3: Perform transformations (reflection, rotation, translation, dilation) on a coordinate plane when given instructions in algebraic form

Practice the reflections, rotations and translations on the interactive site below:

http://www.sciencekids.co.nz/gamesactivities/math/transformation.html

Record on Explain Everything ***

Page 7: upload a 0-5 coordinate plane image available at:

http://www.mathipedia.com/ar7-coordinate-pairs-and-graphing.html

Plot the following points and connect with straight lines to form a triangle (-4,-2) (-2,3) (1,-2). Now plot each point after a translation of (x+3, y-2). In other words, increase the x coordinate by three and decrease the y coordinate by 2. Title "Translation (x+3, y-2)"

Page 8: Copy the coordinate graph again and plot the points (3,2) (4,4) (5,0). Next, plot (in red) the image of each point if (x,y) becomes (x,-y). This describes a reflection across the x-axis. Finally, plot the image of each point (in blue) if (x,y) becomes (-x,y). This describes a reflection across the y-axis. Title "Reflection across x-axis" and "Reflection across y-axis"

Page 9: Copy the coordinate graph again and plot the points (-3,2) (-5,4) and (-1,3). Rotate the figure by changing (x,y) to (-x,-y). This will rotate the figure 180 degrees. Plot the new points in red. Title "Rotation by 180 degrees" 

Rotate the original figure 90 degrees clockwise by switching (x,y) to (y,x), but making both coordinates positive. Plot your new points in blue. Title "Rotation by 90 degrees"

Page 10: Copy the coordinate graph again and plot the points (2,1) (-2,2) and (-1,0). Dilate the figure by a scale of two by multiplying, so (x,y) becomes (2x,2y) Plot the new points in red. Title "Dilation by scale of 2"

Step 4: Write an algebraic description of each transformation when given a figure and its image

Page 11: Copy the image below. Identify the transformation and describe algebraically as (x,y) becomes (___,___)

Page 12: Copy the image below. Identify the transformation and describe algebraically as (x,y) becomes (___,___)

Page 13: Copy the image below. Identify the transformation and describe algebraically as (x,y) becomes (___,___)

Page 13: Copy the image below. Identify the transformation and describe algebraically as (x,y) becomes (___,___)

Evaluation
Classwork points 20 plus Quality points up to 12. Total 32.

Exceeds expectations

4 points

Meets expectations

3 points

Nearly meets expectations

2 points

Fails to meet expectations

1 point

Demonstrates

understanding

of concepts

 Text on pages demonstrates exceptional clarity of understanding Text on pages demonstrates understanding of all concepts Text on pages demonstrates understanding of most concepts Text on pages demonstrates that several concepts have been misunderstood

Demonstrates

effective use

of technology

 Explain Everything pages are exceptionally well constructed Explain Everything pages are well constructed Explain Everything pages are disorganized, unclear or contain some irrelevant material Explain Everything pages show lack of competency in using features.
Completes all tasks

All 13 page complete,and extra information or images included

 All 13 pages completed as assigned 1 or 2 pages incomplete 3 or more pages incomplete
Meets deadline Turned in to Edmodo before deadline Turned in to Edmodo by deadline Turned in to Edmodo 1 or 2 days late Turned in to Edmodo 3 or more days late
Credits