Winking Smiley Face Reflection
1. Give each partnership the Smiley Face picture to use as a pre-image from the Smiley Face Reflection file.
2. Assign each group one of the following tasks:
a. Task 1: Ask one partner in each group to first dilate the pre-image by a scale factor of using the origin as the center of dilation and then to
reflect that dilation across the -axis. Ask the other partner to first reflect the pre-image across the -axis and then dilate that reflection by a
scale factor of using the origin as the center of dilation.
b. Task 2: Ask one partner in each group to first dilate the pre-image by a scale factor of using the point
as the center of dilation and then
reflect across the -axis. Ask the other partner to first reflect the pre-image across the -axis and then dilate that reflection by a scale factor of
using the point
as the center of dilation.
c. Task 3: Ask one partner in each group to first reflect the pre-image across the -axis and then reflect that reflection across the -axis. Ask the
other partner to first reflect the pre-image across the -axis and then reflect that reflection across the -axis.
d. Task 4: Ask one partner in each group to first reflect the pre-image across the line
and then reflect that reflection across the -axis. Ask
the other partner to first reflect the pre-image across the -axis and then reflect that reflection across the line
.
3. If partnerships finish quickly, assign them an additional task. Once all students have completed at least one task, lead a whole group discussion using
the following questions:
a. Did the order in which a series of transformations is performed make a difference? (The answer is yes.) Why do you think the order matters?
Describe what is happening that makes the image sometimes match the pre-image and other times not.
b. What algebraic property is this similar to? (The answer is the commutative property.) Can we say that transformations are commutative? Why
or why not? What evidence do you have either way?
c. Does the double reflection look like another transformation? (The answer is rotation.) How many degrees of rotation does each double
reflection result in? (The answer is twice the angle measurement between the two lines either clockwise or counter-clockwise depending on
the order of the reflections.)
4. This discussion sets the stage for exploring rotations.
Winking Smiley Face Reflection
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y=x
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