TILES AND TURTLES [DAY 4]
GEOMETRY - TRANSFORMATIONS
Explore concepts relating to rigid motion transformations.
Intentionality
Math Talk
Visual Math Talk Prompt #1
Visual Math Talk Prompt #2
Visual Math Talk Prompt #3
Purposeful Practice
Resources & Downloads
Educator Discussion Area
Intentionality & Unit Overview
Length of Unit: 5 Days
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Students will reinforce concepts related to rigid motion transformations by describing and performing translations, rotations and reflections on the coordinate plane.
Intentionality…
The purpose of Day 4 activities is to reinforce concepts from Day 3. Students will engage in a visual warm up that will have them revisit the idea of the transformational approach to congruence. They will then have an opportunity to complete purposeful practice that will serve to develop a deeper understanding of the following big ideas:
- a property of rigid motion transformations (rotation, reflection, and translation) is that the measure of a two-dimensional object under the transformation remains unchanged
- basic rigid motions (translations, rotations, reflections) preserve distances and angle measures of figures
- two figures on a plane are congruent if a series of basic rigid motions can be described that will map one figure onto another
- Translations require a distance and a direction
- The distance and direction of a translation (horizontal and vertical movement) is directly related to changes in the x and y variables
- Rotations require a center of rotation, degree of rotation and direction (clockwise or counterclockwise)
- All points on a figure are rotated the same number of degrees around the point of rotation, in the same direction.
- Reflections require a line of reflection.
- All the points on a figure are equidistant from the line of reflection.
What You’ll Need…
A variety of tools for students to use to think through the problems, including, but not limited to:
- Patty paper
- MIRA geometry tools
- Centimeter paper
- Scissors
- Rulers
Math Talk
Congruent or Not?
Consider utilizing the following image with the prompt:
Which of the following pairs of shapes are congruent?
The purpose of the warm up is to keep the idea of congruence in the foreground as students problem-solve their way through the rigid motion transformation problems and to reinforce the transformational approach to congruence. For each pair of figures, students must articulate what types of transformations would allow for one figure to be mapped onto the other.
A – the two figures are congruent (reflect across a horizontal line running through the middle of the figure).
B – the two figures are not congruent.
C – the two figures are congruent (rotate 90°).
D – the two figures are congruent (reflection + rotation).
Visual Math Talk Prompt #1
The coordinates of the vertices of a figure are shown below – both the image and the preimage.
Describe the transformation that took place. How do you know?
| PREIMAGE | IMAGE |
| E ( -5, 1) | E’ (2, 4) |
| F ( -3, 1) | F’ (4, 4) |
| G ( -1, 3) | G’ (6, 6) |
| H ( -1, 5) | H’ (6, 8) |
| I ( -5, 5) | I’ (2, 8) |
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Visual Math Talk Prompt #2
The coordinates of the vertices of a figure are shown below – both the image and the preimage.
Describe the transformation that took place. How do you know? Is there another transformation, or set of transformations that could create the same result? If so, describe it/them.
PREIMAGE | IMAGE |
J ( -1, 4) | J’ (1, 4) |
K ( -3, 4) | K’ (3, 4) |
L ( -3, 2) | L’ (3, 6) |
M ( -2, 1) | M’ (2, 7) |
N ( -1, 2) | N’ (1, 6) |
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Visual Math Talk Prompt #3
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Purposeful Practice
While Students Are Practicing…
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Purposeful Practice
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Resources & Downloads
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Educator Discussion Area
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