Motion Maps Facilitation Guide Motion Maps Facilitation Guide
Tier 2 Intervention: Geometric Transformations (HS.G-CO.A.5)
Teacher Resource
Objective
Students will perform and describe sequences of rigid transformations (translations, reflections, rotations) using physical tools (tracing paper) and coordinate rules to map one figure onto another.
Materials Needed
Tracing paper (patty paper)
Graph paper / Coordinate grid pads
Straightedges and colored pencils
Student "Transformation Lab" Worksheet
CRA Instructional Sequence
C
Concrete: Tracing Paper Manipulation
Students trace the pre-image and physically slide (translate), flip (reflect), or turn (rotate) the paper. This builds spatial intuition before introducing numbers.
R
Representational: Graphing Points
Students identify the coordinates of the new vertices on a grid. They draw intermediate "ghost" figures for sequences to see each step clearly.
A
Abstract: Coordinate Rules
Connect the physical movements to algebraic rules: \((x, y) \to (x, -y)\) for x-axis reflection, or \((x, y) \to (y, -x)\) for \(90^\circ\) clockwise rotation.
Common Misconceptions
Rotation Direction: Assuming "positive" means clockwise. Remind students that positive rotation is counter-clockwise (quadrant order).
Reflection Axis: Reflecting over the wrong axis or forgetting to count distance from the axis.
Sequence Order: Thinking the order doesn't matter. Use a translation then reflection vs. reflection then translation to show differences.
Questioning Strategies
"If we flip this over the y-axis, which coordinate (\(x\) or \(y\)) changes sign? Why?"
"How can we use the tracing paper to check if our final coordinates are correct?"
"What happens to the shape's size and angles after these moves? (Preservation of congruence)."
Progress Monitoring Checklist
Performs single translation using coordinates.
Identifies reflection axis for a given image.
Physically models 90° and 180° rotations.
Determines coordinates after a 2-step sequence.
Motion Maps Slides MOTION MAPS
Transforming Your World
Slide
Flip
Turn
Warm Up: What's the Move?
A'
A
A. Slide (Translate)
B
B'
B. Flip (Reflect)
Translation
Every point moves the same distance and direction.
Coordinate Rule
(x, y) → (x + h, y + k)
h: Moves left (-) or right (+)
k: Moves down (-) or up (+)
1
Place tracing paper over pre-image.
2
Trace the shape AND the axes.
3
Slide the paper the set distance.
Reflection
A mirror image over a line called the axis of symmetry.
Most Common Rules
Over x-axis: (x, -y)
Over y-axis: (-x, y)
Over y = x: (y, x)
Tracing Hack:
Trace the line of reflection boldly . Fold your tracing paper along that line to see exactly where your new points should land!
"Distance to the line is preserved!"
Rotation
A turn around a fixed center point (usually the origin).
90° CCW
(-y, x)
1/4 turn left
180°
(-x, -y)
Half-turn
270° CCW
(y, -x)
3/4 turn left
Pro-Tip: Use a paperclip or pencil point at the center (0,0) to hold your tracing paper as you turn it.
Transformation Sequences
Step 1
Perform the first move. Label your new points with "primes" (A').
Step 2
Use your intermediate figure as the starting point for move 2. Label A''.
Order Matters! Reflecting then sliding is NOT the same as sliding then reflecting.
Ready to Lab?
Get your Tracing Paper, Straightedge, and Colored Pencils.
!
Watch the intermediate step—don't skip the "ghost" figure!
!
Check your work: Did the shape change size? (It shouldn't!)
MOTION MAPS LAB
Motion Maps Worksheet Motion Maps Lab
Geometry Intervention Series
Name:
Date:
Part 1: The Slide
1. Trace Triangle ABC onto your tracing paper.
Pre-image Coordinates:
A (-4, 5) | B (-1, 5) | C (-4, 1)
New Image Coordinates (A', B', C'):
A': _________________
B': _________________
C': _________________
Graph Here
Coordinate Rule: \((x, y) \to (\) ________ , ________ \() \)
Part 2: The Flip
1. Trace Rectangle DEFG.
Pre-image Coordinates:
D (2, 3) | E (5, 3) | F (5, 1) | G (2, 1)
New Image Coordinates (D', E', F', G'):
D': __________
E': __________
F': __________
G': __________
Graph Here
Coordinate Rule (x-axis): \((x, y) \to (\) ________ , ________ \() \)
Part 3: The Turn
1. Trace Line Segment HI.
Pre-image Coordinates:
H (2, 1) | I (5, 4)
New Image Coordinates:
H': _________________
I': _________________
Graph Here
Coordinate Rule (90° CCW): \((x, y) \to (\) ________ , ________ \() \)
Double Move Challenge
Point P is at (2, -4). Follow the sequence:
MOVE 1
Reflect P over the y-axis.
P' = (____ , ____)
MOVE 2
Translate P' by (x+3, y+2).
P'' = (____ , ____)
Motion Maps Exit Ticket Transformation Checkpoint
Exit Ticket
Student Name
Date
1
Coordinate Rule
A point A (2, 5) is translated 4 units left and 1 unit up. What is the coordinate rule and the new location of A'?
Rule:
(x, y) → ( ________ , ________ )
New Point:
A' = ( ________ , ________ )
2
Reflection
If you reflect the point B (3, -2) over the y-axis, which coordinate changes sign?
x-coordinate
y-coordinate
3
Sequence Logic
Explain in one sentence why a rotation of 180° is the same as reflecting over the x-axis and THEN the y-axis. (Hint: Look at the rules!)
Confidence Level:
😟 Struggling
😐 Getting There
😎 I Got This
Motion Maps Answer Key Answer Key
Motion Maps Lab & Exit Ticket
TEACHER ONLY
Part 1: The Slide (Translation)
New Coordinates:
A' (-4+3, 5-4) = (-1, 1)
B' (-1+3, 5-4) = (2, 1)
C' (-4+3, 1-4) = (-1, -3)
Coordinate Rule:
(x, y) → (x + 3, y - 4)
Part 2: The Flip (Reflection)
New Coordinates (x-axis):
D' (2, -3)
E' (5, -3)
F' (5, -1)
G' (2, -1)
Coordinate Rule:
(x, y) → (x, -y)
Part 3: The Turn (Rotation)
New Coordinates (90° CCW):
Coordinate Rule:
(x, y) → (-y, x)
Double Move Challenge
Point P: (2, -4)
Move 1 (Reflect y-axis): P' = (-2, -4)
Move 2 (x+3, y+2): P'' = (-2+3, -4+2) = (1, -2)
Exit Ticket Key
1. Translation (4 left, 1 up):
Rule: (x - 4, y + 1)
A' (2-4, 5+1) = (-2, 6)
2. Reflection over y-axis:
Correct Answer: x-coordinate changes sign.
3. Sequence Logic:
Sample Answer: A 180° rotation rule is (-x, -y), which is exactly what happens when you change the sign of x (y-axis reflection) and then the sign of y (x-axis reflection).
