Geometry Ladder Relay • Lesson • Lenny.com
Geometry Ladder Relay Collaborative 5-rung mastery review activity for CTE Geometry Unit 1 covering symmetry, reflections, multi-step transformations, parallel transversal angle chains, and exterior angle theorems across four parallel student versions plus a Spanish edition.
MM Matthew McIntyre
Mastery Ladder Tracking Sheet
Printable 1-page tracking sheet for student teams featuring 5 ladder rungs, individual teacher check-off boxes for versions A through D, and a large circular sticker landing zone for group advancement.
Ladder Relay Teacher Guide
Compact 2-page teacher facilitation guide containing 80-minute pacing, the slash-to-check repair protocol, a complete quick-check answer key across all versions, and reasoning evaluation rubrics.
Mastery Ladder Student Packets
Printable 8-page complete student review packet containing Versions A through D (2 pages each), featuring coordinate geometry diagrams, transversal chains, and exterior angle proofs.
Mastery Ladder Spanish Packet
Printable 2-page Spanish student review packet (Versión en Español) featuring enhanced high-clarity coordinate diagrams and mathematically precise transversal angle placements.
Geometry Ladder Relay Collaborative 5-rung mastery review activity for CTE Geometry Unit 1 covering symmetry, reflections, multi-step transformations, parallel transversal angle chains, and exterior angle theorems across four parallel student versions plus a Spanish edition.
MM Matthew McIntyre
Mastery Ladder Tracking Sheet CTE GEOMETRY UNIT 1 REVIEW
COOPERATIVE RELAY SYSTEM
Team Mastery Ladder
Goal: Every team clears Rung 5 through shared discourse & individual mastery.
Team Name / Station
Member A
Member B
Member C (Trio/4)
Member D (Group of 4)
5 Rung 5
Triangle & Exterior Angles
Triangle Sum + Remote Interior
A
B
C
D
TEAM CLEARED STICKER
4 Rung 4
Transversal Angle Chains
Bridge Angles & Algebra
A
B
C
D
TEAM CLEARED STICKER
3 Rung 3
Multi-Step Transformations
Translation + Point Rotation
A
B
C
D
TEAM CLEARED STICKER
2 Rung 2
Reflection Detective
Perpendicular Bisector Proof
A
B
C
D
TEAM CLEARED STICKER
1 Rung 1
Symmetry & Precision
Angle of Rotation & Reflection
A
B
C
D
TEAM CLEARED STICKER
How The Checking System Works
• / = Repair Needed: An error or missing geometric reason needs fixing. Teammates must coach, not give answers!
• ✓ = Mastery Verified: Teacher adds cross stroke when the student successfully repairs and explains their work.
• Dot Sticker: Awarded in the circle only after every active member has a check mark.
Team Collaboration Norms
1. Stay On The Same Rung: No student may work ahead while a teammate is working or repairing.
2. Explain, Don't Hand Over: You may explain geometric concepts, but every student writes their own mathematical reasoning.
3. Oral Defense: Teacher may ask any member to justify their step before awarding a check.
CTE GEOMETRY • MASTERY LADDER PROTOCOL TARGET: 100% OF TEAMS REACH & CLEAR RUNG 5 UNIT 1 SUMMATIVE READINESS
Ladder Relay Teacher Guide TEACHER GUIDE CTE GEOMETRY
UNIT 1 SUMMATIVE REVIEW
Mastery Ladder Relay Facilitation Guide
High-accountability collaborative review protocol preventing single-student carryover.
Suggested 80-Minute Pacing Framework Total: 80 Minutes
00 - 08 min Setup & Norms Assign groups of 2-4, hand out Team Sheet & Packets A-D.
08 - 25 min Rungs 1 & 2 Symmetry & Reflection Detective. Establish check standards.
25 - 45 min Rung 3 Transformations Multi-step translation + rotation about non-origin points.
45 - 65 min Rung 4 Angle Chains Parallel lines bridge reasoning + algebraic equations.
65 - 80 min Rung 5 & Debrief Exterior angle proof & final team stickers. Quick 5-min recap.
The Pen & Dot Sticker Feedback Protocol
/ 1. The Slash (Repair)
When a student has a computational error or lacks precise geometric justification, mark a single slash / on their packet and on their Team Sheet slot. Do not tell them the answer; circle the error zone or prompt: "Check your perpendicular slope" or "Name the bridge angle."
✓ 2. The Check (Mastery)
Once repaired, the student calls you back. Ask a quick oral check: "Why is that line the perpendicular bisector?" If they can clearly articulate the reasoning, draw the second stroke turning the slash into a ✓ .
● 3. The Dot Sticker
When all active students in the group have a ✓ on the current rung, place a small dot sticker in the Team Cleared circle on their Team Sheet. Only with the sticker may the team advance to the next rung together.
Differentiated Group Sizing
• Pairs: Assign Student A and Student B. (Leave C & D blank).
• Trios: Assign Students A, B, and C. (Leave D blank).
• Groups of 4: Assign Students A, B, C, and D.
• Spanish Speakers: Provide the Versión en Español packet. It pairs seamlessly with Version A's mathematics so the student can collaborate directly with teammates using English Version A or B!
Strict Classroom Policies
• No Pre-Working: Faster students may NOT begin the next rung while a teammate is repairing. They must coach and explain methods!
• Random Oral Defense: When checking a rung, you may ask Student B to explain Student A's steps. If B cannot explain, A coaches B before the check is awarded.
• Collaborative Culture: Celebrate the class reaching 100% completion of Rung 5 rather than who finished first.
Teacher Rapid-Audit Prompts (Use During Checking)
• Rung 1: "Show me where the center of rotation is. How many turns to complete 360°?"
• Rung 2: "What two specific things does the line of reflection do to segment AA'?"
• Rung 3: "Point to the center of rotation. Why didn't that point change coordinates during the turn?"
• Rung 4: "What bridge angle did you use? Why are those two angles supplementary?"
• Rung 5: "Explain in your own words why the exterior angle is equal to the sum of the two remote interior angles without using numbers."
CTE GEOMETRY TEACHER FACILITATION GUIDE PAGE 1 OF 2
QUICK-CHECK MATRIX UNIT 1 REVIEW KEY
Master Solutions & Evaluation Rubrics
All numerical solutions, coordinate milestones, and acceptable geometric reasoning standards.
Rung Version A & Spanish Version B Version C Version D RUNG 1 Symmetry Rot: 60° (360°/6)Refl: 1 vertical line through midpoints of bases.Rot: 45° (360°/8)Refl: 1 diagonal line along kite main axis.Rot: 72° (360°/5)Refl: Any 1 of 3 altitude/median lines.Rot: 90° (360°/4)Refl: Any 1 of 5 lines from vertex to opp. midpoint.RUNG 2 Detective CORRECT Midpoint (2,1) on line y=1; AA' is vertical (perp to horizontal line y=1); dist=3. INCORRECT Midpt (3,4) is NOT on line y=x. Slope of AA' is -1/2, not -1 (not perpendicular). INCORRECT Line x=-1 is perp, but does NOT bisect AA'. Dist to A is 3, dist to A' is 2. CORRECT Midpoint (0,0) on line y=x; slope AA' = -1 (perp to 1); dists both √8. RUNG 3 Rigid Motion T: ⟨+4, -2⟩A'(-1,-1), B'(2,-1), C'(-1,2) Rot 90° CW @ A': A''(-1,-1), B''(-1,-4), C''(2,-1) T: ⟨-3, -4⟩D'(-2,0), E'(-2,-3), F'(1,-3) Rot 90° CCW @ E': D''(-5,-3), E''(-2,-3), F''(-2,0) T: ⟨+3, +4⟩J'(-1,3), K'(2,3), L'(-1,1)
Reasoning Evaluation Standards (When to Slash vs. When to Check)
Rung 2: Perpendicular Bisector Justification
Must Include: (1) Verification of 90° / perpendicular slopes, and (2) verification of equal distances or midpoint lying on the reflection line. Stating "it looks flipped" or merely reciting \((x, y) \to (y, x)\) is an automatic / (Slash) .
Rung 3: Transformation Description
Must Include: Translation vector/direction & distance (e.g., "4 units right, 2 down") AND rotation angle, direction (CW/CCW), and center point (e.g., "about vertex A'(-1,-1)"). Omitting the center point gets a / .
Rung 4: Transversal Bridge Chain
Must Include: Explicit naming of the intermediate bridge angle and both geometry theorems used (e.g., "Corresponding angles are congruent, and linear pairs are supplementary"). Skipping the geometric bridge is an automatic / .
Rung 5: Exterior Angle Theorem Proof
Must Include: Showing that both the exterior angle + adjacent interior angle = 180° (Linear Pair), and all 3 interior angles = 180° (Triangle Sum). Equating them and subtracting the common interior angle proves the remote sum.
CTE GEOMETRY TEACHER FACILITATION GUIDE PAGE 2 OF 2
Mastery Ladder Student Packets VERSION A STUDENT 1 CTE GEOMETRY • UNIT 1 REVIEW
TEAM RELAY PACKET
Name:
Team / Station:
Date:
1
Rung 1: Symmetry & Precision
Teacher Check:
/ → ✓
Figure 1: Regular Hexagon
Smallest (+) angle:
Figure 2: Isosceles Trapezoid
Draw one valid line of reflection symmetry directly on Figure 2.
How do you know the angle in Fig 1?
Precision sentence (use center & line of reflection ):
2
Rung 2: Reflection Detective
Teacher Check:
/ → ✓
Claim: A'(2, -2) is reflection of A(2, 4) across line BC (y = 1) x y 0 1 2 4 1 4 -2 Line BC: y = 1 A(2, 4) A'(2, -2)
Is the proposed reflection CORRECT or INCORRECT?
Correct Incorrect
Justify using the definition: Line BC must be the perpendicular bisector of segment AA'. (Show slope/perpendicularity and distance/midpoint):
3
Rung 3: Multi-Step Rigid Motion
Teacher Check:
/ → ✓
Pre-image: A(-5, 1), B(-2, 1), C(-5, 4) A B C
Step 1: Translate ΔABC by vector ⟨+4, -2⟩ to create ΔA'B'C'.Step 2: Rotate ΔA'B'C' 90° clockwise about vertex A' to create ΔA''B''C''.
Point Pre-image Image (ΔA'B'C') Final (ΔA''B''C'') A (-5, 1) A'(____, ____) A''(____, ____) B (-2, 1) B'(____, ____) B''(____, ____) C (-5, 4) C'(____, ____) C''(____, ____)
Describe complete sequence in words (direction, distance, degrees, center):
CTE GEOMETRY • VERSION A DO NOT ADVANCE UNTIL YOUR TEAM CLEARS RUNGS 1-3 PAGE 1 OF 2
VERSION A STUDENT 1 CTE GEOMETRY • UNIT 1 REVIEW
PART 2: RUNGS 4 & 5
4
Rung 4: Transversal Angle Chains + Algebra
Teacher Check:
/ → ✓
Lines p & q are parallel (p ∥ q) p q t 1 2 3 4 5 6 7 8
Target Pair: ∠1 and ∠6
Mastery Ladder Spanish Packet VERSIÓN EN ESPAÑOL ESTUDIANTE GEOMETRÍA CTE • REPASO UNIDAD 1
CARRERA DE RELEVOS
Nombre:
Equipo / Estación:
Fecha:
1
Peldaño 1: Simetría y Precisión
Revisión del Profesor:
/ → ✓
Figura 1: Hexágono Regular
Menor ángulo (+) de rotación:
Figura 2: Trapecio Isósceles
Traza una recta válida de reflexión directamente sobre la Figura 2.
¿Cómo sabes el ángulo de la Fig 1?
Oración de precisión (usa centro y recta de reflexión ):
2
Peldaño 2: Detective de Reflexiones
Revisión del Profesor:
/ → ✓
Afirmación: A'(2, -2) es reflejo de A(2, 4) por recta BC (y = 1) x y 0 1 2 4 1 4 -2 Recta BC: y = 1 A(2, 4) A'(2, -2)
¿Es la afirmación de reflexión CORRECTA o INCORRECTA?
Correcta Incorrecta
Justifica usando la definición: La recta de reflexión debe ser la mediatriz del segmento AA'. (Demuestra perpendicularidad y bisectriz/distancias):
3
Peldaño 3: Movimiento Rígido de Varios Pasos
Revisión del Profesor:
/ → ✓
Preimagen: A(-5, 1), B(-2, 1), C(-5, 4) A B C
Paso 1: Traslada el ΔABC por el vector ⟨+4, -2⟩ para obtener ΔA'B'C'.Paso 2: Rota el ΔA'B'C' 90° en sentido horario sobre el vértice A' para obtener ΔA''B''C''.
Punto Preimagen Imagen (ΔA'B'C') Final (ΔA''B''C'') A (-5, 1) A'(____, ____) A''(____, ____) B (-2, 1) B'(____, ____) B''(____, ____) C (-5, 4) C'(____, ____) C''(____, ____)
Describe la secuencia en palabras (dirección, distancia, grados, centro de rotación):
GEOMETRÍA CTE • VERSIÓN EN ESPAÑOL NO AVANCES HASTA QUE TU EQUIPO SUPERE LOS PELDAÑOS 1-3 PÁGINA 1 DE 2
VERSIÓN EN ESPAÑOL ESTUDIANTE GEOMETRÍA CTE • REPASO UNIDAD 1
PARTE 2: PELDAÑOS 4 Y 5
4
Peldaño 4: Cadenas de Ángulos con Secantes y Álgebra
Revisión del Profesor:
J''(-1,3), K''(-4,3), L''(-1,5) T: ⟨-4, +5⟩
P'(-2,1), Q'(1,1), R'(-2,4)
P''(-5,4), Q''(-5,1), R''(-2,4)
Angle Chain Bridge: ∠1 ≅ ∠5 (corr.), ∠5+∠6=180° (linear pair).
m∠1 = 117°, m∠6 = 63° Bridge: ∠2 ≅ ∠6 (corr.), ∠6+∠5=180° (linear pair).
m∠2 = 62°, m∠5 = 118° Bridge: ∠3 ≅ ∠7 (corr.), ∠7+∠8=180° (linear pair).
m∠3 = 67°, m∠8 = 113° Bridge: ∠4 ≅ ∠8 (corr.), ∠8+∠7=180° (linear pair).
Remote: 58° + 75° = 133° x = 19
Remote: 71° + 31° = 102° x = 15
Remote: 55° + 60° = 115° x = 14
1. Geometric Bridge (Name bridge angle & 2 theorems that prove ∠1 and ∠6 are supplementary):
2. Set up equation and solve for x:
3. Find both angle measures:
\(m\angle 1 = \) _________°
\(m\angle 6 = \) _________°
Rung 5: Triangle Sum & Exterior Angle Proof ΔPQR with exterior angle at vertex R P (3x+10)° Q (5x-5)° R (2x+15)° Ext ∠R
1. Use Triangle Sum Theorem to find x and all interior angles:
2. Calculate measure of Exterior Angle at R:
Linear pair calculation: 180° − m∠R = Ext ∠R = _________°
3. Justify: Explain why Ext ∠R = m∠P + m∠Q using Triangle Sum & Linear Pair properties:
Rung 5 Complete When all active team members have a check, present your Team Sheet for the final sticker!
CTE GEOMETRY • VERSION A END OF PACKET • RETURN TO TEAM LADDER PAGE 2 OF 2
VERSION B STUDENT 2 CTE GEOMETRY • UNIT 1 REVIEW
Rung 1: Symmetry & Precision Figure 1: Regular Octagon
Draw one valid line of reflection symmetry directly on Figure 2.
How do you know the angle in Fig 1?
Precision sentence (use order of rotation ):
Rung 2: Reflection Detective Claim: A'(5, 3) is reflection of A(1, 5) across line BC (y = x) x y 0 1 3 5 1 3 5 Line BC: y = x A(1, 5) A'(5, 3) Midpoint (3,4) ≠ line
Is the proposed reflection CORRECT or INCORRECT?
Justify using perpendicular bisector properties (check midpoint on line and slope of segment AA'):
Rung 3: Multi-Step Rigid Motion Pre-image: D(1, 4), E(1, 1), F(4, 1) D E F
Step 1: Translate ΔDEF by vector ⟨-3, -4⟩ to create ΔD'E'F'.Step 2: Rotate ΔD'E'F' 90° counterclockwise about vertex E' to create ΔD''E''F''.
Point Pre-image Image (ΔD'E'F') Final (ΔD''E''F'') D (1, 4) D'(____, ____) D''(____, ____) E (1, 1) E'(____, ____) E''(____, ____) F (4, 1) F'(____, ____) F''(____, ____)
Describe complete sequence in words (direction, distance, degrees, center):
CTE GEOMETRY • VERSION B DO NOT ADVANCE UNTIL YOUR TEAM CLEARS RUNGS 1-3 PAGE 1 OF 2
VERSION B STUDENT 2 CTE GEOMETRY • UNIT 1 REVIEW
Rung 4: Transversal Angle Chains + Algebra Lines p & q are parallel (p ∥ q) p q t 1 2 3 4 5 6 7 8
Target Pair: ∠2 and ∠5
1. Geometric Bridge (Name bridge angle & 2 theorems that prove ∠2 and ∠5 are supplementary):
2. Set up equation and solve for x:
3. Find both angle measures:
\(m\angle 2 = \) _________°
\(m\angle 5 = \) _________°
Rung 5: Triangle Sum & Exterior Angle Proof ΔDEF with exterior angle at vertex D D (4x+2)° E (3x+14)° F (x+12)° Ext ∠D
1. Use Triangle Sum Theorem to find x and all interior angles:
2. Calculate measure of Exterior Angle at D:
Linear pair calculation: 180° − m∠D = Ext ∠D = _________°
3. Justify: Explain why Ext ∠D = m∠E + m∠F using Triangle Sum & Linear Pair properties:
Rung 5 Complete When all active team members have a check, present your Team Sheet for the final sticker!
CTE GEOMETRY • VERSION B END OF PACKET • RETURN TO TEAM LADDER PAGE 2 OF 2
VERSION C STUDENT 3 CTE GEOMETRY • UNIT 1 REVIEW
Rung 1: Symmetry & Precision Figure 1: Regular Pentagon
Figure 2: Equilateral Triangle
Draw one valid line of reflection symmetry directly on Figure 2.
How do you know the angle in Fig 1?
Precision sentence (use coincide & center ):
Rung 2: Reflection Detective Claim: A'(1, 3) is reflection of A(-4, 3) across line BC (x = -1) x y 0 -1 -4 1 3 Line BC: x = -1 A(-4, 3) A'(1, 3) 3 units 2 units
Is the proposed reflection CORRECT or INCORRECT?
Justify using perpendicular bisector properties (measure/calculate distances from A and A' to x = -1):
Rung 3: Multi-Step Rigid Motion Pre-image: J(-4, -1), K(-1, -1), L(-4, -3) J K L
Step 1: Translate ΔJKL by vector ⟨+3, +4⟩ to create ΔJ'K'L'.Step 2: Rotate ΔJ'K'L' 180° about vertex J' to create ΔJ''K''L''.
Point Pre-image Image (ΔJ'K'L') Final (ΔJ''K''L'') J (-4, -1) J'(____, ____) J''(____, ____) K (-1, -1) K'(____, ____) K''(____, ____) L (-4, -3) L'(____, ____) L''(____, ____)
Describe complete sequence in words (direction, distance, degrees, center):
CTE GEOMETRY • VERSION C DO NOT ADVANCE UNTIL YOUR TEAM CLEARS RUNGS 1-3 PAGE 1 OF 2
VERSION C STUDENT 3 CTE GEOMETRY • UNIT 1 REVIEW
Rung 4: Transversal Angle Chains + Algebra Lines p & q are parallel (p ∥ q) p q t 1 2 3 4 5 6 7 8
Target Pair: ∠3 and ∠8
1. Geometric Bridge (Name bridge angle & 2 theorems that prove ∠3 and ∠8 are supplementary):
2. Set up equation and solve for x:
3. Find both angle measures:
\(m\angle 3 = \) _________°
\(m\angle 8 = \) _________°
Rung 5: Triangle Sum & Exterior Angle Proof ΔLMN with exterior angle at vertex M L (2x+25)° N (3x+15)° M (5x-10)° Ext ∠M
1. Use Triangle Sum Theorem to find x and all interior angles:
2. Calculate measure of Exterior Angle at M:
Linear pair calculation: 180° − m∠M = Ext ∠M = _________°
3. Justify: Explain why Ext ∠M = m∠L + m∠N using Triangle Sum & Linear Pair properties:
Rung 5 Complete When all active team members have a check, present your Team Sheet for the final sticker!
CTE GEOMETRY • VERSION C END OF PACKET • RETURN TO TEAM LADDER PAGE 2 OF 2
VERSION D STUDENT 4 CTE GEOMETRY • UNIT 1 REVIEW
Rung 1: Symmetry & Precision Figure 1: Geometric Square
Figure 2: Regular Pentagon
Draw one valid line of reflection symmetry directly on Figure 2.
How do you know the angle in Fig 1?
Precision sentence (use perpendicular bisector ):
Rung 2: Reflection Detective Claim: A'(-2, 2) is reflection of A(2, -2) across line BC (y = x) x y 0 -2 2 2 -2 Line BC: y = x A(2, -2) A'(-2, 2)
Is the proposed reflection CORRECT or INCORRECT?
Justify using perpendicular bisector properties (check midpoint on line and perpendicular slope):
Rung 3: Multi-Step Rigid Motion Pre-image: P(2, -4), Q(5, -4), R(2, -1) P Q R
Step 1: Translate ΔPQR by vector ⟨-4, +5⟩ to create ΔP'Q'R'.Step 2: Rotate ΔP'Q'R' 90° clockwise about vertex R' to create ΔP''Q''R''.
Point Pre-image Image (ΔP'Q'R') Final (ΔP''Q''R'') P (2, -4) P'(____, ____) P''(____, ____) Q (5, -4) Q'(____, ____) Q''(____, ____) R (2, -1) R'(____, ____) R''(____, ____)
Describe complete sequence in words (direction, distance, degrees, center):
CTE GEOMETRY • VERSION D DO NOT ADVANCE UNTIL YOUR TEAM CLEARS RUNGS 1-3 PAGE 1 OF 2
VERSION D STUDENT 4 CTE GEOMETRY • UNIT 1 REVIEW
Rung 4: Transversal Angle Chains + Algebra Lines p & q are parallel (p ∥ q) p q t 1 2 3 4 5 6 7 8
Target Pair: ∠4 and ∠7
1. Geometric Bridge (Name bridge angle & 2 theorems that prove ∠4 and ∠7 are supplementary):
2. Set up equation and solve for x:
3. Find both angle measures:
\(m\angle 4 = \) _________°
\(m\angle 7 = \) _________°
Rung 5: Triangle Sum & Exterior Angle Proof ΔXYZ with exterior angle at vertex Y X (6x-8)° Z (2x+10)° Y (4x+10)° Ext ∠Y
1. Use Triangle Sum Theorem to find x and all interior angles:
2. Calculate measure of Exterior Angle at Y:
Linear pair calculation: 180° − m∠Y = Ext ∠Y = _________°
3. Justify: Explain why Ext ∠Y = m∠X + m∠Z using Triangle Sum & Linear Pair properties:
Rung 5 Complete When all active team members have a check, present your Team Sheet for the final sticker!
CTE GEOMETRY • VERSION D END OF PACKET • RETURN TO TEAM LADDER PAGE 2 OF 2
Las rectas p y q son paralelas (p ∥ q) p q t 1 2 3 4 5 6 7 8
Par objetivo: ∠1 y ∠6
1. Ángulo puente geométrico (Identifica el ángulo puente y 2 teoremas que demuestren que ∠1 y ∠6 son suplementarios):
2. Plantea la ecuación y resuelve para x:
Ecuación y procedimiento:
3. Calcula la medida de ambos ángulos:
\(m\angle 1 = \) _________°
\(m\angle 6 = \) _________°
Peldaño 5: Suma de Triángulos y Demostración de Ángulo Exterior ΔPQR con ángulo exterior en el vértice R P (3x+10)° Q (5x-5)° R (2x+15)° Ext ∠R
1. Usa el Teorema de la suma de los ángulos de un triángulo para hallar x y todos los ángulos:
2. Calcula la medida del Ángulo Exterior en R:
Cálculo por par lineal: 180° − m∠R = Ext ∠R = _________°
3. Justifica: Explica por qué Ext ∠R = m∠P + m∠Q usando el Teorema de la suma de triángulos y el par lineal:
Peldaño 5 Completado Cuando todos los miembros activos tengan su marca, ¡presenten la Hoja de Equipo para la calcomanía final!
COMPLETADO • LISTO PARA CTE
GEOMETRÍA CTE • VERSIÓN EN ESPAÑOL FIN DEL PAQUETE • REGRESA A LA ESCALERA DEL EQUIPO PÁGINA 2 OF 2
