Pattern Lab Worksheet Shape Shift Art
Regular vs. Irregular Polygon Lab
Name:
Date:
Part 1: The Geometry Briefing
Watch the lesson video and define these critical architectural terms.
Regular Polygon
Hint: It must be BOTH _______________ and _______________.
Equilateral
Irregular Polygon
Equiangular
Part 2: The Pattern Lab
Step 1: Regular Trace
Fold your paper as instructed to create a Regular Hexagon template. Cut it out and trace it multiple times below to create a "honeycomb" pattern. Ensure the edges touch perfectly.
Step 2: Irregular Trace
Create an Irregular Hexagon (6 sides that are NOT equal). Trace it below, trying to make it "tile" or fit together without leaving any gaps between the shapes.
Part 3: Lab Observations
1. Describe what happened when you tried to tile the regular polygon vs. the irregular polygon.
2. A rectangle has four 90° angles. Why did we learn it is an irregular polygon?
Shape Shift Slides 6th Grade Geometry
Shape Shift Art
The Architecture of Regular Polygons
GEO-UNIT // LESSON 01
Warm Up Challenge
Natural Design
Why does a honeycomb use hexagons?
Human Design
Why are floor tiles usually squares?
Geometric Intel
Video Analysis
Embedded media
Watch For:
Definitions of Equilateral
Definitions of Equiangular
The "Rectangle Paradox"
"A regular polygon must have ALL sides and ALL angles congruent."
The Definition
REGULAR
IRREGULAR
If it's missing just one equal side OR angle, it is IRREGULAR.
The Pattern
Challenge
25 MINUTES
1
The Template
Fold your paper square precisely into a Regular Hexagon. Cut it out to use as your master stencil.
2
The Tessellate
Trace your regular shape repeatedly. It should fit together perfectly like a honeycomb with zero gaps.
3
The Struggle
Now, create an Irregular Hexagon template. Try to tile it. What happens when the edges don't match?
The Architect's Quest
Antoni Gaudí
"The straight line belongs to men, the curved line to God."
While most architects use regular polygons for efficiency, Gaudí used irregular organic shapes inspired by nature.
Challenge:
Find one building by Gaudí. How many "irregular" shapes can you spot in the windows or walls?
Design Journal Prompts Design Journal
Post-Lab Reflection
Engineer:
Session:
Key Discussion Prompt
"Why do architects and designers use regular polygons more often than irregular ones in their work?"
Think about your pattern lab today. Consider:
Structural Gaps
Mass Production
Balance & Force
Written Analysis
Illustrative Example
Sketch a real-world example of a regular polygon being used in a building or object.
Extension: How would Gaudí answer this prompt? Would he agree or disagree?
Geometry & Art // Unit 01
Shape Shift Teacher Guide Teacher Facilitation Guide
Shape Shift Art
Duration
50 MIN
Objectives
Define regular polygons as both equilateral and equiangular.
Compare properties of regular and irregular polygons.
Apply polygon properties to create tessellated art.
Materials
• Pattern Lab Worksheet
• Design Journal Prompts
• Square paper for folding
• Scissors & Pencils
• Colored pencils (for extension)
Teacher Tip
The "Rectangle Paradox" (Slide 4) is the most common pitfall. Emphasize that a shape must meet both criteria to be regular. Ask: "If a shape looks 'perfect' but has one long side, is it regular?"
Lesson Flow Step-by-step facilitation
05m
Warm-up & Hook
Use Slide 2. Facilitate a discussion on why nature and construction favor specific shapes. Key question: "What would happen if we used irregular rocks to build a flat floor?"
05m
Direct Instruction (Video)
Slide 3. Students complete the Part 1 definitions on their worksheet while watching. Pause at 1:50 to discuss the rectangle example.
25m
Main Activity: Pattern Lab
Guide students in folding a regular hexagon from a square paper (fold in half, then fold corners to center at 30°). Students trace this regular shape, then create and trace an irregular one. They will see that irregular shapes leave "gaps" in standard tessellations.
10m
Design Journaling
Students respond to the prompt on the journal sheet. Encourage them to use the vocabulary learned (equilateral, congruent, etc.) in their explanation.
05m
Wrap Up & Gaudí Extension
Slide 6. Introduce the "Architect's Quest." Students can research Gaudí's mosaics for homework or as an early-finisher task.
Key Discussion Anchors
The Rectangle Analysis
"Why is a rectangle irregular even though it has four 90-degree angles?"
The Rhombus Case
"It has four equal sides. Why is it NOT a square? Why is it irregular?"
