Tessellations showcase the beauty of repeating patterns and geometric transformations.
Essential Question:
What makes tessellations visually interesting and complex?
Objectives:
Create tessellations using geometric transformations (rotations, reflections, translations).
Explore pattern repetition.
Understand the principles of tessellation in art and nature.
Vocabulary:
Tessellation: Imagine fitting puzzle pieces together perfectly, with no gaps and no overlaps. That's a tessellation! It's like a repeating pattern that covers a whole flat surface. Think of honeycomb shapes or cool floor patterns!
Geometric Transformation: This is a fancy way of saying "shape change." In art and math, we can move, flip, turn, or resize shapes in different ways.
Rotation: When you turn a shape around a point, like a center dot. A pinwheel spinning is a great example!
Reflection: This is when an image is flipped exactly like looking in a mirror. You can see reflections in shiny surfaces or create them by flipping a piece of paper with a drawing!
Translation: Think of sliding a book across your desk. Translation is when you move a shape in a straight line, keeping the size and direction the same. Imagine ants marching in a straight line – that's translation!
Pattern Repetition: This is when a design or shape keeps repeating over and over again, creating a cool pattern. Stripes on a shirt or a row of flowers are both examples of pattern repetition.
Tile: A flat piece of material used to cover a surface, forming a pattern.
Materials & Resources:
Graph paper
Rulers
Colored pencils or markers
Examples of tessellations (e.g., works by M.C. Escher)
Scissors
Glue sticks
Precut geometric shapes (for students needing additional support)
Templates or stencils
Small containers for collecting scraps
Art Historical References:
M.C. Escher’s tessellations
Islamic geometric patterns
Patterns in nature (e.g., honeycombs, turtle shells)
Teacher Preparation:
Set Up Workstations:
Arrange graph paper, rulers, colored pencils/markers, scissors, glue sticks, precut geometric shapes, and templates at each workstation.
Ensure each table has a clear space for working with easy access to materials.
Place a small container at each table for collecting scraps and used materials (e.g., paper scraps, used glue sticks).
Prepare Examples:
Print and display examples of tessellations around the room.
Prepare a few sample tessellations using different geometric transformations to show during the demonstration.
Organize Storage:
Set up storage bins for portfolios and reading books near the entrance.
Label bins for each table group to streamline the clean-up process.
Set Up Visual Aids:
Ensure visual aids, such as examples of tessellations and steps for creating them, are displayed clearly.
Prepare a chart or board with key vocabulary and their definitions.
Activities:
Entrance Routine (2 minutes):
TWS: "Good morning! Enter the room silently and urgently. Place your portfolio and reading book in the bin under your chair and get your eyes on me. Let's get started quickly today."
Introduction (5 minutes):
Brief discussion on tessellations.
TWS: "Good morning, everyone! Today, we are going to explore tessellations and how they create beautiful repeating patterns. Can anyone tell me what a tessellation is?"
"It's a pattern that repeats without any gaps"
"Shapes that fit together perfectly".
Show examples of Tessellations art and discuss their characteristics.
TWS: "Now, let's talk about Tessellations. Tessellations are patterns made of shapes that fit together perfectly without any gaps or overlaps. Let's look at some examples."
TWS: "Look at these tessellations. What do you notice about the shapes and patterns? How do they repeat?" PUSH: why are they interesting?
"The shapes are the same", "They repeat over and over", "They fit together perfectly". = CHARGE Badge for Engagement
Demonstration (10 minutes):
Demonstrate how to create tessellations using geometric transformations with a think-aloud process.
TWS: "Now I am going to show you how to create a tessellation using a simple shape. (CFU) What am I going to do?
Show us how to create a tessellation using a shape.
TWS: "Notice how I use rotations, reflections, and translations to make the pattern repeat. (CFU) What are you paying attention to?"
How you rotate, reflect, and translate the shape", "How the pattern repeats."
TWS: "I will start with a square.
First, I’ll cut a shape out of one side and tape it to the opposite side.
Now, I’ll trace this new shape on my graph paper, rotating it as I go to create a repeating pattern.
How did I use the transformations to create the tessellation?
"You cut and taped the shape to the other side", "You traced and rotated the shape to make it repeat", "You made sure there were no gaps or overlaps." = CHARGE badge for Engagement
Why transformations are important in creating tessellations?"
Activity (20 minutes):
Students create their own symmetrical designs using geometric shapes.
TWS: Now it's your turn! You have 20 minutes to create your tessellations using geometric transformations. Remember, each shape should fit together perfectly without any gaps or overlaps. If you need help, just raise your hand. Let's set our timer for 20 minutes. Also, remember to handle the scissors and glue sticks carefully and to cap your markers when not in use."
Set timer for 20 minutes
TWS: "We are moving into a yellow zone, which means you can talk quietly with your neighbors. If the noise level gets too high, we will move to a red zone of silence."
Circulate the room to provide guidance and support.
Can you show me how you’re using rotations, reflections, or translations in your tessellation?
"I’m rotating my shape to make it fit", "I’m reflecting the shape to repeat the pattern", "I’m translating the shape across the paper.
Timer goes off
TWS: I see some excellent use of transformations. Let's take a few minutes to share our designs. Who would like to show their artwork and explain how they used transformations to create the pattern?
Cleanup, Reflection, & Transition (10 minutes):
TWS: "Macaroni Cheese, Everybody Freeze! Time's up! (Scan for no movement, sounds off) Take one minute to clean up our work areas. Remember to cap your markers, put your scissors and glue sticks back in the bin, and store your tessellations in your portfolios. Let's do this quickly and quietly! I am looking for the first table with the materials put away, artwork stored in the portfolio, and eyes in their independent reading book, which table will earn a CHARGE badge for engagement?"
Set timer for one minute
TWS: "Today, we learned how to create tessellations using geometric transformations. Who can remind us why transformations are important in creating tessellations? Great job, everyone!"
Ensure students follow the entrance routine, be ready for a Positive Do It Again.
CHARGE Badge: First table with their items put away, sounds off, and eyes on me.
Pacing:
Entrance Routine: 2 minutes
Introduction: 5 minutes
Demonstration: 10 minutes
Activity: 20 minutes
Reflection and Clean-Up: 8 minutes
Notes:
Include images of different tessellations and designs for visual reference.
Provide templates or stencils for students who need additional guidance to create tessellations.
Offer one-on-one assistance for students struggling with using the transformations.
Encourage peer collaboration by pairing students to help each other and discuss their designs.