Tessellations (Geometry)

Time Required: One 45-minute session
Skill Level: Intermediate
Recommended Grades: 3rd to 5th

In this activity, students will work in pairs to cover a 3D shape in a tessellation. Students will use visualization, spatial reasoning and geometric modeling to solve a problem through design. Students must recognize geometric shapes and relationships, analyze them and apply them to this novel task.

Note: Any links outside of the3doodler.com are optional resources. We can’t ensure their upkeep or accuracy.

Knowledge

Students have
  • created tessellations on a flat surface

  • researched the tessellations of M.C. Escher

  • had experience using the 3Doodler

Objectives

Students will
  • recognize geometric shapes and relationships.

  • use visual and spatial reasoning to create a geometric model.

  • compose three-dimensional shapes to create a composite shape.

  • design a tessellation on a three-dimensional shape template.

  • tessellate a three-dimensional shape with a 3Doodler.

Materials

Students will need
  • 3Doodler

  • 3D shape templates (1 per pair) (Option)

  • cardstock for printing shape templates

  • pencil (1 per student)

  • color markers (1 set per pair)

  • Terrific Tessellations worksheet (1 per pair)

  • scotch tape (1 per pair)

  • scissors (1 per pair)

Lesson Plan

Instructions

Step 1

PREPARATION
Print 3D shape templates on cardstock before this session.
Print Terrific Tessellations worksheet or have students record answers on a Google doc.

Step 2

Whole group: Define the term “tessellation,” as a set of repeating symmetrical shapes without any overlaps or gaps that completely cover a surface.

Step 3

Share tessellation images with tessellated objects in nature.

Step 4

Share the goal: Students will design a simple tessellation that covers a 3D shape such as a cube, triangular pyramid, rectangular prism or cone.

Step 5

Project your tablet or computer screen on the board for students to view the Terrific Tessellation worksheet.

Step 6

Display a cylinder. Ask how many sides and shapes are in a cylinder. *There are 3 sides composed of 2 circles and 1 rectangle. Record the number of sides and shapes on the Terrific Tessellation worksheet. Ask students to predict whether it's possible to cover a cylinder in tessellations.

Step 7

Using a cylinder shape template, model how to tessellate. Cut out the template and lay it flat. Repeat a simple 2-shape tessellation on the rectangular portion of the template. Color tessellated shapes in a 2-color pattern. Cut out the template rectangle and 2 circles and assemble with tape.

Step 8

Use the 3Doodler to trace over lines and fill in the pattern with appropriate colors. Allow to harden and then peel the plastic off of the paper. Roll and weld the two sides together.

Step 9

Divide students into pairs. Share the template for a cube, a triangular pyramid, a rectangular prism or a cone. Each pair selects one 3D shape to cover with a tessellation, color, fold and 3Doodle.
Instruct students to tessellate with no more than 2 or 3 shapes.

Step 10

Hand out the Terrific Tessellator worksheet for students to record sides, shapes and predictions as they work.

Step 11

Circle to guide and assist. If students finish early, allow them to try again with a different shape template.

Wrap Up

Students will share tessellated 3D shapes along with feedback to the whole group. Ask students if some shapes are better for covering in a tessellation than others? Why? Students will share on Twitter at #3DoodlerEDU

Assessment

Teacher will assess students’ work based on their tessellated 3D shapes and comments.

Possible Extensions

  • Students attempt to cover actual objects with a tessellation, like a tissue box, a large wooden block, stacked Legos, a toothpaste box, a paper towel roll, a soda can, a tennis ball, a coffee mug, etc.

  • Example

Vocabulary

  • tessellation - a set of repeating symmetrical shapes without any overlaps or gaps, which completely covers a surface.

Educational Standards

Common Core
CCSS.MATH.CONTENT.1.G.A.2

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

In This Lesson

Students will create tessellations based on composites of 2D shapes. Students will create 3D shapes out of composite 2D shape templates.

Common Core
CCSS.ELA-LITERACY.SL.4.1.C

Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others.

In This Lesson

Students will participate in discussions with the whole group before and after this activity.

Next Gen Science
3-5-ETS1-1

Engineering Design Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost.

In This Lesson

Students will create a tessellation to cover a template of a 3D shape. Students will follow specified criteria, e.g., use 2-3 shapes for tessellation.

Next Gen Science
3-5-ETS1-2

Engineering Design Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem.

In This Lesson

After activity, students will determine if some 3D shapes are better for covering with tessellations than others.

CS Teachers
1A-A-5-3

Plan and create a design document to illustrate thoughts, ideas, and stories in a sequential (step-by-step) manner (e.g., story map, storyboard, sequential graphic organizer).

In This Lesson

Students will create a stencil design of their tessellations before 3Doodling.

CS Teachers
1A-A-3-5

Decompose (break down) a larger problem into smaller sub-problems with teacher guidance or independently.

In This Lesson

Students will break down the process of covering a 3D shape with a tessellation by making, predictions, analyzing its composition of 3D shapes, designing stencils and covering the 3D stencil with a 3Doodler.

ISTE
1C

Use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

In This Lesson

Students will use the 3Doodler to visually demonstrate how tessellations can cover a 3D shape.

ISTE
4D

Exhibit a tolerance for ambiguity, perseverance and the capacity to work with open-ended problems.

In This Lesson

Students will demonstrate willingness and competency within an open-ended task with more than one possible outcome.

ISTE
6B

Create original works or responsibly repurpose or remix digital resources into new creations.

In This Lesson

Students will use a 3Doodler to design a 3D shape covered in a tessellation.

ISTE
7A

Use collaborative technologies to work with others, including peers, experts or community members, to examine issues and problems from multiple viewpoints.

In This Lesson

Students will use a 3Doodler to cover a 3D shape with a tessellation, consulting with peers before, during and after this investigation.

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