# TESSELLATION WORKSHEET – Translating Sections of a Square

Students follow instructions on the Tessellation Worksheet to create an irregular shape that will tessellate, then use the shape to create a design filled with contrasting colours.

80 Minutes

Mathematics
Visual Arts

#### Vocabulary

colour contrast irregular polygon plane polygon regular polygon tessellation transformation vertex

#### Materials

Pencils Erasers Clear tape Scissors Heavy Weight Paper 5 cm x 5 cm (2" x 2") one per student Crayons Coloured Pencils Black Fine Line Marker

## Steps

### Step One

1. Start with a 5 cm (2 inch) square of heavy weight paper.
2. Cut out a section of the square. Start at one vertex and end at the vertex beside it.

### Step Two

1. Translate the shape by sliding it to the opposite side of the square.
2. Tape the shape to the square being sure to fit it right up against the edge of the square.

### Step Three

1. Cut out a new shape from the straight side of the square.

### Step Four

1. Slide it across to the other side and tape it in place.

### Step Five

1. Decide what your irregular shape reminds you of and tessellate it to fill the space.
2. Outline the shapes and details with marker.
3. Colour the whole thing with crayons or coloured pencils. Try mixing two colours together to make new coloours.

## Learning Goals

Students will be able to:

1. Use transformation to create an irregular shape that will tessellate;
2. Create a design filled with contrasting colours;
3. Explain why the tessellation works; and
4. Demonstrate technical accomplishment and creativity.

## Extensions

1. Have students create a Mathematics of Tessellation book that includes all or some of the following shapes used in tessellations with explanations of why the shapes tessellate:
- repeated use of ONE regular polygon
- repeated use of a unit of shape made up of TWO OR MORE different regular polygons
- triangles or quadrilaterals
- irregular shapes created by transformation and rotation
2. Have students select an art image by M. C. Escher and explain how it works.
3. Have students use the work of M. C. Escher as inspiration for their own tessellating artwork.

## Prepare

1. Prior to this lesson have students explore tessellations involving repeated use of one polygon and shapes made up of 2 or more different polygons.
2. Download tessellations in nature images from the Internet.
Pineapple
Honeycomb
Fish Scales
Snake
3. Download M. C. Escher images from the Internet.
Den Haag
Princessehof
VoorHout
Alhambra
4. Gather books and pictures of tessellations, for example, Toads and Tessellations: A Math Adventure, by Sharon Morrisette, An Optical Artist: Exploring Patterns and Symmetry, by Greg Roza, Tessellations : The History and Making of Symmetrical Designs Pape, by Pam Stephens, Introduction to Tessellations, by Dale Seymour and Jill Britton
5. Create a sample irregular shape that will tessellate.

## Introduction

1. View the images of tesselaltions in nature and discuss them. Review and/or introduce the term tessellation and have students describe the characteristics of a tessellation, e.g.,
patterns of repeated shapes that cover a flat surface with no gaps and no overlaps
2. Discuss what kinds of regular shapes can tessellate and why
- regular polygons (triangles, squares or hexagons)
- regular polygons can only tessellate if the sum of the interior angles is 360 degrees
3. View and discuss the images of Escher's art.
4. Introduce the challenge.

## Activities

### The Challenge

1. Use transformation to create an irregular shape that will tessellate.
2. Create a design filled with contrasting colours.
3. Explain why the tessellation works.
4. Demonstrate technical accomplishment and creativity.

### The Process

1. Make sure everyone understands the challenge.
2. Guide students through the steps outlined in this lesson plan.
3. Observe students as they work.
4. Provide individual assistance and encouragement.

## Sharing

1. Once all the designs are complete display them for a group discussion.
Look closely at the tessellations.
- Choose one that interests you for some reason.
- Share thoughts about the work.
2. During the discussion include references to:
contrasting colours - How does the use of contrasting colours contribute to the effectiveness of the overall design?
- design - How does the use of detail contribute to the effectiveness of the overall design?
- technique – How and why does the tessellation work?

## Assessment

1. Observe students as they work – thoughtful focus, discriminating, seeking more information, elaborating, experimenting
2. Observe students as they discuss the art works – active listening, insightful contributions, supporting ideas with evidence found in the artwork and from personal experience.
3. Use a checklist to track progress. (Download - TESSELLATION_tracking.pdf)
4. Have students use the self-assessment form to evaluate their work. (Download - TESSELLATION_self-assessment.pdf)