Tessellations WebQuest
An Internet WebQuest on Tessellations

created by Ms. Mall
Bartlett High School

Introduction | The Task | The Process & Resources | Conclusion | HyperText Dictionary


Picture this: you and a team of learners are presented with the task of describing different types of tessellations. But instead of looking to an encyclopedia or an art exhibit, you are each asked to explore web sites to find out about different types of tessellations. Each of you is responsible for knowing the answers to the questions in this quest.

In the following WebQuest, you will use the power of teamwork and the abundant resources on the Internet to learn all about tessellations. After learning about tessellations and M.C. Escher, you will come together as a team and use your knowledge to create a tessellation.

The Quest

What are the five main types of tessellations?
What type of figures can be used to tessellate the plane?

The Process and Resources

In this WebQuest you will be working together with a group of students in class. Each group will answer the Task or Quest(ion). As a member of the group you will explore Webpages from people all over the world who care about tessellations. Because these are real Webpages we're tapping into, not things made just for schools, the reading level might challenge you. Feel free to use the online Webster dictionary or one in your classroom.

You'll begin with everyone in your group getting some background before individually exploring webpages on M.C. Escher and sample tessellations. As a group you will then explore a HyperStudio stack on tessellations that will review the different types of tessellations and help you decide what type of project you will create.

Phase 1 - Background: Something for Everyone

What is a tessellation? Name at least five distinct types of tessellations (example: regular tessellations) and sketch a picture of each type in your learning log.

Phase 2 - Looking Deeper from Different Perspectives


1. Individually or working in pairs you will explore the sites in the M.C. Escher and Sample Tessellations categories.

2. Read through the files in these categories. If you look at the files on the computer, copy sections you feel are important by dragging the mouse across the passage and copying / pasting it into a word processor or other writing software.

3. Note: Remember to write down or copy/paste the URL of the file you take the passage from so you can quickly go back to it if you need to prove your point.

4. Be prepared to focus what you've learned into one main opinion that answers the Big Quest(ion) or Task based on what you have learned from the links found in these categories.

Background Information

Use the Internet information linked below to answer these questions specifically related to Background Information. Record all answers in your learning log and include drawing to clarify your answers.

1. What is a regular tessellation? Draw an example.

2. What is a semi-regular tessellation? Draw an example.

3. What is a demi-regular tessellation? Draw an example.

4. How are demi-regular tessellations named? Explain using a drawing.

  • What is a tessellation? - What do tessellations look like? How many kinds of tessellations are there? How do you name a tessellation? Venture to this site if you're looking for the answers to some of these questions.
  • Totally Tessellated - Find out about the different types of tessellations on this student-created site. Also explore the role of tessellations in history and culture throughout the world.
  • Historical and Geographical Connections - Visit this site to learn more about the historical roots of tessellations and view some real-life examples.

M.C. Escher

Use the Internet information linked below to answer these questions specifically related to M.C. Escher. Record all answers in your learning log and include drawing to clarify your answers.

1. What is M.C. Escher's nationality?

2. What does an Escher-style tessellation look like?

3. What is the name of the place in Spain where Escher first drew sketches of tessellations?

4. What is the title of the Escher-style tessellation you like most? Why is this drawing your favorite?

  • Who was M.C. Escher? - Find out about the Dutch artist M. C. Escher and his famous tessellated designs.
  • The M.C. Escher Gallery - Journey to this site to browse some of Escher's artwork and view computer-generated versions of his artwork.
  • Alhambra Sketch, 1936 - View a sketch by M.C. Escher completed while studying symmetry in the plane at the Alhambra in Granada, Spain.

Sample Tessellations

Use the Internet information linked below to answer these questions specifically related to Sample Tessellations. Record all answers in your learning log and include drawing to clarify your answers.

1. How do these sample tessellations differ from those you have seen in previous links located in the Background Information and M.C. Escher categories?

2. Do all triangles tile the plane?

3. Do all quadrilaterals tile the plane?

4. Do all pentagons tile the plane?

  • Beyond Basic Tessellations - If you're finished with your question set and project, venture here to learn more about tessellations and how you can modify your project.
  • Math Quilt Gallery - Explore a showcase for quilters from around the world who are inspired by the wonderful world of tessellations.
  • Symmetry and Pattern: The Art of Oriental Carpets - Explore tessellations through viewing detailed oriental carpets. Find out more about symmetry and patterns in mathematics.
  • Robert Fathauer Prints - A great place to see examples of professional tessellations available for purchase.
  • Pentagons that tile the plane - Mike Korn (no relation to the band) has a goal: to find a single tile shape with five sides which can tile an infinite floor without leaving holes. Can you create a unique one?

Creating Your Own Tessellation

Use the Internet information linked below to explore how to create a tessellation using a computer program. Using a software program to create a tessellation is one of the methods for making your group project.

  • Kali software for the Macintosh - Kali is a free program that allows users to drawn symmetrical patterns using various tiling groups. A very simple way to create both simple or complex tessellations of your own.
  • Tesselmania Demo - Download a demo version of a useful tessellation program, browse a tessellation slide show and create a tessellation of your own.
  • The Geometer's Sketchpad - Symmetries, patterns and tessellations constructed with the Geometer's Sketchpad. View wallpaper groups and download hints on constructing your own tessellations using the Geometer's Sketchpad.

Phase 3 - Debating, Discussing, and Reaching Consensus

You have all learned about tessellations. Now work as a group to discuss answers to the questions and provide a written, group response to the main two questions asked at the beginning of this WebQuest. Each of you will bring a certain viewpoint to the answer: some of you will agree and others disagree. Use information, pictures, facts, opinions, etc. from the Webpages you explored to convince your teammates that your viewpoint is important and should be part of your team's answer to the two questions. Your WebQuest team should write out a detailed answer that everyone on the team can live with.

Phase 4 - Real World Feedback

You and your teammates have learned a lot by dividing up into different roles. Now's the time to put your learning into a project you'll create that will be evaluated by your peers and teachers at your school. Together you will design and create a tessellation that follows the guidelines described in the HyperStudio stack located on the computer. Explore that stack individually or working in pairs. Once you have decided on the details of your project, fill out and give the project proposal sheet to your teacher. After your teacher has approved your plan you may begin working on it.

Your Contact is: the designated contact


Tessellations is a broad and complex topic . . . when you only know part of the picture, you only know part of the picture. Now you all know a lot more. Nice work. You should be proud of yourselves! How can you use what you've learned to create a high-quality tessellation project? What other parts of tessellations could still be explored? Remember, learning never stops.

 created by Filamentality Content by Ms. Mall, Mall_Alison@msmail.asd.k12.ak.us
Last revised Wed Dec 22 20:50:48 US/Pacific 1999