Students explore mathematics in art when they try tackling tessellations. By applying their knowledge of geometric concepts such as polygons, angles, congruence, and transformations, students learn how to recognize tessellations and create their own.
1-2 class periods
Necessary Technical Skills
- Principals and Standards for School Mathematics (NCTM) Geometry: Students should understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.
- Maryland School Performance Program2.12.4 Students will use transformations to move figures, create designs, and/or demonstrate geometric properties.
- See www.explorasource.com for more state standards connections.
- District Standards (fill in your own)
- Define tessellation.
- Recognize examples of regular polygon, semi-regular polygon, and non-regular polygon tessellations.
- Apply knowledge of polygons, angles, transformations, and congruence to create tessellations.
Necessary Technical Skills
- Students must be able to open and edit a Pocket Word file.
- Students must know how to visit websites using Pocket Internet Explorer.
- Students must know how to answer questions using Discourse.
- Beam the Tessellation Assignment Ticket to the first two students as they come through the door. Each student can beam the worksheet to two more students until everyone has the assignment on the handheld. Or you can email the documents to your entire class.
- Introduce this lesson by having students visit a website to view some of M.C. Escher's famous drawings. Try using Totally Tessellated (http://library.advanced.org/16661/background/tessellations.html). This site is listed in the Tessellation Assignment Ticket. The top navigation bar on the website contains a section on Escher. After students have viewed some of his artwork, ask the following:
- What connections are there between this artwork and math?
- You can lead up to this question by asking:
- What kinds of geometric shapes, if any, do you see in the artwork?
- What is symmetry?
- What are four different kinds of symmetry?
- What kinds of symmetry, if any, do you see in Escher's art?
- Give students time to find answers to the questions listed in the Tessellation Assignment Ticket. They should refer to the websites provided in the Tessellation Web Guide as they are researching. Tip: Although you cannot link to a website directly from this Pocket Word file, you can highlight the URL and hold until a menu appears. Select Copy, and then open Pocket Internet Explorer, tap inside the address bar, and select Edit>Paste.
- Once students have completed their research, they should summarize their findings on the Assignment Ticket. Have them save the document using their name and then beam or email it to you.
- If you would like students to try creating their own tessellations, have them visit Totally Tessellated (http://library.advanced.org/16661/background/tessellations.html) and select the Mosaics/Tilings link at the top. This section of the website explains useful techniques that will help students create regular polygon, non-regular polygon, and other tessellations. Some of the animated graphics in this section will not display on handheld computers. However, there are many helpful static graphics in this section that can be viewed on handhelds.
- If you have sets of geometric manipulatives, have students use them to create their own tessellations as they are reading about the techniques suggested on the Totally Tessellated website. Students can cut out their own polygon shapes from construction paper or cardboard if you do not have manipulatives available. Consider having students draw the designs that they create.
- There are many computer graphics programs that can be used to create tessellations. Visit Math Forum: Tessellation Tutorials by Suzanne Alejandre (http://forum.swarthmore.edu/sum95/suzanne/tess.intro.html) for step-by-step instructions on how to create tessellations using some common desktop computer graphics programs.
- Although the following website will only work on desktop computers, it enables students to draw shapes and then automatically tessellates the designs. Students who are having trouble designing their own tessellations may want to get help here: Tessellate! (http://www.shodor.org/interactivate/activities/tessellate/).
- After students have finished their research and tried their hand at creating their own tessellations, use Discourse to assess what they learned from the project. Download the Tessellation Discourse Frames and import them into your copy of Discourse Teacher.
- Revise and edit the questions and answers in Discourse to suit your objectives.
- Ask your students to open Discourse and connect to your computer. Keep the following tips in mind when using these Discourse frames with your students:
- Allow students to progress through the activity in Self-Paced Mode, and click the Class Summary button so that you can assess their understanding as they complete each question.
- If the majority of students are having trouble with a specific question, click the Wait button and take time to reteach the concept. When you are ready for students to continue working in Discourse, click the Wait button again.
- After reviewing a concept that the majority of students had trouble answering, you may want to ask them a related question "on the fly" to assess whether they understood your review. To do so, switch from Self-Paced Mode to Social Mode by clicking the Social Mode button. Make sure that you are in the Content view by clicking the Content button. Next, click Frame>New Frame to insert a blank frame, type in your question and answer, then publish the frame. If you are satisfied with their answers, return the class to Self-Paced Mode and allow them to continue with the review.
*Lesson plan provided by Kevin Dorsey, 9th grade Geometry teacher, River Hill High School in Howard County, Maryland.