Heidi Butler

Time Frame: Two 30 min. sessions

Terrific Tessellations

Topic: Visual arts lesson featuring tessellations that are constructed by individual students.

Rationale: Constructing tessellations fosters the students ability to create, transform, and critique their own piece of artwork. Allowing for students to become aware of repeated patterns in math, and connect these patterns to artwork enables students to see how math is incorporated into the arts. In doing this lesson students get more experience working with angles, lines, and measurement. In creating tessellations students get more experience seeing, and creating their own patterns and shapes.

COMPONENTS/OBJECTIVES:
Artistic Perception:
Each student will first create a shape, then a picture, by cutting, sliding, and tracing over a blank sheet of paper.

Creative Expression: Each student will design a unique tessellation by cutting from corner to corner and sliding across the shape.

Historical and Cultural Context: Students will look at art connections in designs of fabric, quilts, and mosaics from different cultures. In looking at these designs students will see repeated patters of different shapes. The life and artwork of MC Escher is highlighted through examples of his work.

Aesthetic Valuing: In pairs students will discuss one point on another tessellation that they liked, and why.

Math Objective: Given pattern blocks students will experiment with angles, lines, and shapes in discovering which shapes tessellate.

STRATEGY: A combination of direct instruction and guided discovery will be used.

Vocabulary: Tessellation
Tessellation–A tiling, made up of the repeated use of a shape that completely fills a plane without gaps or overlaps.

PROCEDURES
INTRODUCTION:
As a class discuss the meaning of tessellation or tiling of a plane. Generate a list of tessellations that can be found in nature or everyday objects such as kitchen or bathroom tiles, honey comb, patio bricks. Look at items (or pictures) of wallpaper, fabric, quilts, stained glass, windows, mosaics. Look at some of M.C. Escher's artwork and how his tessellations can be found on posters, T-shirts, gift wrap, ties, and mugs. Pass out pattern blocks and have students work in groups to discover which polygons tessellate. I will pose the following questions: What are some characteristics of tessellating shapes? How are the lines and angles of these shapes different? Do all of the regular polygons tessellate? Review the fact that certain polygons, such as triangles, quadrilaterals, and hexagons will tessellate the plane. I will model how to get started on the tessellations. These key points will be addressed: Holding your 3x3 square, start at one corner move right or left and cut to the next corner. You can make this cut however you would like just make sure not to move diagonally across your square. Slide the cut piece directly across shape to the other side, without rotating it in any way, and tape into place Remind students they need to make a smooth cut so that they end up with only two pieces and no left over scraps. Trace this shape on the overhead projector, and create something out of it (dog, fish, etc.). Lead students to identify the fact that cutting and sliding (translation) are used both to transform the initial shape and to tessellate the plane.

PUPIL ACTIVITY SEQUENCE:

1. Distribute 2x3 rectangles and/or 3x3 squares precut out of construction paper.
2. Have students begin cutting in one corner and move right or left, but not diagonal, to the next corner. Slide cut piece directly across lining up the corners, and tape into place. Trace their shape over and over on a blank sheet of paper creating a tessellation.
3. Identify the many color choices to use on their tessellations.
4. Students put name on back in pencil.
5. Begin hanging up finished tessellations on the wall. Students can hang up their own piece of artwork.

CLOSURE: Once the tessellations are complete have students look at the finished artwork on the wall. In pairs have each student identify one point on another tessellation that they liked. The teacher will ask students to summarize the importance of line, shape and color in their tessellations. The students will reflect on how different all of the shapes, lines, and colors are in each of their pictures, yet they are all tessellations.

EVALUATION: Teacher will visually check completed tessellations by each student. Edges must be aligned and shape must by accurately traced over the paper. Teacher will listen to the critiques of students. Student comments should reflect identification of different shapes. Students should be making connections to previous studies in mathematics, and on Escher’s work, focusing on lines and angles.

Materials:

2"x3" and/or 3"x3" rectangles/squares cut out of construction paper (paper must be thick in order for students to easily trace)

colored pens, pencils, crayons etc.

scotch tape

plain white paper

CLEAN-UP: Assigned students will collect markers, pencils, crayons and return them to box. If the tessellations can not remain on display, then enlist student to help return individual pieces to the artist who created them.