Tantalizing Tessellations

1. Introduce students to tessellations by showing several simple examples as well as more complicated ones such as those created by the artist, M. C. Escher. Explain that a tessellation is a design using an image or images that fit together perfectly with no gaps or overlaps. The creators of tile floors incorporate tessellations into their designs. Squares, triangles, and octagons fit easily together, but tessellations can also be created with interesting irregular shapes as well.
2. Using rulers and manila paper or light weight poster board, ask each student to cut a small, perfect square. Something approximately 2”x 2” is sufficient.
3. Have students write a number in each outer corner of the square with #1 in the top left, #2 in the top right, #3 in the bottom left, and #4 in the bottom right.
4. Next, each student should draw a horizontal line across the square. It can be curved or jagged and need not be in the exact center of the square. Then ask them to do the same with a vertical line so that the square is now divided into four (unequal) quadrants.
5. Invite students to cut along these two lines so that the square falls into four pieces. Have them lay the four pieces on a flat surface so the straight edges form a cross in the middle of a new, irregular shape. Arrange the pieces so the numbers now appear in the center of the figure in reverse order (4 in the top left quadrant, 3 in the top right quadrant, 2 in the bottom left quadrant, and 1 in the bottom right quadrant). Tape the pieces together.
6. This new shape will become the template for a tessellation. Invite students to use their templates to trace an outline in the center of a piece of drawing paper. Then show them how to retrace the template multiple times fitting one drawing into another perfectly to create a design.
7. Once drawings are complete, distribute Crayola® Erasable Colored Pencils, Markers, or Crayons and invite students to color their tessellations using two or more colors in such a way as to be sure shapes of the same color do not touch one another. This will create a pattern of contrasting colors that will make the outline of the shapes stand out.
8. If some students “see” something in the shape of their template such as a fish, a flower, or a dog, invite them to add a few simple marks to define details. Otherwise, students may let their designs remain abstract.

LA: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

MATH: Analyze patterns and relationships.

MATH: Draw, construct and describe geometric figures and describe the relationships between them.

VA: Students will investigate, plan and work through materials and ideas to make works of art and design.

VA: Art communicates about and helps viewers understand the natural and constructed world.

Younger students may enjoy creating tessellations with regular geometric shapes such as squares, rectangles, or triangles. Encourage them to create patterns with their use of color.

Turn tessellation patterns into textile designs by transferring them to white fabric using Crayola® Fabric Markers.

Invite students to look for tessellations in their surroundings and bring in photographs showing their discoveries. Tessellations appear in tile floors, textile designs, and even nature (fish scales, honeycomb, pineapples, etc.).