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EGG-STREME TESSELLATION
by Carl Busse
University of Idaho

ITV SERIES CHALLENGE OF THE UNKNOWN: Hatching a Giant Egg on a Computer

GRADE 6

OVERVIEW

The students in this lesson will have had prior experience with pattern blocks and with the pattern block stencils. After a brief review of tiling a plane using pattern blocks, the students will view a video of tessellating an egg shape. Students will focus upon the problem solving strategies used and how tessellation geometry was used to construct the three dimensional figure. Students will then use their own problem solving strategies to create individual tiling patterns that fulfill the requirements of several different assignments.

LEARNING OBJECTIVES

• Students will be able to identify and state the problem and the desired result. With this base knowledge they will be actively aware of the strategies they develop to solve that problem.
• Students will be able to create tiling patterns using pattern blocks and/or pattern block stencils that fulfill the given problems.
• Students will be able to create colored patterns to accentuate these tiling patterns.
• Students will be able to identify and discuss the problems and the problem solving strategies addressed in the segment, Hatching a Giant Egg on a Computer from the video: Challenge of the Unknown.
• Students will be able to identify geometric shapes and patterns in the Hatching a Giant Egg on a Computer video segment.
• Students will be able to use their knowledge of tessellations and color patterns in an authentic manner, by designing a tile pattern for a bathroom floor.
• Students will be able to calculate the predicted cost of this construction project.
• Students will be able to describe in a written format the problems they identified and the strategies they used to solve these problems when designing this tile pattern.

MATERIALS

Each student must have the following:

• Pencil

• Eraser

• Scissors

• Scotch

• Tape/Glue

• Colored Pencils/ Crayons/Markers Blank Paper

• Pattern Block Stencil

• Pattern Blocks

• Cube Pattern

• Bathroom Tile Stencil

• Bathroom Floor Diagram

• Bathroom Tiling Instructions

PREVIEWING ACTIVITIES

Students are to use pattern blocks (hexagon, square, rhombus, and equilateral triangle) to create tiling patterns given instructional limitations. Possible limitations include which pattern blocks can be used in tiling or the area that must be covered by the tiling. Students are to focus their attention on the given problem, the problem solving strategy they will use, the manner in which different pattern blocks fit together, and the tiling patterns that the students create.

FOCUS FOR VIEWING

Students should be instructed to focus their attention on identifying the problem, the problem solving strategies used, and the effectiveness of those strategies. Students should also be instructed to focus their attention on any identifiable patterns and geometric shapes they can find in the egg structure and the decorated eggs.

VIEWING ACTIVITIES

START TAPE at beginning of Hatching a Giant Egg on a Computer. PAUSE after narrator says, "the egg would never get off the ground."

Questions to students:

• What do the people of Vegreville want to build?
• What requirements do they have for this structure?
• Were you able to identify any patterns or geometric shapes in this structure?

RESUME VIDEO & PAUSE after Ron Resch's description of an egg.

Questions to students:

• Why is an egg so difficult to build?
• What patterns or geometric shapes were you able to identify in the decorated eggs?

RESUME VIDEO & PAUSE after paper folding strategy.

Questions to students:

• What is Ron Resch's new strategy for constructing the egg structure?
• What patterns or shapes were you able to identify in the folded paper?

RESUME VIDEO & PAUSE after Ron Resch's explanations of continual failures.

Questions to students:

• Did the strategy work for creating the egg structure? Why not?
• What patterns or shapes did you see in the decorated egg?
• How was the woman dividing the sections of the egg?

RESUME VIDEO & PAUSE after computer graphic egg has been filled with triangles.

Questions to students:

• What was the new strategy?
• Why did it work?
• What geometric figure did they use to create the pattern?

RESUME VIDEO & PAUSE after Ron Resch's explanation of the statistically possible patterns?

Questions to students:

• What is the new problem?
• How would you solve it?
• What patterns or shapes did you see in the computer egg or the completed egg structure?

RESUME VIDEO & STOP TAPE after completed structure with Canadian Mounties at the base is shown.

Questions to students:

• What method did they use to solve this new problem?
• Why do you think that they used this method?
• Did you find any new patterns or shapes in the decorated egg or the egg structure?

POST VIEWING ACTIVITIES

Part 1:

Each student must have a pencil, pattern block stencils, a several blank sheets of paper, and an eraser. Using pattern block stencils (square, equilateral triangle, regular hexagon, and rhombus) students will draw tessellation patterns.

The content of these tessellations will be limited by the given instructions. Students must use problem solving strategies to determine solutions to the given tessellation problems. Possible limitations include:

• Using different combinations of the pattern blocks (i.e. only the square and the triangle, only the triangle and the hexagon, the triangle, square, and the rhombus, etc.)
• Creating defined areas that the tessellation is not bound by, but is to cover completely (i.e. a square 6" x 6", a circle with a 8" diameter, etc.) Present the students with several different problems with increasing difficulty.

Part 2: Each student must have a pencil, pattern block stencil, poster board cube pattern, scissors, and crayons/markers/colored pencils, and scotch tape/glue.

Using the same pattern block stencils used in part one, students will create a tessellation pattern on the cube pattern. After the pattern has been completely drawn, students should select a color pattern that uses at least three colors and add it to their tessellation pattern.

After the coloring is completed, the students will cut out the cube pattern and fold it into a cube and fasten the edges together. The cubes can then be displayed. For added difficulty, instruct the students that the tessellation pattern on the cube must be constant around all of the edges as well. Students may have to go through several strategies and trials to create a pattern that will fulfill this requirement.

ACTION PLAN

Students must have a pencil, bathroom tile stencils, eraser, blank paper, bathroom floor diagram, and instructions.

This lesson is based upon an authentic application of tiling and allows the students to see how several of the mathematical concepts and procedures they have learned can be used together in real world applications.

EXTENSIONS

Social Studies:

Study of Ukrainian history, culture, and/or immigration to Canada.

Study of various Canadian cultures.

Study of other cultures that use patterns in their artwork.

Study of the various uses of eggs in different cultures. Science

Study of the shape of an egg and the functional purpose of this shape.

Study of the strength of an egg and how that relates to its shape.

Computers

Lab work with computer programs that tessellate.

Art

Decorate eggs in the traditional Ukrainian style.

For additional lesson plans and ideas relating to this topic and many others try TeacherSource at PBS Online! You will find activities, lesson plans, teacher guides and links to other great educational web sites! Search the database by keyword, grade level or subject area! Mathline and Scienceline are also great resources for teachers seeking teaching tips, lesson plans, assessment methods, professional development, and much more!

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