This is a tessellation. What shapes do you see? Describe them. How are the shapes alike? How are the shapes different? POM Do the Tessellation P 1
What happens at the corners (vertices) of the shapes? Are all corners the same? Explain. How many yellow shapes can you see? How did you figure it out? How many different shapes can you see in all? POM Do the Tessellation P 2
Level B The top of a table is comprised of different colored polygons. 1. Create a similar design using construction paper. 2. Describe all the symmetries in the design. 3. Re- arrange the shape into different rectangles. Show your solutions. 4. How many rectangles can you make using all the shapes? 5. Can you make a different square (different design) using all the same shapes? Explain. POM Do the Tessellation P 3
Level C Brenda and Nick are remodeling their floor. The floor they want is made of triangular tiles. They want to pick out different shaped triangles to determine which triangle they would like to use. They selected five different types; an equilateral triangle, an isosceles triangle, a right triangle, an acute scalene triangle, and an obtuse scalene triangle. Nick believes not all of these triangles will tessellate (cover the plane with no holes or overlaps). Which triangles will tessellate and which will not? Justify your findings by providing a complete rationale or a proof to verify your conjecture. POM Do the Tessellation P 4
Level D Consider the polygon and its position on the coordinate plane. The objective is to use the minimum number of reflections to return to the original location and orientation of the polygon. The rules require that the reflections used cannot undo the previous moves. Show all your work on the graph. Be sure to explain how you know your series of reflections return you back to the original location and position. Is there a way to shorten the number of reflections you used? Conjecture what would need to be the fewest moves to cover the pre- image, under the condition stated in the problem. POM Do the Tessellation P 5
Level E M.C. Escher used glide reflections to create designs. Determine how this tessellation was created. What basic polygon did he use as the foundation of the design? How many steps did he use? Create your own glide refection tessellation. POM Do the Tessellation P 6
Primary Version Level A Materials: For the teacher: A picture of the tessellation. For each student: pattern blocks, paper, and pencil. Discussion on the rug: (Teacher shows the picture of the tessellation) Look at this picture very closely, what different shapes do you see? (Students volunteer the shapes they see). What do you notice about the different shapes? (Students respond with ideas about color, size, and orientation). (Teacher asks) How can I use some of these to make a square? (Teacher calls on students to demonstrate and explain). (Teacher asks) How many pieces did we use? How do we know it is a square? Can we make a square a different way? (Class explores these ideas). In small groups: (Each student has the materials). The teacher says to the class, You have a set of blocks on your table, please try to build the pattern you see in the picture. (Students work in pairs to build the tessellation). The teacher says to the class, Draw the picture you see. Do your best to make your drawing look the same as the one POM Do the Tessellation P 7
you built? How many shapes are in your drawing? What are the names of the shapes in your drawing? (At the end of the investigation, have students either discuss or dictate a response to these summary questions). What shapes are in your drawing? How many shapes did you use? Tell me how you figured out how to make the picture. POM Do the Tessellation P 8
Primary Version Level A Tessellations POM Do the Tessellation P 9
POM Do the Tessellation P 10