Mark 3-inch intervals along both long and both short edges of a sheet of colored paper with your pencil and ruler. Double-check the measurements to make sure that they are accurate.
Trace straight lines to connect the markings on each side of the paper. When the lines are connected, you will have a grid of 3-inch squares. Cut off any excess paper that does not fall inside of the squares.
Cut an even 2 inches from the long side of the 3-by-5 index card to create a 3-by-3 square. This square will the base for your tessellation shape.
Draw a line that dips from the top right corner to the upper left corner of the square. The line may be wavy or angular. Be sure to include both corners in your cutout shape. Erase and redraw your line until it creates the shape you want. When you are happy with your design, cut along the line to remove the top section of the square.
Draw a second wavy or angular line along the left hand side of the index card. Again, be sure to include the corners. Cut out the left hand section and set aside.
Slide the section that you cut from the top of the index card straight down to the bottom edge. Line it up so that it is flush against the edge of the paper without jutting out past either corner. Tape it securely in place.
Slide the section that you cut from the left of the index card across to the right hand edge. Line it up so that it is even with the edge and aligned between the corners. Tape this piece in place as you did with the top piece.
Trace the taped index card nine times onto one of the sheets of colored paper. Carefully cut out each shape.
Align the upper left corner of one of the colored shapes with the top left corner of your grid paper. The shape should fit into the square with the two taped-on sections in the bottom and right adjacent squares. You will see the negative shapes of the cut-outs on the grid paper. When the position is precise, glue the paper in place.
Glue the rest of the colored pieces onto the gridded paper in alternating squares. You will begin to see your tessellation take form. Be sure to keep them aligned precisely to preserve the mathematical effect. You will notice that alternating shapes at the far right and bottom of the paper go over the edge. Glue these in place also.
Cut off the parts of the shapes that go off the paper. Take these sections and glue them in place at the top and far left of the grid to fill in the pattern. Your basic tessellation pattern is complete.
Draw a design on both colors of the pattern to make the shapes look like an animal, person or object. This is optional, but will add a lot of fun to the overall effect.