Math 106 - CooleyMath For Elementary Teachers II OCC

Activity #22 – Tessellations I

California State Content Standard –Measurement and Geometry for Grade One
2.0 Students identify common geometric figures, classify them by common attributes, and describe their relative position or
their location in space:
2.2Classify familiar plane and solid objects by common attributes, such as color, position, shape, size, roundness, or
number of corners, and explain which attributes are being used for classification.

Tiles, Tiling, and Tessellation

A simple closed curve, together with its interior, is a tile. A set of tiles forms a tiling or tessellation of a figure if the figure is completely covered by the tiles without overlapping any interior points of the tiles.

Objective:To make a quadrilateral tessellatein a tessellation activity that combines art and mathematics.

Materials:Large index card(s), lots of no-lined white paper or poster board, scissors, ruler, tape

and colored pencils (optional).

Procedure:

1)Take one piece of white paper and draw on it a quadrilateral no bigger than the palm of your hand. Use your ruler and pencil, and make sure the lines are straight. Try to make an interesting quadrilateral, (square-ish ones are boring). Also try not to make thin long sides like a matchstick these are difficult to hold on to. When you are done, cut out your quadrilateral.

2)We want to mark the midpoints of each side of the quadrilateral with our pencil. To do this we fold each side in half, having the two endpoint touching and crease in the middle. Trace over your crease with your pencil and repeat for all four sides.

3)Number each of the midpoints 1, 2, 3, and 4 in order. You may number in either a clockwise or a counter-clockwise direction. The direction does not matter but the sides need to be numbered consecutively.

4)Place the quadrilateral in the middle of a CLEAN NEW piece of paper that is laying flat on your desk. Trace around the quadrilateral trying to get the outside lines as straight as possible. When you are done you can trace over your figure with a ruler.

5)Rotate the quadrilateral 180 degrees around the midpoint of side 1. Trace the image.

6)Continuing rotating the image 180 around the midpoint of each of its sides, and trace the new image. Do side 2 first, then 3, when you rotate around side 4 you will get back the first figure you traced.

7)Now you should have an eight-sided figure. Cut out this eight-sided figure along the outside edges. Ignore the lines on the inside. This is the polygonal region that will serve as a template that will tessellate. You may want to retrace this figure on the large index card.

8)Now tape four pieces of paper together along the outside edges. Do not overlap them, but lay the edges flush and tape over the edges on one side only. You should have a large white rectangle. Turn it over we will be drawing on the side without the tape.

9)In the middle of your paper lay down your polygonal template and trace around it. Pick up the

template and place it next to your tracing so that the edges are touching and trace around again. Repeat until you have covered your paper with the tessellation. With a ruler and a dark pencil or marker trace over the outlines and then color in your shapes and try to make them look like animals or objects.

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