1. Tessellations………
Creating Tiles that Tessellate

2. Translating Tiles Start with a square.
cut one side
Cut into a corner and cut out at the opposite corner on the same side.
tape to opposite side
Slide the cut out piece to the opposite side and tape together. Be sure to line up the corners.

3. a tessellating shape is formed
Translating Tiles
cut second plain side
Cut into a corner on one of the remaining uncut sides, and cut out at the opposite corner on the same side.
tape to opposite side
Slide the second cut out piece to the opposite side and tape together. Be sure to line up the corners.
a tessellating shape is formed
You have created a design that translates horizontally and vertically.

4. Translating Tiles
fit together
Trace your design, fitting it together multiple times. Be sure not to leave any gaps. (No overlap; no white space.)
fill in design
Create a design that fits the shape of your tile. Fill in your tiles, repeating the design in each tile. Be sure to use different colors to make your tessellation interesting.

5. Rotating Tiles Start with a square.
cut one side
Cut into a corner and cut out at the opposite corner on the same side.
tape to adjacent side
Rotate the cut out piece to an adjacent side and tape together. Be sure to line up the corners.

6. a tessellating shape is formed
Rotating Tiles
cut second plain side
Cut into a corner on of the remaining uncut sides, and cut out at the opposite corner on the same side.
tape together
Rotate the second cut out piece to an adjacent side and tape together. Be sure to line up the corners.
a tessellating shape is formed
You have created a design that rotates with a 90 degree angle of rotation.

7. Rotating Tiles
Trace your design, fitting it together multiple times. Be sure not to leave any gaps. (No overlap; no white space.)
Create a design that fits the shape of your tile. Fill in your tiles, repeating the design in each tile. Be sure to use different colors to make your tessellation interesting.

8. Rotating Tiles with Reflection
Start with a square.
square
Fold diagonally.
fold
Cut into a corner and cut out at the opposite corner on the same side. Be sure to cut the same through both layers of the paper.
cut

9. Rotating Tiles with Reflection
Rotate to adjacent side..
Tape together. Be sure to line up corners.
You have created a tessellating design with reflection that rotates.

10. Rotating Tiles with Reflection
Trace your design, and rotate, fitting it together multiple times. Be sure not to leave any gaps. (No overlaps; no white space.)
Create a design that fits the shape of your tile. Fill in your tiles, repeating the design in each tile. Be sure to use different colors to make your tessellation interesting.

11. Translating Tiles with Reflection
Start with a square.
square
Fold diagonally.
fold
Cut into a corner and cut out at the opposite corner on the same side. Be sure to cut the same through both layers of the paper.
cut

12. Translating Tiles with Reflection
Slide the cut out piece to the opposite side and tape together. Be sure to line up the corners.
Tape together. Be sure to line up corners.
You have created a tessellating design with reflection that translates.

13. Translating Tiles with Reflection
Trace your design, fitting it together multiple times. Be sure not to leave any gaps.
Create a design that fits the shape of your tile. Fill in your tiles, repeating the design in each tile. Be sure to use different colors to make your tessellation interesting.

14. Translating Tiles with Rotation & Reflection
Start with a square.
Fold into fourths.
Cut into a corner and cut out at the folded corner on the same side. Be sure to cut the same through all four layers of the paper.

15. Translating Tiles with Rotation & Reflection
Unfold the paper and rotate cut out sections to adjacent sides.
Tape together. Be sure to line up corners.
You have created a tessellating design with reflection that rotates.

16. Translating Tiles with Rotation & Reflection
Trace your design, and rotate, fitting it together multiple times. Be sure not to leave any gaps.
Create a design that fits the shape of your tile. Fill in your tiles, repeating the design in each tile. Be sure to use different colors to make your tessellation interesting.