Tessellations………Creating Tiles that

Tessellate

Translating Tiles

Start with a square.

Cut into a corner and cut out at the opposite corner on the same side.

Slide the cut out piece to the opposite side and tape together. Be sure to line up the corners.

square

cut one side

tape to opposite side

Translating Tiles

Cut into a corner on one of the remaining uncut sides, and cut out at the opposite corner on the same side.

Slide the second cut out piece to the opposite side and tape together. Be sure to line up the corners.

You have created a design that translates horizontally and vertically.

cut second plain side

tape to opposite side

a tessellating shape is formed

Translating Tiles

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.

fit together

Rotating Tiles

Start with a square.

Cut into a corner and cut out at the opposite corner on the same side.

cut one side

Rotate the cut out piece to an adjacent side and tape together. Be sure to line up the corners.

square

tape to adjacent side

Rotating TilesCut into a corner on of the remaining uncut sides, and cut out at the opposite corner on the same side.

Rotate the second cut out piece to an adjacent side and tape together. Be sure to line up the corners.

You have created a design that rotates with a 90 degree angle of rotation.

cut second plain side

tape together

a tessellating shape is formed

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.

Rotating Tiles with Reflection

square

Start with a 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

Rotate to adjacent side..

Tape together. Be sure to line up corners.

You have created a tessellating design with reflection that rotates.

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.

Rotating Tiles with Reflection

Translating Tiles with Reflection

square

Start with a 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

Translating Tiles with Reflection

Tape together. Be sure to line up corners.

Slide the cut out piece to the opposite side and tape together. Be sure to line up the corners.

You have created a tessellating design with reflection that translates.

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.

Trace your design, fitting it together multiple times. Be sure not to leave any gaps.

Translating Tiles with 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.

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.

Translating Tiles with Rotation & Reflection

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.