Summit Hill ElementaryArt EDventures

“Tessellating Triangles”5th Grade/Math Tiling

M.C. Escher

Brought to you by S.H.E. PTA

Meet M. C. Escher

1898-1972

"Are you really sure that a floor can't also be a ceiling?"

A Supportive Father

• Mauritis Cornelis (M.C.) Escher or “Mauk” as he was nicknamed, was born in Holland in 1898 around the time the automobile was invented.

• He was the youngest of three boys from a wealthy family. His dad encouraged “Mauk” to learn carpentry, take piano lessons, travel and to eventually pursue art as a career.

“Hand with Reflecting Sphere” By M.C. Escher

From Architect to Print Maker

• Escher wasn’t a very good student. His teachers remember him as being a good artist.

• While in Architecture School his professors encouraged him to pursue his artistic talents. He switched from designing buildings to designing prints instead.

• Escher had no math training beyond High School but is very famous for creating images that included a lot mathematics.

“Cycle” By M.C. EscherCan you see any math or architecture in this print?

Math Made Visual

• Scientists and Mathematicians around the world are big fans of his art because it is filled with their concepts.

• For example, Eschers “Gravity” piece features a geometric (mathematic) shape called a polyhedra. (hit enter)

• His “Drawing Hands” piece cleverly symbolizes another math concept of an infinite loop (or never ending loop.) (hit enter)

“Gravity”

“Drawing Hands”

Interplay With Shapes

• He is best known for his prints with interacting shapes.

• Escher liked his art to fill the entire picture plane (or surface) so there was no empty space.

• He often used a math process of dividing a picture plane into geometric shapes called tiling.

• Then he would change these shapes so they interacted with each other—almost like pieces in a puzzle, to create art called tessellations.

“Sky and Water I”

Can you see the interacting puzzle-like shapes?

See The Tessellation?Shapes that completely cover a picture plane with no overlap (like tiles on a bathroom floor) are known in math as tiling. When you fill the “tiles” with pictures or colors to create patterns you have art that is called tessellations.

Square Tiles Triangular Tiles Hexagonal Tiles

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Escher’s Inspiration

Twenty of his

tessellation prints include

insect shapes.

Escher liked to use the

insect world for

inspiration- he respected the order he found within

nature.Untitled

Can you relate these images like

Escher?

Order of Nature

What shape is in this tessellation?

What Image Do You See First?

“Circle Limit 5”

Triangular Tessellation

Cannonball Jellyfish

Nurse Shark

Moray Eel

Sea Star•Escher traveled the world to study

buildings and bathrooms with beautiful tile for his tessellations projects. His favorites were in Spain.

•Next time you are in a bathroom – take a look at the floor. You might just find a tessellation under your toes!

•Now it’s time to create a triangular tessellation of your own!

Meet M. C. Escher

1898-1972

"Are you really sure that a floor can't also be a ceiling?"

Tessellations SampleCandy Colors

Now it’s time to color your triangular tessellation. Color like shapes the same color. For example all the “gumballs” are blue. All the “candy hearts” are purple. All the “gummy fruit slices” are orange.

Background ColorWhen you are finished coloring your candy shapes, go ahead and color in the background a solid color. Do not repeat a color that you have already used!

You have just tessellated a triangle 8 times to create a tile!

Wowza!

Project Art EDventuresFolding

• Take square piece of paper and fold in half to make two triangles.

• Open and repeat in the other direction so you now have four triangles.

• Open and fold in half to make two.

• Open and repeat so you now have 8 total triangles.

• You should have a single triangle too (handed out): It should fit inside one of your folded triangles perfectly.

Candy Shapes• Ask the kids to think of different kinds of

candy shapes and draw them on the white board. For example, the kids may call out “gum balls!” -draw a circle. “Licorice!” - draw a skinny rectangle. “Candy hearts!”-draw a heart, etc.

• Then ask the kids to chose three types of candy shapes from the board and to draw them inside their single triangle. The simpler the better! Tell them to make their marks dark!

Lines• Now ask the kids to draw two lines on their

triangle. The lines have to go from one side of the triangle to another and go off the edge. (It’s ok to touch or disect their candy but the end design will be easier if it does not.

Project Art EDventuresTriangle to Square

• Fold you paper into a triangle so your transferred triangle touches the empty folded triangle to your upper left. Then trace over the back side to transfer your design again.

Transfer Your Triangle• Fit your loose triangle inside your folder

square with the pencil marks down. You should be able to see the lines through the paper. Now trace over these lines. Press firmly because you want the carbon to transfer onto your paper square.

Trace over your loose triangle.

It will transfer!

Open it up and you will have filled a square! Go over your lines do they are DARK!

Trace over the backside

Folded edge to your right.

Project Art EDventuresRectangle to Rectangle

• Fold you paper into a rectangle. Now you want to fill the right side of your paper that is still blank.

Square to Rectangle• Fold your paper into a rectangle with the

pencil marks inside your square touching the empty square just above it.

Open it up and you will have filled a rectangle! Go over your lines so they are DARK!

Fold your paper up into a “landscape” rectangle.

Trace over the entire backside.

Folded edge on this side.

Open it up and you will have filled the entire square! Go over your lines so they are DARK!

Trace over the entire backside square.

Folded edge on the bottom.

Supply List

• Light Weight Paper – like copy paper. Precut into (get the size) large squares. (One per child.)

• Triangles –precut to be the same size as one of the eight smaller folded triangles within your squares. (One per child.)

• Pencils, erasers and sharpeners. (One per child.)

• Crayons-one box per child. You can do this lesson with colored pencils or markers. In order to completely color this in 45 minutes, we have found crayons to work the best. And, there is usually no need to take time to sharpen crayons.

Art EDventuresMade possible with your donations to S.H.E.’s PTA

Art EDventuresMade possible with your donations to S.H.E.’s PTA

M.C. Escher

• Dear Mom, Dad or Caretaker,

• Hi! I went on an Art EDventure today called “Tessellating Triangles.” We learned about a Dutch artist named M.C. Escher. Although he didn’t take math past high school, Escher is famous for including mathematical concepts in his art. It was fun discovering how he used a math concept called tiling in his art to create amazing puzzle-like prints. He also liked to play tricks on your eyes by cleverly using never ending loops and geometric shapes like polyhedras.

• We learned how to tessellate a triangle into a tile too. Ask me how I did it! (My hand sure needed a “shake break” after I was through!)

“Sky and Water I”

• Dear Mom, Dad or Caretaker,

• Hi! I went on an Art EDventure today called “Tessellating Triangles.” We learned about a Dutch artist named M.C. Escher. Although he didn’t take math past high school, Escher is famous for including mathematical concepts in his art. It was fun discovering how he used a math concept called tiling in his art to create amazing puzzle-like prints. He also liked to play tricks on your eyes by cleverly using never ending loops and geometric shapes like polyhedras.

• We learned how to tessellate a triangle into a tile too. Ask me how I did it! (My hand sure needed a “shake break” after I was through!)

M.C. Escher “Sky and Water I”