1. Art and Math… How are they related?
Tessellations
Art and Math…
How are they related?

2. Art and Math… How are they related?
One way art and math are related is through the manipulation of shapes.
In math, this is called Transformation. The term refers to four specific ways to manipulate shapes.
In art, we use Transformation techniques to create compositions called Tessellations.

3. What’s a tessellation?
A tessellation uses congruent figures to cover a plane in a symmetrical way without overlapping or leaving gaps.
Designs featuring animals, birds, etc. which can fill a page without overlapping to form a pattern (or mosaic).
origami
honeycomb
concrete patio tiles

4. Uses for tessellations… Talk with your “elbow partner” and identify some uses for tessellations. Be ready to tell me what your partner said.

5. Tessellations have been seen throughout art history, from ancient architecture to modern art.

6. artist M.C. Escher dutch 1898-1972
M.C.Escher said, "Mathematicians go to the garden gate but they never venture through to appreciate the delights within."
1958 Circle Limit III
Sky & Water, woodcut

7. Early work of M.C. Escher 1936 Strong Men 1938 Fish 1938 Dogs
1937 Lions

8. artist Robert Fathauer american, born 1960-
In 1993, he founded a business, Tessellations, to produce puzzles based on his designs. Over time, Tessellations' product line has grown to include mathematics manipulatives, classroom posters, and books as well.
Three Fishes, 1994
Marathon, 2004, commissioned for the Chicago marathon

9. Types of Tessellations
1- Translation- moving every point of the figure the same distance in the same direction
2- Rotation- rotating the figure from a single point
3- Reflection- reflecting every point of the figure over an axis, as if looking in a mirror

10. Let’s practice… TRANSLATION
1- Draw a line from the TOP RIGHT corner to the TOP LEFT corner.
2- Draw a line from the TOP LEFT corner to the BOTTOM LEFT corner.
3- Cut out – now you will have 3 pieces.
4- Slide the TOP piece to the bottom and tape down.
5- Slide the LEFT piece to the right and tape down.
6- Align the original corners of the new ‘transformed’ shape with the grid corners in the upper left box of the grid paper.
7- Trace once.
8- Slide shape to the right; trace.
9- Slide shape to the bottom; trace.
ROTATION
4- Rotate the TOP piece counter-clockwise holding down the TOP RIGHT corner; ending up on the right side. Tape down.
5- Rotate the LEFT piece clockwise holding down the BOTTOM LEFT corner; ending up at the bottom. Tape down.
8- Hold down the TOP RIGHT corner and rotate counter-clockwise. Realign corners; trace.
9- Hold down the LOWER RIGHT corner and rotate counter-clockwise. Realign corners; trace.
10- Hold down the BOTTOM LEFT corner and rotate counter-clockwise. Realign corners; trace.

11. Let’s practice… REFLECTION
1- Draw a line from the BOTTOM RIGHT corner to the BOTTOM LEFT corner.
2- Draw a line from the BOTTOM RIGHT corner to the TOP RIGHT corner.
3- Cut out – now you will have 3 pieces.
4- FLIP over the RIGHT PIECE (from top to bottom), then slide to the left side. Tape down.
5- FLIP over the BOTTOM PIECE (from right to left), then slid to the top. Tape down.
6- Align the original corners of the new ‘transformed’ shape with the grid corners in the upper left box of the grid paper.
7- Trace once.
8- FLIP over the shape (from top to bottom), then slide to the RIGHT. Trace.
9- FLIP over the shape (from top to bottom), then slide to the RIGHT. Trace.
10- FLIP over the shape (from right to left), then slide DOWN. Trace.
11- FLIP over the shape (from top to bottom), then slide to the LEFT. Trace.

12. Which type of tessellation is this artwork?
M.C. Escher

13. Which type of tessellation is this artwork?
Robert Fathaurer

14. Your turn…
1- Choose one of the 3 types of Tessellations to practice on your own.
2- Flip your grid paper over and trace the grid. (if you choose Reflection, trace the 6 box grid).
3- Trace once in the upper left box.
4- Move the shape around the page according to the Tessellation method you chose.

15. Project: Tessellation
Create a unique artwork using one of the 3 tessellation methods learned.
1- Completely cover a 12” x 18” page.
2- Use 2 or more colors.
3- Add hand-drawn details to create a recognizable figure.

16. Assessment Rubric Assignment: Tessellation
Criteria 1 –Technique- 20 points - Did student successfully tessellate a plane using on of the 3 methods of translation, rotation, or reflection?
Technique – Placement - 20 points - Did student correctly line-up shapes to eliminate overlapping and gaps?
Criteria 2 – Design- 20 points -- Did student effectively use color and repetition to create a strong design? Did student create a recognizable object by drawing details?
Criteria 3 – Effort- 20 points – Did student use time wisely and try their best. Did they developed their ideas fully, and also finish their project (didn’t rush)?
Criteria 4 – Craftsmanship- 20 points – Did the student skillfully use art tools & materials, pay attention to details, and present a neat artwork?

17. How To Create Your Tessellation
Supplies:
3” x 3” card (for tessellation template)
Pencil
Scissors
Tape
Ruler
Black Felt-tip Pen
12” x 18” white paper
Construction paper of various colors
1- Choose which tessellation method you will use (Translation, Rotation, or Reflection).
2- PRACTICE making your tessellation template on scratch paper in a 3” x 3” box.
3- Create your tessellation template on the 3” x 3” card, following the directions on the “Let’s Practice” sheets.
4- Lightly draw 3” x 3” grid on your 12” x 18” white paper.
5- Trace your template once onto your white grid paper.
6- Move your template around the page following the directions on the “Let’s Practice sheet. Trace each placement. Fill the entire 12” x 18” page.
7- Trace your template onto construction paper and cut out shapes.
8- Glue construction paper shapes onto white grid paper in checkerboard pattern.
9- Erase grid lines from white grid paper.
10- Add detail lines with black felt tip pens (check out from Mrs. Smether’s).