1. The Art of Mathematics Donna Smith, Mathematics teacher, retired Fairfax County, Virginia Public Schools Julie Springer, Senior Educator & Manager of Teacher Programs National Gallery of Art, Washington, DC

2. How It All Began Dan Flavin, Untitled (In honor of Harold Joachim) 3, 1977

3. Flavin Family Workshop

4. Lesson on Horizontal & Vertical Lines

5. Goal Encourage the use of art in the mathematics classroom to reinforce mathematical concepts and vocabulary. Rationale The more students are exposed to visual examples of mathematical principles, the more likely they are to remember them. Through art we can broaden their knowledge base and help them connect academic instruction to the world around them.

6. Frosted Fractions (Grade 2-5) Counting on Art, National Gallery Website Wayne Thiebaud, Cakes, 1963 http://www.nga.gov/education/classroom/counting_on_art/act_fractions.shtm

7. Fractions Detail, Wayne Thiebaud, Cakes, 1963 What fraction of the circle does the shaded area represent?

8. Slopes of Lines Sol LeWitt, Wall Drawing No. 681 C, 1993 What is the slope of the line graphed on the coordinate plane?

9. Pythagorean Theorem a²+ b² = c² Robert Morris, Untitled, 1976 Find the length of the third side of the triangle. 12 5

10. Geometry: Area of Shaded Region Jasper Johns, Target, 1958What is the area of the shaded region? Johns drew a picture of 2 concentric circles The smaller has a radius of 4 inches. The larger has a radius of 7 inches. What is the area of the region between the 2 circles?

11. Symmetry: Reflection Dan Flavin, “monument” for V. Tatlin, 1969-1970 Draw the lines of symmetry on each shape

12. Transformations: Slide, Flip, Turn Andy Warhol, detail of Marilyn Diptych, 1962 Which transformation could move the triangle P to triangle P’ in a single step?

13. Reflective or Rotational Symmetry Mel Bochner, Amazing!, 2011Describe the symmetry for the letter “S”

14. Calculus: Volume of a Solid of Revolution Andy Goldsworthy, Roof, 2004-2005 http://upload.wikimedia.org/wikipedia/com mons/8/89/Shell_integration.svg

15. Matrices Andy Warhol, 200 Campbell’s Soup Cans, 1962What are the dimensions of this matrix?

16. Geometry: Tessellations Escher, Sky and Water, 1938 Graphical Models are made up of lots of small objects. Can you create an interlocking pattern with some of the objects below, by copying them and then pasting lots of times? Remember you can rotate the shapes as well and group them together….

17. Four Components of Each Lesson Artist – Picture and Key Biographical Notes Work of Art – Title and Date Mathematician – Picture and Key Biographical Notes Mathematical Concept

18. Horizontal & Vertical Lines Lesson 1

19. Artist: Sol LeWitt American artist 1928 - 2007 Practitioner of both Minimal and Conceptual art “In conceptual art, the idea or concept is the most important aspect of the work. The idea becomes the machine that makes the art.”

20. Lesson on Horizontal & Vertical Lines Sol LeWitt, Wall Drawing No. 681 C, 1993

21. Diagram for Wall Drawing No. 681 C

22. Certificate as “object” when not on wall

23. Mathematician: René Descartes French philosopher and mathematician, 1596 – 1650 Developer of Cartesian Coordinate Graphing System Father of Analytical Geometry “I think, therefore I am.”

24. Worksheet for Lines Lesson Horizontal LineVertical Line Graph Example of equation Description of equation Slope Y-axis intercept X-axis intercept Is parallel to Is perpendicular to Slope-intercept form Function Other

25. Worksheet for Lines Lesson Horizontal LineVertical Line Graph↔↕ Example of equationy = 2x = -5 Description of equationEquation with only yEquation with only x Slope0Undefined Y-axis interceptEquals the numberNo, except for x = 0 X-axis interceptNo, except for y = 0Equals the number Is parallel tox-axisy-axis Is perpendicular toy-axisx-axis Slope-intercept formYes, with m = 0Cannot be written FunctionYesNo Other

26. Matrices Lesson 2

27. Artist: Andy Warhol Pop artist, 1928 – 1987 Challenged traditions of fine art by embracing imagery from mass culture, advertising, comics Employed silkscreen and mechanical means of reproduction to complement imagery “I wish to be remembered as a soup can”

28. Matrices: Vocabulary Andy Warhol, 200 Campbell’s Soup Cans, 1962

29. Mathematician: Arthur Cayley English educator, lawyer, professor, 1821 – 1895 One of the first to study matrices Developed the theory of invariants “As for everything else, so for a mathematical theory: beauty can be perceived but not explained.”

30. Matrices 1.Onion 2.Consommé 3.Tomato 4.Mushroom 5.Green Pea 6.Cream of Asparagus 7.Scotch Broth 8.Cream of Celery 9.Chicken Gumbo 10.Vegetable 11.Beef Noodle 12.Clam Chowder 13.Vegetarian Vegetable 14.Pepperpot 15.Cream of Chicken 16.Black Bean 17.Bean with Bacon 18.Chicken Noodle 19.Cream of Mushroom 20.Beef 21.Chicken with rice KEY: 123456743834933191013 43111214103121321103169 214 23431011224123282261533 12411123432161714163143163 3121816 1714163102223 313113421021716141710223 33 719111512116201410149101722322 41021762116141020510119108 14 121631343945108 11101410142014 11 1113 113132014333

31. Andy Goldsworthy, Roof, 2004-2005 National Gallery of Art

32. Andy Goldsworthy (left) inspires studio projects using natural and/or ephemeral materials

33. Gillbob 316, Green Eggs and Ham Happy 108 th Birthday, Dr. Seuss!