Math in Art
Festival
Math in Action
for
2003
Festival website:
faculty.gvsu.edu/goldenj/mathinart.html
John Golden
goldenj@gvsu.edu
Credit Where Credit is Due
The Math in Art festival is the brainchild of Susan Walborn, math specialist at Aberdeen Math/Tech
Academy, an open admission citywide school in the Grand Rapids Public School system. In addition to
being an excellent math teacher, Susan is an artist representative and co-owner of a gallery/stationary store
in Grand Rapids (Yours Truly on Cherry St. near Lake.) She was looking for a school wide festival to end
the year on a positive note, after long struggles with possible school closings, etc. The idea of the festival
quickly took off and was adopted by the school, students, parents, teachers and administration. Susan
brought in Joanne Pereira, an art intern from the Maryland Institute College of Art, who was invaluable.
Without wanting to exclude anyone by singling out another, Dana Bradt did phenomenal organization of
parents and activities for the Festival Day. The support from Principal Barb Todd was also amazing.
This year the festival is on again, with funding support from the Grand Rapids Council of the Arts, an artist
in residence, and actual compensation for the student intern. This year Mike Klann is the artistic director
(and a 2nd grade teacher), Amy Archangeli is the art intern, Dana is the administrator (and PTA president)
and Susan is the mathematics director. We’re working in cooperation with Chris Bengston, the technology
specialist. (I'm either a co-mathematics director or a consultant. I can't remember the title!)
What it is
The idea is to have a combined math/art lesson that has as an end product a piece of art. Classes then voted
anonymously on their pieces, choosing the top three to go to a school wide art show to be held
simultaneously with a festival day. On the festival day, attendees voted on their favorite works from the
entire show, and then the top honorees were given awards and trophies. Also at the festival were over 20
booths where students and family members could make an art/math project on the spot, such as
tessellations, mosaics, kites, etc. The 2002 festival was very successful, with over 300 students and family
members returning to the school in the evening. Susan and/or I designed all the math lessons, with
considerable input on the art content from Joanne. The lessons taught included:
Grade
Math topic
Art product (topic)
Kindergarten
Motions
Friezes
First
Probability
Abstract line drawing
Second
Reflections
Kaleidoscopes (color connotation)
Third
Polyhedra
Sculpture (graphic design)
Third
Isometric drawing
Isometric Building Pictures
Fourth
Symmetry
Quilting Patterns (adapted from Everyday Math)
Fifth
Golden Ratio, Fibonacci Numbers
Geometric abstract collage (Mondrian)
Fifth
Fractals, Pascal's Triangle, Patterns
Fractal triangle patterns
Sixth
Fractal patterns
Fractal carpet (texture)
© 2002, 2003 John Golden, Susan Walborn
Permission granted for educational use.
Many of the lessons above had detailed lesson plans made as part of a preservice teacher education class
(Math 322). Those are available at the festival website, along with many pictures and a copy of tonight’s
handout. We have some new mathematical topics being developed for the 2003 festival. These will likely
include the Jordan Curve Theorem and Jackson Pollack, design and mathematics of Celtic knotting, logical
sequencing and flip books, reflectional symmetry and stained glass window design, and the four color
theorem with map design. As always we strive for both exciting math and art, with a high quality end
product.
Today
On the following pages we will zip through some of what the students did for second, third and fifth grades.
Fifth Grade – Golden Ratio
On the next page is a section of square grid paper with an x marked in one square. We are going to create a
rectangular spiral by adding a square to the long side of the rectangle, and then repeating this step in a
clockwise fashion. Students recorded data in a grid like below and found patterns in the results. The art
project then involved using squares proportional to the patterns below, first making a plan to scale, and then
making a large scale collage according to their plan. They had proportional square pieces to trace and cut
out for the final collage, but had to measure out by hand the squares for their plan. Since the art lesson
included a presentation on Mondrian, we were expecting some imitation of him. But the students were
completely original, ambitious and impressive.
Step
1
Short side
1
Long side
1
Step
8
2
1
2
9
3
10
4
11
5
12
6
13
7
14
Short side
Long side
What patterns do you see?
What about the geometric pattern we were following made the patterns you found?
© 2002, 2003 John Golden, Susan Walborn
Permission granted for educational use.
© 2002, 2003 John Golden, Susan Walborn
Permission granted for educational use.
Second grade -- Kaleidoscopes
The lesson began with students looking into actual kaleidoscopes, observing what they saw. This included
things that indicated the reflectional symmetry. We then disassembled one of the kaleidoscopes to help
complete the picture. Students used hinged mirrors to see how reflections of a few shapes created a full
circle with many of the patterns they observed.
On the following page there is a circle with a wedge indicated. Fill in the wedge with 3 or 4 simple
geometric shapes. (The students made their own wedges through folding and used precut colored pieces of
origami paper with many varieties of shape.) Using the MIRA, reflect over side A of the wedge, sketching
in the reflections of your shapes. Include a sketch of the reflection of line A. Now reflect your reflected
shapes over the reflection of side A. Continue the process until you are back to line B. When the MIRA is
placed on line B, the last drawn shapes should be reflections of the original.
The students did this on tracing paper mounted on embroidery hoops. Hung in a window, this produced
the effect of the kaleidoscope. These were among the most striking pieces of the festival.
© 2002, 2003 John Golden, Susan Walborn
Permission granted for educational use.
Third Grade – Pascal meets Sierpinski
This lesson began by having the third graders generate Pascal’s Triangle, after deducing the pattern the
instructor used to fill it in. They did quite a few rows… as you may take the time to do now!
For you we’ll make a special
challenge, however. After the
sixth row (the one beginning
1, 6, …) just fill in the rest
of the triangle with E if the
number would be even
and O if the number
would be odd. The
next page has a
Pascal’s Triangle
cheat sheet, if it
is desired.
Shade in the
squares that
have an
odd
number.
After the students filled in their numbers, and checked for correctness, they chose two number patterns of
their own. Examples were ends in ___, had two of the same digit, multiple of ___ and other more creative
offerings. They then had to color in a Pascal’s triangle by coloring their one pattern one color of their
choice and their other pattern another color, with a predetermined rule for what they would do if a number
fit both. To add some creative options, they had a number of different pyramid styles to select from.
Overall, this was not as artistically impressive as some other projects, but was one of the mathematically
richest. The pattern recognition, determination and discovery were really deep, and when the class pooled
their results they had covered many of the classic patterns of upper elementary mathematics.
© 2002, 2003 John Golden, Susan Walborn
Permission granted for educational use.
Each of the grids was
a full sized sheet of
paper, and there were
10 varieties of grids
available.
Pascal’s Triangle Values:
1 1
1
1
1
1
1
1 2
3
4
5
6
7
1 3
6 10
15
21
28
1 4 10 20
35
56
84
1 5 15 35
70
126
1 6 21 56
126
252
1 7 28 84
210
1 8 36 120
330
1
1
1
1
1
1
1
8
9
10
11
12
13
14
36
45
55
66
78
91
105
120
165
220
286
364
455
560
210
330
495
715
1001
1365
1820
2380
462
792
1287
2002
3003
4368
6188
8568
462
924
1716
3003
5005
8008
12376
18564
27132
792
1716
3432
6435
11440
19448
31824
50388
77520
1 9 45 165
495 1287
3003
6435
12870
24310
43758
75582
125970
203490
1 10 55 220
715 2002
5005 11440
24310
48620
92378
167960
293930
497420
1 11 66 286 1001 3003
8008 19448
43758
92378
184756
352716
646646
1144066
1 12 78 364 1365 4368 12376 31824
75582
167960
352716
705432
1352078
2496144
1 13 91 455 1820 6188 18564 50388
125970
293930
646646
1352078
2704156
5200300
1 14 105 560 2380 8568 27132 77520
203490
497420
1144066
2496144
5200300
10400600
1 15 120 680 3060 11628 38760 116280 319770
817190
1961256
4457400
9657700
20058300
1 16 136 816 3876 15504 54264 170544 490314
1307504
3268760
7726160 17383860
37442160
© 2002, 2003 John Golden, Susan Walborn
Permission granted for educational use.