intersecting math and art

The art lessons I teach are based on the elements of design, and many incorporate math in some way, especially geometry. When I ask students to tell me what they notice in works by Wasily Kandinsky or Pablo Picasso, many of the responses include words like square, triangle, line, acute, obtuse, parallelogram, isosceles, and other math words. Any art lesson that includes the creation, manipulation, and use of different kinds of shapes and lines, whether students are drawing, painting, or making collages, is likely related to math. Here is a review of a few of my favorite art-making activities with math connections:

Geometric People

These figures are created entirely from geometric shapes (mostly rectangles). The lesson includes a discussion about joints, human body proportion, length and width, and the depiction of movement. A great introduction is to look at art by Keith Haring and to do a movement activity that requires students to arrange their bodies in different poses. For this lesson I really encourage students to create their figures to show or imply movement.

Geometric Shape Collage

This works with students of all ages, with directions that change according to the age group. Younger students are asked to use one circle, two lines, three triangles, and four colors; older students use one circle, two lines, three non-congruent triangles, four different quadrilaterals, and five colors. The finished art work can be used as a jump-off point for more math practice, with computation, calculating perimeter or area, or other math practice.

Kandinsky-Inspired Abstract Design

This is adapted from an activity in the book “Drawing With Children” by Mona Brooks. I usually have students look at a Kandinsky print and tell me what they notice. Invariably, math vocabulary bubbles up:  acute angles, triangles, parallel lines, etc. Then I have them draw one thing at a time, starting with three dots anywhere. The drawing directions use tons of math vocabulary (parallel, perpendicular, larger, smaller, etc.) They asked to color it however they choose, leaving part of the composition white. These are always successful, colorful, and interesting!

Cityscapes With Symmetry

This drawing activity connects to mathematics with its focus on symmetry, proportion, and a little work with geometric shapes. Students can be creative while applying their knowledge of symmetry. I like to use construction paper crayons on black paper, but I’ve also used regular crayons on white paper. Sometimes the skyline is glued onto a previously-created watercolor wash. This art lesson is inherently successful; even if mistakes are made in the symmetry, the end results are always beautiful.

Mondrian-Inspired Line Designs

These are all about lines and patterns created with lines. Students simply divide the paper with two horizontal and three vertical lines, creating several quadrilateral spaces, a few of which are filled with line patterns. When finished, the original lines are covered over with construction paper strips to give the whole piece a more dramatic look. Fun, easy, and relaxing!

Artists use math all the time. Sometimes this is in obvious ways with the use of lines, shapes, perspective, and proportion. Sometimes it is more subtle, such as in the use of balance and proportion in an overall composition. I often tell students they are “doing math” as well as “making art" because I want them to understand that math is a useful tool that isn't only something we do in school on a worksheet. Teachers might try incorporating math into art work, then extending the math even further through discussion of students' compositions.

All the art lessons described here... and many others... are available in my store at TeachersPayTeachers. Some are available as individual lessons and most are also available in bundles of three or four related art lessons.

And by the way..... if you think there is no time for art, take a look at Making Time For Art, which is free at my TeachersPayTeachers.com store. It has lots of ideas for integrating art across the curriculum, with math and other subjects as well, and suggestions for buying art materials and creating an art center.

Really.... art is for everyone!

snowmen with personality

In a second grade class where my job was to teach art all morning, I read the book The Biggest, Best Snowman Ever. After a short discussion about the story, I told the students they were going to make a torn paper collage of a snowman so big that the only thing they'd be able to see was part of the face. Then I proceeded to have them show me some facial expressions.... happy.... sad.... angry.... surprised.... shocked.... thoughtful.... etc.... and I drew some quick expressions on the board, the way they might look on a snowman's face (with "coal" eyes and mouth).

I showed students how to tear out the side of a snowman's head out of white paper, leaving the corner intact, and then gluing it onto a blue paper so that the corners lined up. Then I asked them to create a snowman face with a "carrot" nose and "coal" for eyes and the mouth... and to be sure to show some kind of interesting facial expression on their snowman.

I suggested that they tear out all the parts first and arrange them how they like them before they glue anything down. Most of the students followed these directions. Not all, but most. The hardest part of this collage activity is the initial tearing of the head shape. I showed students how to measure a finger length from the top left corner of the paper, and a finger length from the bottom right corner of the paper, put dots at those points, then tear a head shape that begins and ends at those dots. Just a couple of students still had trouble getting a workable head shape; for those students, I drew a very faint pencil line for the head shape and had them tear on the line.

This is a simple activity, using only 9x12 construction paper and glue, that requires some fine motor coordination, some eye-hand coordination, a little patience, and a little creativity and imagination. As students worked, I wandered around and asked what facial expression they were creating on their snowman. For hats, I had students just look for any color construction paper from the scrap bin. One student chose the same blue as the background for the hat, so I had him switch that out so we could actually see the hat.

When the snowmen faces were done, we lined them up on the white board tray and looked at each one individually. They definitely did show a wide variety of facial expressions!

Before they began their snowman faces, I had students create different facial expressions and drew them on the white board to show how changing the size of the eyes, the shape of the mouth, and direction of the eyebrows could give the snowman some personality.  

P.S. This lesson is available in my TeachersPayTeachers store. :-)

chagall-inspired drawings

Here is a fun and easy drawing activity that requires practically no prep and which encourages students to get outside the box and unleash some fanciful creativity. The drawing part is done with a Sharpie or a black crayon on white drawing or construction paper.

I usually do this lesson with third or fourth grade students, and occasionally with second grade. It begins with a "looking at art" discussion of work by Marc Chagall. I always use I and the Village and another painting for this part. I have students tell me what they notice; I chart the responses that are "objective" ("I see the Eiffel Tower") and talk about the responses that are "subjective" ("It's weird.") I also ask for words that describe Chagall's work, and here again there is the objective vs. subjective issue. "Fanciful" works, while "weird" does not. "Creative" works while "pretty" does not. At some point, I introduce the words surreal and surrealist with a rudimentary definition: not realistic, but with real things.


The "art-making" part requires some listening, as students draw what they are asked to draw, one item at a time, while also occasionally reorienting their paper. For example, I usually start with directions to draw the profile of a face at the edge of the paper. I reference the green face in Chagall's I and the Village so they know what a profile is. When that's done, I ask them to turn their paper in a different direction and draw any kind of animal, but make part of the animal go "off the paper"... and again, I reference "I and the Village" and show how the horse's head is the only part of the horse that shows.

I continue to give directions for drawing, one item at a time, always turning the paper after each drawing. They are asked to draw things like a person, another person a different size, three buildings, some trees, a house, a road, mountains, a bird, another animal inside one of the drawings, a shape (circle, triangle, etc) "behind" the other drawings, etc. I generally make this up as I go along, using Chagall's work as my own reference for ideas. As I observe their drawing process, I will make suggestions to overlap drawings, watch how they use their space, to draw in the largest empty area, etc., to help them learn to use positive and negative space.

When the drawings are complex and dense, I stop (there will always be a few students whose drawings are very small no matter what I say, so their papers will have a lot of white space. Oh well) and ask them to color in most of the picture however they want, and to leave some parts white. I suggest that they do some shading, and insist that they use bright colors. Over time, I have learned to ban black, brown, and gray for this assignment. Just because. I do have them look at the colors that Chagall used, and see how bright they are.

When their compositions are complete, they are mounted on black construction paper and students write about their work using the title "My Surreal Art" .... because thinking about their own art work is just as important as talking about someone else's!

This Marc Chagall lesson is one of three art lessons included in Abstract Art For Kids, available for purchase at my TeacherPayTeachers store. The lesson bundle also includes a math-connected drawing activity inspired by Wasily Kandinsky, and a collage activity inspired by Henri Matisse.

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pentangles

Recently I began running into these things called Zentangles every once in a while, which look suspiciously like the doodles in the margins of all my college notebooks. I began to remember how it would be easier for me to concentrate on lectures if, between note-taking, I was doodling. Just a fact of life for the visual among us.....

I started thinking that this would be fun to do as an art lesson with kids. All the Zentangles I saw were simply black on white, with lots of repetitive lines, dots, squiggles, etc, to fill up space in a seemingly random way. Would it be relaxing for kids, or would it be frustrating? How would I present it?

My idea was to introduce it with no talking. I gathered kids together.... this was a second grade.... and put up a sheet of 9x12 white paper on the wall and started with one long, sweeping, curving line. I added more lines next to it, several grouped together, then started off in another direction. I kept "adding to" with groups of dots, or little zig-zags, or whatever. Then I stopped.

"What was I doing?" I asked them, and among their responses, I started writing down some key items.... "drawing lines".... "drawing dots".... "doing the same thing again and again"... etc..... until I had some guidelines on the board next to my demonstration paper. Then I gave them directions:

Start with one long line across the paper. Make sure it goes off the edges. Add five more lines right next to it. Then, either make more of those lines or go in a new direction. Here's the rule:  You need to really, really think about what you are doing and you have to repeat each line, dot, shape, or design at least five times.

Five times.  So now I had another idea:  As students finished, I had them choose one colored pencil to color in five spaces, anywhere on the paper, all with the same color. And I renamed them Pentangles. :-)

Here's the best part:  This class is notoriously chatty. Yak yak yak all day long. During this activity, you could practically hear a pin drop! Usually during art time there is a noticeable amount of chatter, conversation, etc., but this activity just inherently seemed to turn the classroom into a whole group of little mindful people, all concentrating on their own designs.

We mounted the finished product on colored construction paper, and they are awesome!