# Math Art Part 2: Decomposing and composing squares and triangles

I wanted to show you another example of math art, this time using squares and triangles. This project also falls under the standards dealing with decomposing and composing shapes. With this project, students can create some unique designs while learning about squares, triangles, symmetry, fractions, and elements of art such as color and design. It would be a great project for first grade (using 2 squares) or for higher grades using 3 to 4 squares.

A great literature connection to this project is the book “The Greedy Triangle” by Marilyn Burns. (Click link to connect to Amazon.) The triangle in this book isn’t content with being 3-sided and transforms himself into other shapes (with the help of the Shapeshifter). Lots of great pictures showing real objects in the shape of triangles, squares, pentagons, hexagons, and more.

Marilyn Burns is a great math educator to check out, if you haven’t already. She has a company called Math Solutions (check out MathSolutions.com). Marilyn and her consultants have wonderful resources and advocate for constructivist views regarding math education. She is also the author of Number Talks and many math and literature lesson ideas.

### The 4 Triangle Investigation

Materials needed:

• Pre-cut squares 3″, 4″ or 5″ (I used brightly colored cardstock.)
• Scissors and glue
• Background paper to glue shapes to

Directions

1. Model how to cut a square in half (diagonally) to make two right triangles. (I advocate folding it first so that the two resulting triangles are as equivalent as possible.)
2. Guide students into showing different ways to put two triangles together to form another shape. Rule: Sides touching each other must be the same length. Let students practice making these shapes on their desk top (no gluing needed).
3. Help students realize they may need to use these actions:
• Slide the shape into place
• Flip it over to get a mirror image
• Rotate it around in a circular motion to align the edges
4. Students are then given 2 squares (to be cut into 4 triangles) and investigate different shapes they can make following the above rule. Here are some possibilities:
5. As the teacher,  you can decide how many creations you want each student to attempt.
6. These shapes can be glued onto construction paper (and cut out if desired).
7. As an extension, shapes can be sorted according to various attributes:
• # of sides
• symmetry
• # of angles
• regular polygons vs. irregular

# Math Art Part 1: Fraction circle art (3rd-5th)

Incorporating art with other subjects is a great way to engage students. In this post I will share one project which helps students gain hands-on experience with fractions. More to come in future posts.

## Fraction Circle Art

This project is inspired by Ed Emberley’s book “Picture Pie.” This is my favorite of his collection in which he shows dozens of ways to use fractions of circles to create almost anything. This book features mostly animals, flowers, and geometric designs. Students start with a circle (pre-cut with a circle cutting press is best, but you can also make nice circles by tracing around a can or drinking glass and cutting them out). Then the circle is folded and cut into these different fractional parts to create the design: halves, fourths, eighths, and sixteenths. These pieces are manuevered (think translations!!) and combined to make the desired art.

The pictured creations were made by 3rd and 4th graders during a session I conducted with them at Eisenhower Elementary. Here are a few of them.  So nice!!