by C. Elkins, OK Math and Reading Lady
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!!
- pre-cut circles in a variety of colors of construction paper
- glue stick and scissors
- 9 x 12 background construction paper
- Black marker or pen for details
- pictures for motivation and ideas
- Optional: Larger construction paper for matting
After showing some examples I had made and a few examples from the book, I wrote these tips on the board. I emphasized the statement in red several times: “Arrange all pieces before gluing.” This is because some of the pieces need to overlap and I wanted students to make sure everything fits.
We discussed how many times to fold the circle to get it into the desired size. Precise folding and cutting was emphasized. To distinguish the fourth/quarter sections from the rest, students noted it is the only fractional part with a right angle. By looking at samples, they quickly became adept at recognizing whether the pieces used were halves, quarters, or eighths. I also modeled how they might need to flip or rotate a piece. And . . . I focused on building perseverance — that trial and error are beneficial to arranging the pieces to get the desired effect. Finally, by showing them my samples, I stressed they were only to be used as a construction guide and inspiration to make what they wanted – put their own spin and creativity into it.
Of course, listening to students “math talk” while doing this project is beneficial to the teacher. You learn so much about students’ understanding by mingling around while they are working on their projects. I made it a point to randomly ask a student to describe what size pieces he/she was using, or what size piece was needed. Students sometimes asked again how to get a circle into eighths or to smaller sixteenths. If they needed sixteenths, they soon discovered that half of an eighth equals a sixteenth. Folding was too difficult, so I showed how to “eyeball” it to cut the eighth in half. Some students also needed even smaller pieces, so then cutting a sixteenth in half resulted in a 32nd size piece. This gave great opportunity to relate multiplication and division to fractions: “What is 8 x 2?” Sixteen. “So when you cut an eighth into two parts (half), you get a size of a sixteenth. Sixteen of these would make a whole circle.” Then this led to “What is 16 x 2?” Or “How many 8th or 16ths are in a fourth section?”
To add more of a math component to this project (for perhaps 5th grade and up), students can calculate the total number of circles used to complete their project. This would require adding fractions. With the top piece:
- Black and yellow butterfly used 4 eighths (equal to 1/2 circle).
- Pink butterfly used 4 fourths (equal to 1 whole circle).
- Ladybug used 1/2 of a red circle and 1/8 of a black circle (laid over top of the red piece).
- Total: 1/2 + 1 + 1/2 + 1/8 = 2 1/8 circles. Hopefully students would not feel the need to convert these fractions and know that 1/2 + 1/2 = 1.
With the bottom piece:
- Bird’s body was made with 2 fourth pieces (equal to half a circle).
- Bird’s tail, beak, and wing used 1/8 of a circle each (1/8 + 1/8 + 1/8 = 3/8).
- Total Bird = 1/2 (or 4/8) + 3/8 = 7/8 of a circle.
- Cat’s face used 3 eighth pieces
- Cat’s body also used 3 eighth pieces
- Cat’s ears used 2 eighths pieces.
- Cat face, body, ears 3/8 + 3/8 + 2/8 = 8/8. So the cat face, body & ears used 8/8 or 1 whole circle.
- Cat’s tail used a sixteenth of a circle.
- Total Cat: 1 1/16
- Total of the bottom piece: Bird = 7/8 and Cat = 1 and 1/16. Find a common denominator (16) to make equivalent fractions. Bird = 14/16. Total = 14/16 + 1 and 1/16 = 1 and 15/16 which is just 1/16 away from 2 complete circles.
With each class, this took about 1.5 hours to complete from start to finish (includes explanation time). The circles I provided were all the same size, but various size circles would be fine. Anything cut from the construction paper had to be circular or a fractional part of a circle. In some cases (for spots or eyes), small circles were cut from scrap paper. Black pen was used for tiny features (small eyes, whiskers, feet, butterfly bodies, etc.). Stems of plants were created using 1/16 or 1/32 size pieces.
Enjoy your week! Let me know if you try this or have other math/art projects – send your pics. Cindy