Fractions are one of the most difficult concepts for math students to understand, yet it is one of the most important topics in third grade. Studies have shown that a strong understanding of fractions at an early age is a clear indication of predicting success in algebra and overall math achievement. Fractions are used in all areas of everyday life, from cooking to building to data analysis. Aside from fractions being numbers, I feel it is important for my third graders to have a strong understanding that fractions are simply part of a larger whole.
As a way to visually introduce my students to the topic of fractions, I had them equally divide several circles into halves, fourths, and eighths. Students then had the opportunity to determine which fraction pieces were larger, how many of each would be needed to create a whole, and which smaller fraction pieces could fit together to create a larger fraction piece. We discussed the idea of these pieces being "equivalent", but I did not put very much emphasis on this idea since I wanted the students to feel comfortable just exploring the fraction pieces.
After sharing a collection of pictures from Ed Emberley's book, Picture Pie: A Cut and Paste Drawing Book, I then challenged the students to create their own work of art using the fraction pieces they made. This book shows how a circle, divided like a pie, can be used to make pictures. I circulated around the room encouraging students to explain to me which fraction pieces they were using by identifying the pieces using their unit names. Students then had to write the number and names of the fraction pieces used.
This was my first attempt at letting the students create something with very little criteria. While some students first tried to complete their picture with only two fraction pieces, the majority of students really tried to use a variety of pieces and attempted to fill the page with their creation. With a minimal amount of prompting, all students added fraction pieces and were able to use mathematical language in explaining the pieces used. This activity proved to be a success and now students have a common activity we can refer back to as we continue our study of the challenging, yet important concept of fractions.