1. How did you and your teaching partner decide to do this project? (Please describe the context of your project, this can include influence from previous projects, context of your school, community, etc.):
Fractions: There is a fine line between Numerator and Denominatoris title of our project. Kira has found that in her teaching career she encounters students who struggle with understanding the procedural or conceptual concepts of the foundations of math fractions. They labor over understanding how a fraction have the same value such as ½ is equivalent to 4/8 or 25/50. Students are challenged when it comes to visualizing, seeing or thinking about part and whole concepts.
We decided to integrate visual art into the math sessions in the hope that students would learn how to visualize, see and make connections to fractions, proportions and ratios. Instead of one large art project, the class created 3 separate works that acted as stepping stones in learning of fractions. In our talks, Kira also wanted students to be able to incorporate work about themselves creating a very personal art work.
This project started as STEM in structure but as the students began their designs, so much more learning came to the forefront that we did not anticipate. Read on to see what was discovered!
2. Big Idea: Relationships
3. Inquiry: How can we use visual art to help students become more fluent in their understanding of the concepts of fractions and their relationship to ratios and percentages?
4. Grade Level: 6th grade
5. Academic Subject: Math
6. Artistic Discipline: Visual Art
7. How many years have you worked together as partners? This is our 6th year working together.
8. Please describe what you did and what you made for this project:
For our project, the 6th grade class created several individual and collaborative art works.
PROJECT #1: 8-page Sketchbook
We jumped right in to making an art piece based on fractions during our first session. The students learned how to create an 8-page sketchbook out of one large piece of paper. The process involved folding the whole sheet intoeight equal parts and one small cutting. As they folded, we had them shout out which fractions were being created at the various steps. These included half, fourths and eighths. We then discussed how the relationship between the whole sheet and the 8 pages that they created. The class also realized that by turning the sketchbook inside out, eight new pages were available to draw on which lead to it being a 16-page sketchbook.
This sketchbook was used for taking notes in both math and art, solving math problems, and drawing sketches and plans. In the first session, students wrote their own inquiry question centering around math and art. However, during our second session, we added a math problem that we had not planned. The 6th graders had turned in their CAPE media consent forms at that session. We collected 31 forms out of 33 total students. In the process of collecting these forms, we asked them to solve the following questions in their sketchbooks:
- First, solve how many forms have been returned in fractional form?
- Second, figure out the total percentage of returned forms?
This was an Aha! moment for us and we continued to use this problem in out PowerPoint presentations so that it would encourage those remaining students to turn in their forms so we could reach 100%.
PROJECT #2: Fractional Hopscotch
Collaboration was the key to the second project.The concept was that the class would be divided into four groups and each group would be responsible for collaboratively planning and creating a game called Fractional Hopscotch. Ellen showed samples of the game in her PowerPoint presentation while Kira created the four groups.
In their groups, the 6th graders had to negotiate the design of their game. They drew designs in their sketchbooks. Once they had agreed upon a final design, each group was given a few roles of painters/artist tape, and the members proceeded to collaboratively measure and tape their design on the floor of the science room.
The hopscotch needed to start with zero and end with a whole number. The steps in the game needed to include all the fractions in between zero and the chosen number. We encouraged students to use an even whole number in order to create more steps. Below are photos of the groups creating their fractional hopscotch games, their plans and the final designs.
PROJECT #3: Identity Origami
The final project consisted of making 12 open origami boxes and filling them with small drawings that symbolize each student. The number 12 represents the age of a 6th grader while the drawings serve as representations of the students’ talents, passions, likes and their history.
Over the course of three sessions, Ellen gave a presentation about origami and then taught the students how to create open boxes by folding colorful origami paper. After making these boxes, Ellen presented a lesson on symbols and contour line drawings. The students had to first generate a list of 12 things that represent themselves, and they wrote these lists in their sketchbooks. Both Kira and Ellen checked these lists and gave feedback in class. Students then proceeded to draw symbols on paper, cut them out and then glue them inside of each of the 12 boxes.
9. What were you hoping the students would learn during this project?:
Kira: I was hoping the students would be exposed to learning about different artists and art forms, such as origami. I also wanted them to learn how they could combine math and art to create art works. Within this project they were able to use fractions, measurements and various shapes create their art.
Ellen: I was hoping that students would come to a greater understanding of how math can be both an underlying or prominent part of the art making process. I also hoped that through the fractional hopscotch project that students learned that creating visual art is not always a solo venture and that collaboration is vital in art making.
10. What surprised you during this project?:
Kira: There were several aspects of the project that surprised me. First, I was glad to see that some of the diverse learners who joined this project were able to accomplish a large portion of the projects. Next, the class reflected a lot on their work. Finally, the students were really into the arts integrated sessions. They always looked forward to doing the projects.
Ellen: I also was surprised with a few facets of the projects. To begin, I was surprised at how well the students collaborated on their hopscotch games. They negotiated and were able to work through their differences, and they made sure to allow everyone to take part in some way. I also was surprised at an outcome that came about during the folding of the origami papers. Some students struggled with the process and since the class was so large, I couldn’t always get to everyone to work with them one-on-one in our 45-minute sessions. What happened was that the students who had completed their origami boxes began to assist other students: peer to peer teaching! Our big idea of relationships not only applied to the math concepts, but I also saw it defining the way the students worked together in both peer to peer teaching and collaborative groups.
11. What worked in this project and why? What didn’t work and why?:
Kira: The PowerPoint presentation and the videos helped give the students visual examples so they better understood the product and process. For example, Ellen demonstrated folding the origami boxes several times. However when she needed to work with students one-on-one, she had a YouTube video of the same folding method playing on the screen so the entire class could follow if they needed help. Seeing all of these examples of process and product was extremely help.
What didn’t work was having too many students who needed one-on-one aides. This slowed our time down, and we were stretched in terms of adults helping.
Ellen: I thought the student collaborations worked very well as I mentioned above. What didn’t work so well was the time frame. We only had 45-minute sessions which made the project feel very rushed at times especially with such a large class of 33 students.
12. How did you assess student learning?: (ex. Was it formative or summative? Was it a written, verbal or performative based assessment? Were students provided with teacher or peer feedback? Did you use a rubric or portfolio system? Etc.)
A rubric was used for the following criteria:
Out of 100%
- 25% for completion of notes, reflections and drawings within the 8-page sketchbooks and the creation of the sketchbook
- 25% for collaboration on the planning, designing and execution of fractional hopscotch game and for presenting the final product (oral)
- 25% for oral presentations in which students talked about at least three of their drawn symbols that they identify within their identity origami art piece
- 25% for completion of the student’s 12 origami boxes
13. How did you share your student’s learning process with others? Who did you share it with?:
One of the hopscotch designs was replicated and taped onto the hardwood floor along with the students’ identity origami at CAPE’s annual Convergence exhibition at the Bridgeport Art Center. The work was on display from mid-May to early June.
On Friday, June 15th, Pirie held its annual Fine Arts Day. The 6th grades identity origami works, sketchbooks and original fractional hopscotch games were all on display. Ellen created a PowerPoint slide show of the arts integrated project that Kira presented to the whole school community which included all students, staff, teachers and several Pirie families. After her presentation in the gym, classes were able to walk around the school hallways to see the art work that had been hung up. Students were also able to visit the science room to see the hopscotch games and could ask questions to Alima, Tyler and Ahmed, three 6th graders who acted as docents.
14. Standards Addressed: (Common Core and National Core Arts):
Common Core Domain- Number Sense
6NS1B.4 – Apply and extend previous understanding of multiplication and division to divided fraction to fractions.
6NSA.1 – Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, by using visual fraction models and equations to represent the problem.
Common Core Domain – Ratios & Proportions Operations
6RPA.1 – Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6RPA.2- Understand the concepts of a unit rate a/b associated with a ratio a/b and use unit rate language in the context of a ratio relationships.
National Art Standards Visual Arts: 6th grade
VA:Cr1.1.6a Combine concepts collaboratively to generate innovative ideas for creating art.
VA:Cr2.1.6a Demonstrate openness in trying new ideas, materials, methods, and approaches in making works of art and design.
VA:Pr5.1.6a Individually or collaboratively, develop a visual plan for displaying works of art, analyzing exhibit space, the needs of the viewer, and the layout of the exhibit.
VA:Re8.1.6a Interpret art by distinguishing between relevant and non-relevant contextual information and analyzing subject matter, characteristics of form and structure, and use of media to identify ideas and mood conveyed.
Generate a collection of ideas reflecting current interests and concerns that could be investigated in art- making.