Milk-Jug Mosaic: Creating Mathematical Dove of Peace
Potts, Kathleen K., Teaching Children Mathematics
A large outdoor dove-of-peace mosaic became our school's tangible expression of hopes for peace as we celebrated the fiftieth anniversary of the Nobel Peace Prize award in 1947 to the Friends Service Council and the American Service Committee for their humanitarian work. Our celebration at Goshen Friends School (West Chester, Pennsylvania) featured "peace" as a yearlong all-school theme for studying and learning. Our students and teachers discussed the idea of peace and how it touches our lives personally and as citizens of the world. We talked about and practiced nonviolent conflict-resolution techniques and constructive means of diffusing anger.
Our third, fourth, and fifth graders decided to extend the celebration to the schoolyard by creating a peace-dove mosaic from gallon milk jugs filled with colored water. This multigrade project gave students opportunities to use a variety of mathematical skills--such as estimating and multiplying large quantities, making grids, and computing the area and circumference of a circle--all while creating a lifelong memory of a peaceful community of friends. This article describes our rich experiences in this endeavor and concludes with ideas for adapting the project for other occasions and involving other mathematics skills.
Planning the Peace Design
A design featuring a dove of peace emerged as the winner among several ideas for peace designs submitted by both students and adults. A collaborative effort resulted in a design with a white dove at the center, surrounded by blue to represent the sky and an outer circle of green to represent the earth. The design was drawn on a sheet of paper in a six-inch square and reproduced for students who were asked to draw a one-inch grid on the entire design (see fig. 1). Next, students were asked to make a twelve-inch square on a large sheet of paper and were taught how to draw a two-inch-square grid on it. Students drew an enlargement of the original peace design on this larger grid, working box by box, to recreate a design that was four times its original size. Later, students referred to this larger drawing to construct the outdoor display on a twelve-foot square with a grid of two-foot squares on it.
Collecting Milk Jugs
All students in grades 3, 4, and 5 were asked to look at the drawing and imagine the twelve-foot circle, then to estimate the number of gallon milk jugs that they thought would be needed to fill that circle. Their estimates varied considerably, ranging from 70 to 1000, with most of the estimates being quite low, about 150. The estimates of the fourth and fifth graders tended to be higher than those of the third graders.
In the meantime, jug collection began. Everyone in the school, from three-year-old preschoolers to fifth graders, contributed jugs and assisted in their daily collection. The third graders were responsible for storing the jugs and keeping track of how many had been collected.
To determine when they had collected enough milk jugs, the third graders began concretely to find how many jugs would fill the large twelve-foot square. They found that 16 jugs filled a two-foot square. They counted 36 squares in the whole grid and then used a calculator to compute that 36 x 16, or 576, jugs would fill the twelve-foot square, which they knew was more than would be needed for the actual design.
Fourth and fifth graders also found this amount without using a calculator, then used one of two approaches to figure out how many milk jugs would be needed for the circular design. Some students decided to subtract from 576 the number of jugs that were between the outside circle and the square. First they subtracted 16 jugs for each corner square and then 8 jugs for each of the four other squares that would be partially filled. They figured that about 576 -- 64 -- 32, or 480, jugs would fit inside the circle.
Some fifth graders used a different approach, having recently studied the circumference and area of a circle. Thinking about the green jugs on the border of the circle, they found the circumference of the circle using C = 2[pi]r: 2 x 3.14 x 6 = 37.68 feet. Then they measured the diameter of a milk jug, which was about 6 inches, or 1/2 foot. Allowing two milk jugs per foot, they found 37.68 x 2 = 75.36, or 75, jugs. To this number they would add the number of jugs needed to fill the inside of the circle. The area of the circle was 3.14 x 36, or 113.04, square feet. Using 4 jugs per square foot, they computed 113.04 x 4 = 452.16, or 452, jugs. So they would need about 75 + 452 = 527, or roughly 530, milk jugs. The students recognized that placing jugs on the lawn would not render the design as precisely as drawing it on paper, so they were comfortable with their estimation of 530 jugs. Everyone was surprised at how much larger the calculated number of jugs was than his or her original estimate.
Constructing the Outdoor Display
The milk-jug collection was continuing. Although we began this project in November, the targeted completion date was 10 December, the day the Friends Service Council had received the prize in 1947. Even the bus drivers were contributing jugs. The third graders stored them in a small space between the school wall and a stone fence. They strung them in groups of 20 to keep track of the total more easily.
Finally, the students had collected enough jugs to begin work on the peace dove. They enthusiastically pitched in to construct the outdoor display. The fifth graders had previously calculated that they would need 75 green jugs for the border of the circle. The third graders placed jugs by l0s and filled 75 with green-colored water. The fifth graders measured a twelve-foot square on the lawn. They used stakes and string to create the two-foot-square grid on it. They located the center of the square and used a string on a pivot to make a circle within the square. As they rotated the string, they placed green jugs accordingly. They quickly formed the twelve-foot green circle. It looked very small to the students, who could not believe that more that 500 milk jugs would be needed to fill it completely.
The fifth graders used the model twelve-inch design drawn earlier to guide outlining the dove with white jugs. When they were satisfied with the outline, they filled it in with additional white jugs. Finally, the fourth graders filled in the spaces between the white dove and green circle with blue jugs. As the mosaic was being completed, the students painted the caps of jugs to correspond with the color of the water they contained. The completed display required 537 milk jugs, more than the students had calculated yet very close to their estimate of 530. The final circle appeared quite small in its outdoor setting, and its creators were amazed to realize how many jugs had been needed to make it. The children were justifiably pleased with their work.
The milk-jug-mosaic remained on the schoolyard through most of the winter. The preschoolers who had contributed jugs to our efforts were delighted to see the creation when they played nearby. When the temperature dropped below freezing, some of the colored lids popped off.
On a beautiful December day, a local fire company brought its cherry-picker truck to the school and from its extended ladder took a special photograph of the project. All the students in grades 1 through 5 lay on the ground around the peace display for the photograph (fig. 2). In early spring, the third graders reluctantly dismantled the display. They emptied the jugs and tied them in groups, readying them to be taken to the local recycling center.
Adapting and Extending the Project
The milk-jug-mosaic project commemorated the fiftieth anniversary of an event that was important to our school community. This multigrade project can solve as a model for other schools, which can adapt it to commemorative events that they select, for example, the fiftieth anniversary of the opening of the school; the 100th anniversary of the 1903 Wright brothers flight at Kitty Hawk, North Carolina, as the start of air and space travel; or important events that students predict will occur in the first decade of the twenty-first century. On a smaller scale, classes in a grade level might collaborate on a mosaic for a holiday or a significant current event or on an art design that reflects the spirit of their grade. The process of identifying possible events and then choosing them by a vote of students provides opportunities for children to apply their knowledge and skills of data collection and graphing.
This type of project supplies a context in which children use measurement, estimation, and computation to solve problems. It also has potential for engaging children in other mathematics topics. For a mosaic project like ours, students at each grade level could create a graph of their estimates for the number of jugs needed. Means and ranges of estimates could be discussed. Students could also make bar graphs or pictographs for the number of colored jugs that they used. Fourth graders might determine what fractional parts of all the jugs are of each color. When the milk jugs freeze and their lids pop off, the children could explore the probabilities that lids of a certain color will pop. They could find the theoretical probability for each color and compare it with the empirical probability, that is, what actually happens. Other questions could explore how much time a class would need to drink the milk in all the jugs, how much time a student's family would need to drink that much milk, and how much the milk would cost. Our school's parent-teacher organization funded the cost of making note cards from the picture of the mosaic in figure 2. The third graders ran the note-card business and used their mathematics skills in figuring the cost for each card, paying back a loan, and filling orders.
A multigrade milk-jug-mosaic project is worthwhile in many respects. It allows children to use a variety of mathematical skills and fosters cooperative problem solving within classes and across groups in different grades. Finally, as we witnessed with our peace project, it can result in a product, the outdoor display, and involve a process, a collaborative mathematical learning experience, that the students will value and treasure as a lifelong memory.
Kathleen Potts, is a third-grade teacher at Goshen Friends School, West Chester PA 19380. She enjoys combining mathematical understanding with creative pursuits.…
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Publication information: Article title: Milk-Jug Mosaic: Creating Mathematical Dove of Peace. Contributors: Potts, Kathleen K. - Author. Magazine title: Teaching Children Mathematics. Volume: 6. Issue: 7 Publication date: March 2000. Page number: 438. © 1999 National Council of Teachers of Mathematics, Inc. COPYRIGHT 2000 Gale Group.
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