# Milk-Jug Mosaic: Creating Mathematical Dove of Peace

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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. …