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This paper describes an activity using a dog treat ball to introduce systems of first-order differential equations. Beads are placed in the first of two hemispherical chambers of a food-dispensing dog toy. As the ball is turned, students track the number of beads in the first chamber, the second chamber, and the exterior of the ball. Students develop a working assumption, write a system of differential equations to model the number of beads in each region, and use a spreadsheet to compare their experimental and model results. [ABSTRACT FROM AUTHOR]