Fish Bowl Design

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The Fish Bowl simulation was part of the last activity of a four-week ESCOT Problem of the Week (ePOW) called Pi Machine, which was built as part of the ESCOT (Educational Software Components of Tomorrow) research project and was featured on the Math Forum. These ePOWs were designed to be used for middle school math.

The Pi Machine ePOW consisted of four mathematical simulations and associated activities about pi and other geometrical properties of circles and spheres.

  • In activity 1, students use a simulation to approximate pi by estimating the ratio of darts thrown randomly at a dart board that land inside the circle to those that land outside.
  • In activity 2, students investigate the relation between the radius and area of circles using a simulation with two concentric circles.
  • In activity 3, students experiment with the length of the radius of the inner circle so that half of the points fall inside the inner circle, and the other half fall in the outer circle.
  • In activity 4, featured here, students use the Fish Bowl simulation of a fish swimming in a spherical bowl to deal with the same concepts but in 3D.


  • Math (Middle School)


ISTE National Educational Technology Standards

  • Creativity and Innovation:
    • use models and simulations to explore complex systems and issues

NCTM Math Standards

  • Geometry
    • understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;
    • create and critique inductive and deductive arguments concerning geometric ideas and relationships
  • Data Analysis and Probability
  • Process standards
    • problem solving
    • connections

Sample Fish Bowl Lesson Plans & Explorations