objects depicted in a model, as well as their behavior and relationships to each other, represent theoretically important objects, behavior, and relationships in the natural world. Models allow scientists to summarize and depict the known features of a physical system and predict outcomes using these depictions. Thus, they are often important tools in the development of scientific theories.

A key concept for students to understand is that models are not meant to be exact copies. Instead, they are deliberate simplifications of more complex systems. This means that no model is completely accurate. For example, in modeling air molecules with Air Puppies, certain characteristics of molecules are represented, such as the fact that they move constantly without intention, and other characteristics are not, such as their being composed of hydrogen and oxygen atoms. Students need guidance in recognizing what characteristics are included in a model and how this helps further their understanding of how a system works. When first introduced to the Air Puppies model, students often ask, “Do Air Puppies breathe air? Do they sleep? Do they die?” They need to figure out which aspects of Air Puppies are useful for understanding how air molecules work.

FIGURE 6-2 Mitchell and Antwaune show Air Puppies in and outside a bottle as numbers (100 calm and 100 excited puppies).


For the past 200 years, science has moved toward increasing quantification, visualization, and precision. Mathematics provides scientists with another system for sharing, communicating, and understanding science concepts. Often, expressing an idea mathematically results in the discovery of new patterns or relationships that otherwise might not be seen.

In the grade-level representation activities that follow, third-grade children investigating the growth of plants wondered whether the shoots (the part of the plant growing above the ground) and the roots grow at the same rate. When they plotted the growth on a coordinate graph that displayed millimeters of growth

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