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Growing students’ understanding of ratio, proportions and slope

 * A little more about Grow Beasts:** Grow Beasts are small toys made from a super-absorbent polyacrylamide polymer. When placed in a liquid they absorb it and gradually expand. The expansion process can take several days. When they are removed from the liquid, evaporation begins and the Grow Beast shrinks. This can also take several days but the Grow Beast will eventually return to more or less its original shape and size. Generally Grow Beasts are grown in water but they will absorb and grow in many liquids. The fact that it absorbs liquid slowly and “grows” enables students to make repeated measurements. The characteristics of the liquid greatly influence the rate of growth.

At the outset students wonder how big the Grow Beast will grow. Their interest in the question leads them to take measurements, compile data, plot points and crunch numbers in order to develop linear projections. They develop projections based on proportional reasoning, but as the growth rate slows they find that they must deal with a non-linear rate of change.

The work evolves naturally from the authentic context of the investigation and enables students to construct their understanding of some fundamental concepts and procedures in middle school mathematics.

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