Tutorial details

The tutorial develops skill in reasoning about the scaling of objects in the context of the growth of an earthworm. Students use the concepts of surface area and volume to express the oxygen absorption and oxygen use rates of the worm. They then reason about the maximum size the worm can have while still absorbing enough oxygen to survive.

Section I: Absorption and consumption rates

Students first translate complicated units from verbal descriptions to expressions. They approximate the worm as a cylinder, then express the oxygen use and absorption rates of a worm in terms of a worm’s dimensions and mass. They then make calculations.

Section II: Modeling growth patterns

Students examine graphs of oxygen absorption and use for three different types of worm growth. They use these graphs to determine whether there is a limit to the worm’s growth (i.e., whether the oxygen use curve ever exceeds the absorption curve).

Section III: Approximations

Students determine how the endcaps of the worm affect the amount of oxygen it absorbs.

Section IV: Supplement

This section includes challenging questions involving log-log plots.

For instruction tips, login or register as a verified educator to see the Instructor Guide.

None.

Equipment

List

• tutorial instructor slides
• tutorial student slides or worksheet

Discussion