One of the major themes that runs through many facets of science is the notion of surface area to volume ratio. I remember being a Peace Corps Volunteer in Kenya and using an experimental, guided-inquiry curriculum, inspired by the British Nuffield science program. Students made plasticine cubes of various sizes. I’m not sure why British people have an aversion to clay, but plasticine seems to be their school sculpting material. Then students measured the surface area of the cubes and calculated the volume. Then they calculated the surface area to volume ratio and discover that the larger the object, the smaller the surface area to volume ratio.
Which helps to explain many types of adaptations in biology and why individual cells can’t be the size of houses; they would simply not have enough surface area to absorb the materials they need, like oxygen, or to expel waste. From villi in the intestines to convolutions in the brain, our bodies have many adaptations to increase surface area.
Adaptive Curriculum has a guided inquiry Activity Object called “Surface Area to Volume Ratio in Organisms.” A clever engagement draws the students into the interactive experience. You have a plate of cheese with different size cubes that you are going to put into the microwave. But first, learners predict whether the large cubes or the small cubes will melt first.
Obviously, the small cheese cubes will melt before the larger ones. If you thought this, you have experienced a discrepant event. In actuality, the large cubes melt first. Since the microwave heats from the inside, the smaller cubes lose their heat faster than the large ones. The larger cubes, thus retain more heat and melt faster. Discrepant events are powerful, because learners want to know why they were wrong.
From this, learners virtually change the size of cubes and see the changes in surface area, volume, and surface area to volume ratio. Then body sizes and shapes of animals are explored, as students learn about the implications of size and shape for heat loss.
My Peace Corps teaching and Adaptive Curriculum are different modes of guided inquiry and discovery learning, but both can help produce deep and life long learning.