Group 3: MATH & BIOLOGY Teachable Unit: PASSING GAS Gas Exchange is a Unifying Concept in Biological Systems This teachable unit, Passing Gas, will be presented to a student body consisting of majors and non-majors at the introductory level. Passing Gas will have examples that can be utilized in sequences dealing with cellular, organismal and ecological biology. The Passing Gas unit assumes that the students will have basic competency in algebra, geometry and high-school level biology.

Unit Learning Goals Biology students will become more comfortable using math in biological applications. Students will develop quantitative skills. Students will use math to analyze biological phenomena at multiple scales. Students will understand that gas exchange is a unifying concept in biology.

Learning Outcomes of Tidbit 1 Students will use quantitative skills in novel situations involving gas exchange. Students will determine the mathematical relationship between parameters that influence levels of gas exchange in an animal system.

WHY COULD INSECTS THIS LARGE NEVER EXIST?

Exoskeleton too weak When shed exoskeleton when molting, collapse under weight Can’t get enough oxygen Limits on ant hill size Lung capacity

Clicker Question review from last semester As the radius of a cell increases, the surface area to volume ratio of the cell a)Increases b)Decreases c)Stays the same d)Insufficient data to answer this question

A Review: Surface Area/Volume and Maximum Cell Size Volume of a sphere = 4/3πr 3 Surface area of a sphere = 4πr 2 nutrients wastes

Mini Lecture on Respiratory System of Insects Exoskeleton with waxy cuticle prohibits simple diffusion through epidermis No blood vessels, so no lungs Tube system that carries O 2 from surface to cells and takes up CO 2 flatworm Tracheal tube system

Tracheal volume data Length of BeetlesTracheal volume (as % of body volume) 17mm1.9% 18mm2.1% 27mm3.3% 47mm5.7% 60mm7.4% 62mm7.6% 80mm9.9% 129mm 15.8% Graph the data and determine the relationship between tracheal volume and beetle body length.

What is the mathematical formula describing the relationship between these two variables? A) x 2 + y 2 = 0 B) y = mx + b C) y = log x D) y = 1/x What does this information tell us about insect size and tracheal system size? Let’s do some math!

SMALL INSECT Oxygen depleted if tube diameter stays the same Large Insect Tracheole volume larger to accommodate needs SUMMARY OF THE PROBLEM LARGE INSECT

Based on your data, what is the theoretical maximum length of a beetle? The largest living beetle today actually is 170 mm. What do you think limits the body volume that an insect can devote to the tracheal system?

Entrance Ticket for Next Class During the Carboniferous (350 mya) there were insects much larger than any found on Earth today. Develop a hypothesis from this observation. How would you test your hypothesis?

The relationship between body length and the % of the body volume taken up by tracheal tubes in beetles is defined by a line with a slope of Even today there are insects much longer than the beetles we examined in this exercise. If you assume that a maximum volume of tracheal tubes is 20% of total insect volume, and the slope of the relationship between length and tracheal volume is 0.056, what is the length of this insect? What does this insect look like? Explain your answer. Individual take-home question

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SCIENTIFIC TEACHING Active Learning Clicker Brainstorming Group problem solving Entrance ticket Assessment-all of above formative Individual take-home question is summative Diversity Auditory/visual/kinesthetic Spatial/mathematical Social learning