Group 3: MATH

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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.

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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.

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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.

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WHY COULD INSECTS THIS LARGE NEVER EXIST?
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• Exoskeleton too weak
• When shed exoskeleton when molting, collapse
  under weight
• Cant get enough oxygen
• Limits on ant hill size
• Lung capacity

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

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A Review Surface Area/Volume and Maximum Cell
Size
nutrients
wastes
Volume of a sphere 4/3pr3 Surface area of a
sphere 4pr2
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flatworm
Mini Lecture on Respiratory System of Insects
Tracheal tube system

• Exoskeleton with waxy cuticle prohibits
• simple diffusion through epidermis
• No blood vessels, so no lungs
• Tube system that carries O2 from surface
• to cells and takes up CO2

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Tracheal volume data
Length of Beetles Tracheal volume (as of
body volume) 17mm 1.9 18mm 2.1 27mm 3.3
47mm 5.7 60mm 7.4 62mm 7.6 80mm 9.9 12
9mm 15.8
Graph the data and determine the
relationship between tracheal volume and beetle
body length.
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Lets do some math!

• What is the mathematical formula describing the
  relationship
• between these two variables?
• A) x2 y2 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?

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

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• 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?

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Individual take-home question

• 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 0.123. 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.

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A Walking Stick

• http//www.insectchat.com/showthread.php?p2856

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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