Instructional materials summary – Harvard SI 2012
Title of teachable tidbit: ___Exponents Rule from Molecules to Ecosystems__
General Topic:
Interface of Math and Biology
Two sentence synopsis of tidbit:
Students in this tidbit will learn how to apply the exponents rule to various biological processes.
They will also learn how to create and interpret graphs using raw and log-transformed data.
Type of activity (or activities):
Clicker, shout out, think-pair-share, group exercise
Designed for what level course and
type of students?
These students should have taken undergraduate calculus and biology
Materials required:
Clickers, graph papers, calculators, handouts,
Comments on out of class
preparation required by students
and instructor:
read background on log transformation and log formulas
General comments:
List five keywords that would allow
others to search for this activity in
a database:
Log, exponent, ecosystem, molecule, graphing
Names and institutions of group
members:
Liliana Davalos, Giancarlo La Camera, Ed Luk (Stony Brook University)
Felicia Carvalho, Sue Ford (St. John’s University)
Contact person for questions:
Liliana Davalos
Feliicia Carvalho
Giancarlo La Camera
Sue Ford
Ed Luk
Exponents Rule from Molecules
to Ecosystems
Group 2: Interface of Biology and Math
Ed Luk, Giancarlo La Camera, Liliana Dávalos – Stony Brook University
Felicia Carvalho, Sue Ford – St. John’s University
Facilitators: Xinnian Chen, Martin Samuels
Exponents Rule from Molecules to
Ecosystems
• Context and Audience: 2-week unit in a course for
sophomore or juniors majoring in Biology, ~40 students
• Background: 2 semesters of college math, introductory
biology 1 and 2. Preceding units of the course cover
linear, inverse relationships, and power relationships
• Assumed knowledge: Students know mathematical
formulas but cannot apply to real-world problems
(Bloom’s levels 1 and 2)
– Basic arithmetic
– Have knowledge logarithms and antilogs
– Know equations for straight line
Objectives / learning outcomes
Students will be able to:
1. Justify the decision to log-transform data;
2. Create and interpret graphs using raw and
log-transformed data.
How many butterfly species?
5000 square miles
100 butterfly species
2500 square miles
How many butterfly species?
Train route Goa forest by Mohan P.
http://www.publicdomainpictures.net/pictures/10000/velka/417-221153452NXrX.jpg
The Florida Bugaboo Fire - Lake City, Fla., May 15, 2007 by Mark
Wolfe/FEMA
http://www.photolibrary.fema.gov/photodata/original/29930.jpg
Think-pair-share
Question: 5000-square mile forest has 100
butterfly species; how many species in 2500square mile remnant?
• Think for a moment about how many species
there will be
• Talk with your neighbor for one minute about
what you think
• Share with the class
Area (miles2)
# Butterfly species
222
314
371
528
877
8171
40942
70205
157600
668536
35
39
40
42
49
122
207
248
323
549
Area
(miles2)
# Butterfly
species
●
500
35
314
39
371
40
528
42
877
49
8171
122
400
# Butterfly Species
222
●
300
●
●
200
●
Area in miles2
0
60
0,
00
0
549
00
668536
40
0,
323
0
157600
●
●
●
00
248
20
0,
70205
100
00
207
2,
5
40942
How many species
in 2500 miles2?
A.
B.
C.
D.
E.
About 25
About 50
About 75
About 90
I cannot tell how
many species
there will be
This is the log-transform
●
●
500
400
●
300
●
# Butterfly Species
# Butterfly Species
400
●
200
●
10
300
● 10
●
100
90
●
200
●
75
●
50
●
Area in miles2
50
,0
10 00
0,
00
0
2,
50
5, 0
00
10 0
,0
00
00
0
1,
0
50
0
60
0,
00
0
00
40
0,
00
0
●
20
0,
00
●
●●
●
●
●
●
2,
5
90
75
50
25
Area in miles2
How did that work?
• Logarithmic transformation used to
rescale the x or y values, or both
This transformation has converted the data to a linear equation
y = mx +b
●
400
●
# Butterfly Species
300
●
●
200
150
10
● 10
●
100
75
50
●
●●
●
●
0
0 00
0 0 00 0
5 0 1 ,0 2 ,5 5 ,0 1 0 ,0
0
00 0
,0 0,0
0
5 10
Area in miles2
Handouts
•
•
•
•
Groups 1&3 take dataset 1
Groups 2&4 take dataset 2
Groups 5&6 take dataset 3
For your dataset:
– Which data would you transform, X or Y?
– Why did you choose that axis?
– Plot 4 data points using your log transformed data
on the graph paper provided to you.
100000000
time after
inoculation
10
20
30
40
50
Cell #
80000000
60000000
40000000
20000000
0
0
10
20
30
40
Time after inoculation (days)
50
60
cell #
11000
97600
993000
10000000
85000000
Log ???
Cell proliferation
time after
inoculation
cell #
10
11000
20
97600
30
993000
40
10000000
50
85000000
10
Log Cell #
8
6
4
2
0
0
10
20
30
40
50
Time after inoculation (days)
60
Log cell #
4.0414
4.9894
5.9969
7
7.9294