# Cape Mathematics Unit 2 Worksheet 8 Counting Probability

Description

Cape Mathematics Unit 2 Worksheet 8 Counting Probability document sample

Shared by:
Categories
-
Stats
views:
25
posted:
1/12/2011
language:
English
pages:
21
Document Sample

```							Title: Biodiversity: Importance and Measurement

Name: John Hammond

Date: 3/8/2010

Goals:
Students will:
1. Experience how diversity is important for ecosystem resilience
2. Learn about the benefits society gains from diverse ecosystems
3. Look at how we measure diversity in an effort to maintain and
compare ecosystems

Objectives:
Students will:
1. Perform an activity about ecosystem interconnectedness using a web
of yarn
2. Discuss the web nature of an ecosystem
3. Learn how genetic diversity allows an ecosystem to survive and
rebound from disease and disasters using a tree role-playing activity
4. Perform an activity involving measurement of diversity
5. Use mathematical skills to fill out a table of relative abundances
6. Explore a diversity index using new mathematical concepts

Benchmarks:
Mathematics – Grade 6
Number and Operations
6.1.3 Use and analyze a variety of strategies, including models, for solving problems with
multiplication and division of decimals.
6.1.4 Develop fluency with efficient procedures for multiplying and dividing fractions
and decimals and justify why the procedures work.
6.1.5 Apply the inverse relationship between multiplication and division to make sense of
procedures for multiplying and dividing fractions and justify why they work.
6.1.6 Apply the properties of operations to simplify calculations.
6.1.7 Use the relationship between common decimals and fractions to solve problems
including problems involving measurement.

Number and Operations and Probability
6.2.1 Develop, analyze, and apply the meaning of ratio, rate, and percent to solve
problems.
6.2.2 Determine decimal and percent equivalents for common fractions, including
approximations.

Algebra
6.3.1 Use order of operations to simplify expressions that may include exponents and
grouping symbols.
6.3.2 Develop the meanings and uses of variables.
6.3.3 Write, evaluate, and use expressions and formulas to solve problems.

Page 1 of 21
6.3.4 Identify and represent equivalent expressions (e.g., different ways to see a pattern).
6.3.5 Represent, analyze, and determine relationships and patterns using tables, graphs,
words and when possible, symbols.
6.3.6 Recognize that the solutions of an equation are the values of the variables that make
the equation true.
6.3.7 Solve one-step equations by using number sense, properties of operations, and the
idea of maintaining equality on both sides of an equation.

Mathematics – Grade 7
Number and Operations and Algebra
7.1.1 Develop, analyze, and apply models (including everyday contexts), strategies, and
procedures to compute with integers, with an emphasis on negative integers.
7.1.2 Extend knowledge of integers and positive rational numbers to solve problems
involving negative rational numbers.
Number and Operations, Algebra, and Geometry
7.2.1 Represent proportional relationships with coordinate graphs and tables, and identify
unit rate as the slope of the related line.
7.2.3 Use coordinate graphs, tables, and equations to distinguish proportional
relationships from other relationships, including inverse proportionality.

Mathematics – Grade 8
Data Analysis and Algebra
8.2.1 Organize and display data (e.g., histograms, box-and-whisker plots, scatter plots) to
pose and answer questions; and justify the reasonableness of the choice of display.
8.2.2 Use measures of center and spread to summarize and compare data sets.
8.2.3 Interpret and analyze displays of data and descriptive statistics.
8.2.4 Compare descriptive statistics and evaluate how changes in data affect those
statistics.
8.2.5 Describe the strengths and limitations of a particular statistical measure, and justify
or critique its use in a given situation.
8.2.6 Use sample data to make predictions regarding a population.
8.2.7 Identify claims based on statistical data and evaluate the reasonableness of those
claims.

Science – Grade 6
Interaction and Change
6.2L.2 Explain how individual organisms and populations in an ecosystem interact and
how changes in populations are related to resources.

Scientific Inquiry
6.3S.1 Based on observation and science principles propose questions or hypotheses that
can be examined through scientific investigation. Design and conduct an investigation
that uses appropriate tools and techniques to collect relevant data.
6.3S.2 Organize and display relevant data, construct an evidence-based explanation of the
results of an investigation, and communicate the conclusions.
6.3S.3 Explain why if more than one variable changes at the same time in an
investigation, the outcome of the investigation may not be clearly attributable to any one
variable.

Science – Grade 7

Page 2 of 21
Interaction and Change
7.2L.2 Explain the processes by which plants and animals obtain energy and materials for
growth and metabolism.
7.2E.1 Describe and evaluate the environmental and societal effects of obtaining, using,
and managing waste of renewable and non-renewable resources.
7.2E.3 Evaluate natural processes and human activities that affect global environmental
change and suggest and evaluate possible solutions to problems.

Scientific Inquiry
7.3S.1 Based on observations and science principles propose questions or hypotheses that
can be examined through scientific investigation. Design and conduct a scientific
investigation that uses appropriate tools and techniques to collect relevant data.
7.3S.2 Organize, display, and analyze relevant data, construct an evidence-based
explanation of the results of an investigation, and communicate the conclusions
including possible sources of error.
7.3S.3 Evaluate the validity of scientific explanations and conclusions based on the
amount and quality of the evidence cited.

Science – Grade 8
Scientific Inquiry
8.3S.1 Based on observations and science principles propose questions or hypotheses that
can be examined through scientific investigation. Design and conduct a scientific
investigation that uses appropriate tools, techniques, independent and dependent
variables, and controls to collect relevant data.
8.3S.2 Organize, display, and analyze relevant data, construct an evidence-based
explanation of the results of a scientific investigation, and communicate the conclusions
including possible sources of error. Suggest new investigations based on analysis of
results.

Page 3 of 21
Background Material:
Retrieved March 17, 2010 from
http://www.coastalwiki.org/coastalwiki/Measurements_of_biodiversity
―
Measurements of biodiversity

A variety of objective measures have been created in order to empirically measure
biodiversity. The basic idea of a diversity index is to obtain a quantitative estimate of
biological variability that can be used to compare biological entities, composed of direct
components, in space or in time. It is important to distinguish ‗richness‘ from ‗diversity‘.
Diversity usually implies a measure of both species number and ‗equitability‘ (or
‗evenness‘). Three types of indices can be distinguished:

1. Species richness indices: Species richness is a measure for the total number of the
species in a community. However, complete inventories of all species present at a certain
location, is an almost unattainable goal in practical applications.

A visualization of the species richness: with respectively 5 and 10 species.

2. Evenness indices: Evenness expresses how evenly the individuals in a community are
distributed among the different species.

A visualization of the evenness of 5 species.

3. Taxonomic indices: These indices take into account the taxonomic relation between
different organisms in a community. Taxonomic diversity, for example, reflects the
average taxonomic distance between any two organisms, chosen at random from a
sample. The distance can be seen as the length of the path connecting these two
organisms along the branches of a phylogenetic tree.

Page 4 of 21
These three types of indices can be used on different spatial [1]

   Alpha diversity refers to diversity within a particular area, community or
ecosystem, and is usually measured by counting the number of taxa within the
ecosystem (usually species level)

   Beta diversity is species diversity between ecosystems; this involves comparing
the number of taxa that are unique to each of the ecosystems. For example, the
diversity of mangroves versus the diversity of seagrass beds.

   Gamma diversity is a measure of the overall diversity for different ecosystems
within a region. For example, the diversity of the coastal region of Gazi Bay in
Kenia.

Diversity measurement is based on three assumptions

1. All species are equal: this means that richness measurement makes no distinctions
amongst species and threat the species that are exceptionally abundant in the same way as
those that are extremely rare species. The relative abundance of species in an assemblage
is the only factor that determines its importance in a diversity measure.

2. All individuals are equal: this means that there is no distinction between the largest
and the smallest individual, in practice however the smallest animals can often escape for
example by sampling with nets.

Taxonomic and functional diversity measures, however, do not necessarily treat all
species and individuals as equal.

3. Species abundance has been recorded in using appropriate and comparable units. It is
clearly unwise to use different types of abundance measure, such as the number of
individuals and the biomass, in the same investigation. Diversity estimates based on
different units are not directly comparable.
―

http://en.wikipedia.org/wiki/Shannon-Wiener_index has a mathematical proof of
evenness maximizing the Shannon index

Retrieved March 17, 2010 from http://www.globalissues.org/article/170/why-is-
biodiversity-important-who-cares

―

Page 5 of 21
Why is Biodiversity Important?

Biodiversity boosts ecosystem productivity where each species, no matter how small,
all have an important role to play.

For example,

   A larger number of plant species means a greater variety of crops
   Greater species diversity ensures natural sustainability for all life forms
   Healthy ecosystems can better withstand and recover from a variety of disasters.

And so, while we dominate this planet, we still need to preserve the diversity in wildlife.

A healthy biodiversity offers many natural services

Ecosystems such as the Amazon rainforest are rich in diversity. Deforestation threatens
many species such as the giant leaf frog, shown here. (Images source: Wikipedia)

A healthy biodiversity provides a number of natural services for everyone:

   Ecosystem services, such as
o Protection of water resources
o Soils formation and protection
o Nutrient storage and recycling
o Pollution breakdown and absorption
o Contribution to climate stability
o Maintenance of ecosystems
o Recovery from unpredictable events
   Biological resources, such as
o Food
o Medicinal resources and pharmaceutical drugs
o Wood products
o Ornamental plants
o Breeding stocks, population reservoirs

Page 6 of 21
o   Future resources
o   Diversity in genes, species and ecosystems
   Social benefits, such as
o Research, education and monitoring
o Recreation and tourism
o Cultural values

That is quite a lot of services we get for free!

The cost of replacing these (if possible) would be extremely expensive. It therefore
makes economic and development sense to move towards sustainability.

A report from Nature magazine also explains that genetic diversity helps to prevent the
chances of extinction in the wild (and claims to have shown proof of this).

To prevent the well known and well documented problems of genetic defects caused by
in-breeding, species need a variety of genes to ensure successful survival. Without
this, the chances of extinction increases.

And as we start destroying, reducing and isolating habitats, the chances for interaction
from species with a large gene pool decreases. Side Note»

Species depend on each other

While there might be ―survival of the fittest‖ within a given species, each species
depends on the services provided by other species to ensure survival. It is a type of
cooperation based on mutual survival and is often what a ―balanced ecosystem‖ refers to.

―

Retrieved March 17, 2010 from http://en.wikipedia.org/wiki/Biodiversity
―

"Biological diversity" or "biodiversity" can have many interpretations and it is most
commonly used to replace the more clearly defined and long established terms, species
diversity and species richness. Biologists most often define biodiversity as the "totality of
genes, species, and ecosystems of a region". An advantage of this definition is that it
seems to describe most circumstances and present a unified view of the traditional three
levels at which biological variety has been identified:

   species diversity
   ecosystem diversity
   morphological diversity
   genetic diversity

Page 7 of 21
But Professor Anthony Campbell at Cardiff University, UK and the Darwin Centre,
Pembrokeshire, has defined a fourth, and critical one: Molecular Diversity (see Campbell,
AK J Applied Ecology 2003,40,193-203; Save those molecules: molecular biodiversity
and life).

This multilevel conception is consistent with the early use of "biological diversity" in
Washington, D.C. and international conservation organizations in the late 1960s through
1970's, by Raymond F. Dasmann who apparently coined the term and Thomas E.
Lovejoy who later introduced it to the wider conservation and science communities. An
explicit definition consistent with this interpretation was first given in a paper by Bruce
A. Wilcox commissioned by the International Union for the Conservation of Nature and
Natural Resources (IUCN) for the 1982 World National Parks Conference in Bali. The
definition Wilcox gave is "Biological diversity is the variety of life forms...at all levels of
biological systems (i.e., molecular, organismic, population, species and ecosystem)..."
Subsequently, the 1992 United Nations Earth Summit in Rio de Janeiro defined
"biological diversity" as "the variability among living organisms from all sources,
including, 'inter alia', terrestrial, marine, and other aquatic ecosystems, and the ecological
complexes of which they are part: this includes diversity within species, between species
and of ecosystems". This is, in fact, the closest thing to a single legally accepted
definition of biodiversity, since it is the definition adopted by the United Nations
Convention on Biological Diversity.

The current textbook definition of "biodiversity" is "variation of life at all levels of
biological organization".

For geneticists, biodiversity is the diversity of genes and organisms. They study processes
such as mutations, gene exchanges, and genome dynamics that occur at the DNA level
and generate evolution. Consistent with this, along with the above definition the Wilcox
paper stated "genes are the ultimate source of biological organization at all levels of
biological systems..."

…

Selection bias amongst researchers may contribute to biased empirical research for
modern estimates of biodiversity. In 1768 Rev. Gilbert White succinctly observed of his
Selborne, Hampshire "all nature is so full, that that district produces the most variety
which is the most examined."

Nevertheless, biodiversity is not distributed evenly on Earth. It is consistently richer in
the tropics and in other localized regions such as the Cape Floristic Province. As one
approaches polar regions one generally finds fewer species. Flora and fauna diversity
depends on climate, altitude, soils and the presence of other species. In the year 2006
large numbers of the Earth's species were formally classified as rare or endangered or
threatened species; moreover, many scientists have estimated that there are millions more
species actually endangered which have not yet been formally recognized. About 40

Page 8 of 21
percent of the 40,177 species assessed using the IUCN Red List criteria, are now listed as
threatened species with extinction - a total of 16,119 species.

Even though biodiversity declines from the equator to the poles in terrestrial ecoregions,
whether this is so in aquatic ecosystems is still a hypothesis to be tested, especially in
marine ecosystems where causes of this phenomenon are unclear. In addition, particularly
in marine ecosystems, there are several well stated cases where diversity in higher
latitudes actually increases. Therefore, the lack of information on biodiversity of Tropics
and Polar Regions prevents scientific conclusions on the distribution of the world‘s
aquatic biodiversity.

A biodiversity hotspot is a region with a high level of endemic species. These
biodiversity hotspots were first identified in 1988 by Dr. Norman Myers in two articles in
the scientific journal The Environmentalist. Dense human habitation tends to occur near
hotspots. Most hotspots are located in the tropics and most of them are forests.

Brazil's Atlantic Forest is considered a hotspot of biodiversity and contains roughly
20,000 plant species, 1350 vertebrates, and millions of insects, about half of which occur
nowhere else in the world. The island of Madagascar including the unique Madagascar
dry deciduous forests and lowland rainforests possess a very high ratio of species
endemism and biodiversity, since the island separated from mainland Africa 65 million
years ago, most of the species and ecosystems have evolved independently producing
unique species different from those in other parts of Africa.

Many regions of high biodiversity (as well as high endemism) arise from very specialized
habitats which require unusual adaptation mechanisms, for example alpine environments
in high mountains, or the peat bogs of Northern Europe.

…

Biodiversity found on Earth today is the result of 3.5 billion years of evolution. The
origin of life has not been definitely established by science, however some evidence
suggests that life may already have been well-established a few hundred million years
after the formation of the Earth. Until approximately 600 million years ago, all life
consisted of archaea, bacteria, protozoans and similar single-celled organisms.

The history of biodiversity during the Phanerozoic (the last 540 million years), starts with
rapid growth during the Cambrian explosion—a period during which nearly every
phylum of multicellular organisms first appeared. Over the next 400 million years or so,
global diversity showed little overall trend, but was marked by periodic, massive losses
of diversity classified as mass extinction events.

The apparent biodiversity shown in the fossil record suggests that the last few million
years include the period of greatest biodiversity in the Earth's history. However, not all
scientists support this view, since there is considerable uncertainty as to how strongly the
fossil record is biased by the greater availability and preservation of recent geologic

Page 9 of 21
sections. Some (e.g. Alroy et al. 2001) argue that, corrected for sampling artifacts,
modern biodiversity is not much different from biodiversity 300 million years ago.[18]
Estimates of the present global macroscopic species diversity vary from 2 million to 100
million species, with a best estimate of somewhere near 13–14 million, the vast majority
of them arthropods.

The existence of a global carrying capacity has been debated, that is to say that there is a
limit to the number of species that can live on this planet. While records of life in the sea
shows a logistic pattern of growth, life on land (insects, plants and tetrapods)shows an
exponential rise in diversity. As one author states, "Tetrapods have not yet invaded 64 per
cent of potentially habitable modes, and it could be that without human influence the
ecological and taxonomic diversity of tetrapods would continue to increase in an
exponential fashion until most or all of the available ecospace is filled."

Most biologists agree however that the period since the emergence of humans is part of a
new mass extinction, the Holocene extinction event, caused primarily by the impact
humans are having on the environment. It has been argued that the present rate of
extinction is sufficient to eliminate most species on the planet Earth within 100 years.

New species are regularly discovered (on average between 5–10,000 new species each
year, most of them insects) and many, though discovered, are not yet classified (estimates
are that nearly 90% of all arthropods are not yet classified). Most of the terrestrial
diversity is found in tropical forests.

…

The relevance of biodiversity to human health is becoming a major international political
issue, as scientific evidence builds on the global health implications of biodiversity loss.
This issue is closely linked with the issue of climate change, as many of the anticipated
health risks of climate change are associated with changes in biodiversity (e.g. changes in
populations and distribution of disease vectors, scarcity of fresh water, impacts on
agricultural biodiversity and food resources etc). Some of the health issues influenced by
biodiversity include dietary health and nutrition security, infectious diseases, medical
science and medicinal resources, social and psychological health, and spiritual well-
being. Biodiversity is also known to have an important role in reducing disaster risk, and
in post-disaster relief and recovery efforts.

One of the key health issues associated with biodiversity is that of drug discovery and the
availability of medicinal resources. A significant proportion of drugs are derived, directly
or indirectly, from biological sources; Chivian and Bernstein report that at least 50% of
the pharmaceutical compounds on the market in the US are derived from natural
compounds found in plants, animals, and microorganisms, while about 80% of the world
population depends on medicines from nature (used in either modern or traditional
medical practice) for primary healthcare. Moreover, only a tiny proportion of the total
diversity of wild species has been investigated for potential sources of new drugs.
Through the field of bionics, considerable technological advancement has occurred which

Page 10 of 21
would not have without a rich biodiversity. It has been argued, based on evidence from
market analysis and biodiversity science, that the decline in output from the
pharmaceutical sector since the mid-1980s can be attributed to a move away from natural
product exploration ("bioprospecting") in favour of R&D programmes based on
genomics and synthetic chemistry, neither of which have yielded the expected product
outputs; meanwhile, there is evidence that natural product chemistry can provide the
basis for innovation which can yield significant economic and health benefits. Marine
ecosystems are of particular interest in this regard, however unregulated and
inappropriate bioprospecting can be considered a form of over-exploitation which has the
potential to degrade ecosystems and increase biodiversity loss, as well as impacting on
the rights of the communities and states from which the resources are taken.

Agriculture production, pictured is a tractor and a chaser bin.

A wide range of industrial materials are derived directly from biological resources. These
include building materials, fibers, dyes, resirubber and oil. There is enormous potential
for further research into sustainably utilizing materials from a wider diversity of
organisms. In addition, biodiversity and the ecosystem goods and services it provides are
considered to be fundamental to healthy economic systems. The degree to which
biodiversity supports business varies between regions and between economic sectors,
however the importance of biodiversity to issues of resource security (water quantity and
quality, timber, paper and fibre, food and medicinal resources etc) are increasingly
recognized as universal. As a result, the loss of biodiversity is increasingly recognized as
a significant risk factor in business development and a threat to long term economic
sustainability. A number of case studies recently compiled by the World Resources
Institute demonstrate some of these risks as identified by specific industries.

―
Other good websites to review
http://darwin.bio.uci.edu/~sustain/bio65/Titlpage.htm - An online textbook by Peter J.
Bryant from the School of Biological Sciences, University of California, Irvine

http://www.eoearth.org/article/biodiversity - A helpful article by J. Emmett Duffy about
biodiversity

Page 11 of 21
Materials:
Activity 1:
1 ball of yarn
Activity 2:
3x5 cards
Permanent Marker
Activity 3:
Plastic Bags
Paper
Scissors

Material Costs:
List the equipment and non-consumable material and estimated cost of each
Yarn............................................................................................................\$2.50
Permanent Marker ......................................................................................\$2.50
Plastic Zipper Bags ....................................................................................\$1.49
Scissors ......................................................................................................\$3.99
Estimated total, one-time, start-up cost: ........................................................\$10.48

List the consumable supplies and estimated cost for presenting to a class of 30
students
3x5 cards ....................................................................................................\$0.99
Graph Paper ...............................................................................................\$2.50
Paper, for little pictures and handouts................................. free from school
Estimated total cost each year: .........................................................................\$3.49

Preparation:
Before Class:
1. Roll up the yarn into a ball instead of the loose football you buy it in
2. Label the 30 cards
a. Side 1 with D or Df for Douglas-fir
b. Other side with other trees – Use initials for Western Red Cedar, Red
Alder, Douglas-fir, Madrone, Cottonwood, Lodgepole Pine, Ponderosa
Pine, Broadleaf Maple, White Oak, Western Juniper, or any other
native trees for your region. Needs to be a diverse community.
3. Cut up little tree pictures included at end and place in bags in correct
proportions. 3 sites per group (2-3 students)
a. Site 1 – 13 Douglas-fir, 3 Alder, 2 Maple, 2 Madrone
b. Site 2 – 2 Douglas-fir, 6 Alder, 6 Maple, 6 Madrone
c. Site 3 – 16 Douglas-fir, 4 Alder, 0 Maple, 0 Madrone
4. Print handouts

Page 12 of 21
Procedure:
During Class:
1. Give first part of lecture
2. Activity 1
a. Students get in a loose circle
b. The first student throws the ball of yarn to another student across the
circle
i. The ball of yarn may not unroll smoothly, so it may be better to
throw shorter distances if the yarn doesn‘t come off the roll
easily
c. Continue throwing the ball of yarn so each student holds one loop of
yarn. If there are less students and enough yarn, then students could go
again, so each student holds two loops of yarn
d. Now with a web of yarn, instruct one student to release their loop of
yarn. Instruct other students to tighten the slack created by the release.
i. Discuss one species or population dying and the effects on the
rest of the ecosystem
e. Instruct another student or take volunteers to release their yarn. The
other students take up the slack and keep the web tight.
f. Once activity has run its course, gather up yarn to roll up later, and
students have a seat
3. Middle lecture portion
4. Activity 2
a. Hand out 1 card to each student
b. Instruct students to write down, for class of 30, five names on their
own card on the Douglas-fir side.
i. The activity can be scaled up or down in proportion to class
size. A smaller class size could write down 3 or 4 names on
their own card.
c. Students should mill around and meet people and write down their
names. Students should return to their seats when finished but remain
standing.
d. Either pick or walk around the room and tap on shoulder 3 students
i. These students receive the ―disease.‖ Instruct those selected
students to sit and read the names off their card. Those students
now have the disease as well and they will sit. Choose one of
the students who just sat down and ask them to read the names
off their card. Continue this until almost all students are sitting.
Not all of the students will get to read the names off their card.
e. Discuss how a lack of genetic diversity (all the same species) means
that a disease takes a greater toll on a community
f. Now have students flip card over and repeat steps c and d.
g. After enough students have read their names, almost no students will
be sitting.

Page 13 of 21
h. Discuss how more genetic diversity equals a greater resilience to
disease and other disasters – reference questions on PowerPoint
presentation.
i. Note – The activity can be scaled up or down as previously stated by
adjusting the number of cards handed out and the number of names
each student writes down. You can also adjust the number of different
species of trees in the second half of the activity. The key is that
during the first activity, almost all of the students should ―get the
disease.‖ In the second half, almost no students should be ―infected.‖
Adjust the number of names and species accordingly to achieve the
most descriptive result.
5. Continue with last part of lecture
6. Activity 3
a. Hand out a set of bags (Sites 1, 2, and 3) to each group of students. A
group of students is 2-3. Four is probably too many since there are
only 3 baggies. Also hand out worksheets and graph paper. One
worksheet and graph paper per student.
b. Instruct to students to take out the populations of each bag on the
tables or desks and look at the populations.
i. Discuss how the diversity of each looks subjectively
c. Discuss relative abundance as a measure and instruct students to fill
out tables in handout with the relative abundances for each species in
each site.
i. Calculators are not completely necessary as the fractions can
be mental-mathed since totals are out of 20.
d. Instruct students to graph the relative abundances (species vs.
abundance)
i. Discuss what kind of graph is best. The idea is to visualize the
diversity of each site. A bar graph is good and probably the go-
to graph for middle school students. Pie charts are good too.
We want to see levels relative to each other or amounts relative
to the whole.
ii. Discuss what the graphs say.
e. If appropriate, have students figure the Shannon-Wiener index for each
site.
i. Read the instruction on the handout while students follow
along. Students can figure themselves from the instructions or:
1. Place a similar calculator as what the students have on a
document camera or use transparent overhead
calculator
2. Use an online calculator on an overhead projector if
computer has internet access - http://web2.0calc.com/
3. Walk the students through the steps, writing down each
component of the summation and then adding them up

Page 14 of 21
at the end. Avoid confusion about the natural logarithm
in the formula
ii. Discuss each the index for each site. Maximum evenness
maximizes the index.
After lesson and after class:
1. Completion of the handout serves as the assessment. Each student should have
tables filled out and graphs made.
2. Place components back into baggies and collect cards. The cards can be
recycled. The baggies and pictures can also be recycled or thrown out.
3. Ball yarn back up.

Sources:
• Activity 1 adapted from
<http://sftrc.cas.psu.edu/LessonPlans/Wildlife/WholeCloth.html> by Stephanie
L. Rau
• Activity 2 adapted from
<http://www.accessexcellence.org/AE/ATG/data/released/0534-
KathyParis/index.php> by Kathy Paris
• Activity 3 adapted from Smithsonian National Air and Space Museum,
―Reflections on Earth: Biodiversity and Remote Sensing‖
<http://www.nasm.si.edu/education/teaching_resources.cfm>
• http://www.globalissues.org/article/170/why-is-biodiversity-important-who-cares
• http://en.wikipedia.org/wiki/Biodiversity
• http://www.coastalwiki.org/coastalwiki/Measurements_of_biodiversity

Page 15 of 21
1. Which site is the most diverse?

2. Calculate relative abundance for each tree species.

Relative abundance = # of Individuals / Total number of organisms
Site 1
Tree Species                      Alder                          Madrone        Total
Fir                        Maple                                     Index
Population            13            3               2               2            20         -

Relative
-
Abundance

Site 2
Tree Species                      Alder                          Madrone        Total
Fir                        Maple                                     Index
Population            2             6               6               6            20         -

Relative
-
Abundance

Site 3
Tree Species                      Alder                          Madrone        Total
Fir                        Maple                                     Index
Population            16            4               0               0            20         -

Relative
-
Abundance

3. Graph the relative abundances for each site. What do the graphs tell you about richness
of species, diversity, and evenness?

4. Figure the Shannon-Wiener index for each site.


D     pi ln pi      
Don’t let this confuse you. D means diversity. The symbol that looks like an E means that
we will add up everything to the right of the symbol i number of times. The lowercase p is
just the relative abundances you already figured out in your tables. The “ln” means
natural logarithm. You should have a button on your calculator for this operation.
1. Take your first relative abundance and multiply it by the natural log of the same
number. Write this number down.
2. Repeat step 1 for the next abundance and write that number down.
3. Once you have run out of abundances, you should have four numbers written down.
Just add those four numbers together and put a negative sign in front.
4. Congratulations, you have figured the Shannon-Wiener index for your site

Page 16 of 21
Douglas-fir

Page 17 of 21
Douglas-fir

Page 18 of 21
Alder

Page 19 of 21

Page 20 of 21

Page 21 of 21

```
Related docs
Other docs by xye25736
Capital Investment Decisions