Too Many To Count! (Teacher’s version)
This activity allows students to simulate field surveying techniques used to study plant
populations. It also shows them how rapidly invasive plants can take over natural areas
and displace native plants. The activity can be simplified for younger students; more
math applications can be added for older students.
You will need (for each student or pair of students):
One copy of Figures 1, 2 & 3 (whichever one/s apply)
Ruler
Pencil
1” x 1” square of card stock
Calculator (optional)
1. Estimating population density using quadrats (Figure 1 only)
Scientists often wish to know the population of plants or animals in an area. Counting
individuals is extremely tedious and is usually not practical. Instead, scientists take subsamples and use these sub-samples to estimate the total population. This activity will
simulate the use of quadrats to estimate the population of plants in a given area.
Procedure:
Explain to the students that each leaf on Figure 1 represents an individual plant. The
students are scientists who wish to know how many plants are in the plot (rectangle).
They will use quadrats (represented by the card stock squares) to estimate the number
of plants on the page.
a. Place Figure 1 flat on the desk/table.
b. Hold the “quadrat” about 8-10” above the paper (randomly) and drop it onto
the paper. If the entire square does not land within the rectangle printed on
the page, repeat this step.
c. Without moving the square, draw around the outline of the square using a
pencil.
d. Remove the square and count the number of leaves within your penciled
outline. Record this number in a data table.
e. Repeat steps b – d until you have a total of ten numbers in your data table.
Hints: If there are no leaves where the quadrat lands, record a zero in the
data table (as long as the entire quadrat was within the rectangle printed on
the page). If half or more of a leaf is in the quadrat outline, count the leaf; if
less than half a leaf is in the quadrat, do not count it.
f. Calculate the average of your ten numbers (add all ten together and divide
the total by ten). This is the number of plants per square inch.
g. Measure the area of the rectangle (area = length x width)
h. Multiply your average number (step f) by your total area (step g). This is your
total plant population estimate. Round this off to the nearest whole number.
Record this on your data sheet.
Note to teachers: Once all students have calculated their estimated population, you can
collect these numbers and use them to calculate the mean, median & mode. The data
can also be graphed as shown below.
Sample class data
Student #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Estimate
188
331
221
193
166
276
304
276
249
221
188
188
207
166
193
Class average (mean) = 224
Median = 207
Mode = 188
Tally the # of students whose estimate falls into each range of data (151-200; 201-250;
251-300; 301-350):
Data range
151-200
201-250
251-300
301-350
# of students
7
4
2
2
Graph of plant population estimates by
students in my class
# of students
Plot these data on a bar graph:
8
7
6
5
4
3
2
1
0
151-200
201-250
251-300
Estimate
301-350
2. Studying population change over time (Figures 2 & 3)
Figures 2 and 3 represent the same area as Figure 1, as an invasive plant species
moves into the area and starts to displace the native plants. Invasive plants are
represented by the red leaves
; native plants by green leaves .
Your students will use the quadrat procedure described above to estimate the
populations of both native and invasive plants in Figures 2 and 3. This time they will
need to count and record (separately) the number of red leaves and the number of
green leaves in their quadrats.
Math extensions (Figures 1, 2 & 3):
Have students graph their population estimates over time (Figure 1, Figure 2, Figure 3)
for native plants and invasive plants.
Assume that the Figures are at 5 year intervals. (Figure 1 is time 0, Figure 2 is 5 years
later; Figure 3 is 10 years later than figure 1). Use your estimated population of
invasive plants to calculate the growth rate (# plants/in²/yr) between 0 and 5 years, 5
and 10 years, and 0 and 10 years.
Compare data from Figures 2 and 3. What is the percent change of invasive plants?
Native plants? E.g. if there were an estimated 36 invasives in Figure 2 and 148 in
Figure 3, this represents an increase of 116 plants, or 322% ((116/36)x 100).
Convert data from inches to cm (remember that 1 in² = 6.45 cm²).
Other applications:
Have students use their data from ONLY their first quadrat to make their estimates.
Write all of these values on the board and compare the range of data with the range
collected using students’ average values. There should be a much broader range of
data when the single data points are used—this should help show the importance of
collecting replicate data.
Other sampling methods—The figures can also be used to demonstrate belt transect or
transect & quadrat techniques. For a belt transect, draw two parallel lines on the page,
so the lines are 1” apart. For easiest math, the lines should be either horizontal or
vertical. Count the number of plants between the two lines (using the 50% rule as
described for quadrats). This gives the number of plants in the “belt” area. Measure the
belt area. Divide the number of plants counted by the belt area to get plants/in².
Measure the total area of the “study site” (rectangle). Multiply the plants/in² by the total
area to get total estimated population. Discuss with students—what are the advantages
and disadvantages of this technique? (If plants are trees, quadrat won’t work; may not
represent actual population distribution; may not be random; may be too large an area
to really count in “real life,” etc.)
For transect & quadrat, draw two lines anywhere (any angle) on the page (using a
ruler). Have students use a ruler to mark every inch along the lines. Have students
place the quadrat so the top left corner of the quadrat is at the first inch mark on one
line and the side of the quadrat is along the line. Students should trace the outline of
the quadrat, then move it to the third inch mark, and so on. Repeat for the other line.
Students should count the number of plants in each quadrat as in the exercises above.
Discuss with students—what are the advantages and disadvantages of this technique?
(If transect is randomly placed, can remove bias inherent with use of quadrats; will not
work for trees; may not give large enough sample size, etc.)
To discuss with the students:
•
•
•
Why should the quadrat be dropped randomly? What is experimental bias?
Why might results from Figure 2 not accurately represent the actual
populations? (Populations are not evenly distributed on the page) How could
this be fixed? (Take more data samples).
What is “wrong” with the design of this experiment (from a scientific
standpoint)? (Measurements should be using the metric system).
For the teacher only! Actual data: Figure 1 = 210 plants
Figure 2: 168 native plants, 42 invasives
Figure 3: 53 native plants; 153 invasives
Too Many To Count! (Student handout)
1. Estimating population density using quadrats
In this activity, you are scientists who want to know how many plants are in a particular
area. The model for the area is Figure 1; plants are represented by leaf symbols on the
page (each leaf represents one plant). The study area is represented by the rectangle.
It is not practical to try and count every plant on the page, so you will be using a
sampling system to estimate the total number of plants. You will be using “quadrats”
(represented by squares of card stock) to take sub-samples of the total population of
plants. You will use these sub-samples to estimate the total population on the page.
You will need (each student or pair of students):
One copy of Figure 1
Ruler
Pencil
1” x 1” square of card stock
Calculator (optional)
Procedure:
a. Place Figure 1 flat on the desk/table.
b. Hold the “quadrat” about 8-10” above the paper (randomly) and drop it onto
the paper. If the entire square does not land within the rectangle printed on
the page, repeat this step.
c. Without moving the square, draw around the outline of the square using a
pencil.
d. Remove the square and count the number of leaves within your penciled
outline. Record this number in a data table.
e. Repeat steps b – d until you have a total of ten numbers in your data table.
Hints: If there are no leaves where the quadrat lands, record a zero in the
data table (as long as the entire quadrat was within the rectangle printed on
the page). If half or more of a leaf is in the quadrat outline, count the leaf; if
less than half a leaf is in the quadrat, do not count it.
f. Calculate the average of your ten numbers (add all ten together and divide
the total by ten). This is the number of plants per square inch.
g. Measure the area of the rectangle (area = length x width)
h. Multiply your average number (step f) by your total area (step g). This is your
total plant population estimate. Round this off to the nearest whole number.
Record this on your data sheet.
Too Many To Count! (Student handout)
2. Studying population change over time (Figures 2 & 3)
Once you have learned how to estimate population densities using quadrats, you will
apply this procedure to study how the plant population might change over time as a
second species of plants moves into the area.
Figures 2 and 3 represent the same area as Figure 1, as an invasive plant species
moves into the area and starts to displace the native plants. Invasive plants are
represented by the red leaves
; native plants by green leaves . Figure 2
represents an early stage of the invasion, while in Figure 3 the invasion is well under
way.
Use the quadrat procedure described above to estimate the populations of both native
and invasive plants in Figures 2 and 3. This time you will need to count and record
(separately) the number of red leaves and the number of green leaves in each of your
quadrats. You will record these data on the appropriate data sheets.
Name(s) ____________________________________________
Date: ____________________
DATA SHEET FOR FIGURE 1
Data Table
Quadrat #
# of plants
1
2
3
4
5
6
7
8
9
10
A. Total # of plants in 10 quadrats = ______________ plants.
B. Average # of plants = ____________ (plants per inch²). [A/10]
C. Area sampled = ____________ in².
D. Estimated plant population = _____________ plants. [B x C]
Name(s) ____________________________________________
Date: ____________________
DATA SHEET FOR FIGURE 2
Data Table
Quadrat #
# of native
plants
# of invasive
plants
1
2
3
4
5
6
7
8
9
10
A. Total # of native plants in 10 quadrats = ______________ natives.
B. Total # of invasive plants in 10 quadrats = ______________ invasives.
C. Average # of native plants = ____________ (natives per inch²). [A/10]
D. Average # of invasive plants = ____________ (invasives per in²). [B/10]
E. Area sampled = ____________ in².
F. Estimated native plant population = _____________ plants. [C x E]
G. Estimated invasive plant population = ____________ plants. (D x E)
H. Of the total number of plants counted (A + B), what fraction were native? (A/(A+B)) ________
I. Of the total number of plants counted (A + B), what fraction were invasives? (B/(A+B)) ______
Name(s) ____________________________________________
Date: ____________________
DATA SHEET FOR FIGURE 3
Data Table
Quadrat #
# of native
plants
# of invasive
plants
1
2
3
4
5
6
7
8
9
10
A. Total # of native plants in 10 quadrats = ______________ natives.
B. Total # of invasive plants in 10 quadrats = ______________ invasives.
C. Average # of native plants = ____________ (natives per inch²). [A/10]
D. Average # of invasive plants = ____________ (invasives per in²). [B/10]
E. Area sampled = ____________ in².
F. Estimated native plant population = _____________ plants. [C x E]
G. Estimated invasive plant population = ____________ plants. (D x E)
H. Of the total number of plants counted (A + B), what fraction were native? (A/(A+B)) ________
I. Of the total number of plants counted (A + B), what fraction were invasives? (B/(A+B)) ______
Figure 1—Pre-invasion
Figure 2—Early invasion
Figure 3—Late invasion