Lesson Title: Assessing the quality of habitat for Monarch Butterflies
Discipline Focus: life science, mathematics
Grade level: Middle – High school
Length of lesson: 45 minutes
Stage 1 – Desired Results
Content Standard(s):
Understanding (s)/goals
Students will understand:
1) the nature of an average
2) the purpose of calculating an average (i.e. to estimate the real value of some characteristic in a population)
3) how the distribution on a population in space affects your ability to estimate it’s size
4) how different sampling methods may affect your population estimate
5) What is accuracy?
Essential Question(s):
1) Why would you want to estimate a
2) Are most living things evenly spread across
3) When you cannot count every individual in a
4)
5) population’s size? space? population, what measure do you use to estimate it?
How can you estimate the accuracy of a population estimate?
Is there one best way or does it depend?
Student objectives (outcomes):
Students will be able to:
1) calculate an average
2) assess the accuracy of that average (how close does it come to the real populations size?)
3) discuss how the distribution of organisms in space affects their ability to estimate the populations size.
4) Identify which sampling method was the best for estimating the population size of two differently arranged populations.
Stage 2 – Assessment Evidence
Performance Task(s):
After going through the exercise, students will be able to more accurately estimate the size of a new unknown population.
Other Evidence:
1)
2)
Level of engagement and participation of students in activities and discussion.
Demonstration of correct concepts in follow-up discussion.
Stage 3 – Learning Plan
Learning Activities:
Materials for each group:
8.5x11 blank sheet of paper (optional: field photo); 8.5x11 sheet of grid paper (~25 x 60 cells)
One population sheet: A=uniform (2823 dots), B= moderately clustered (949 dots), C=highly clustered (684 dots)
Cutting tool (i.e. Exacto knife)
Optional: calculator; worksheet for extension activity

Background:
Scientists are very interested in monitoring the quality of different habitats for monarch butterflies. Monarch butterflies rely exclusively on milkweed (
Asclepias syriaca ) to lay their eggs and as food for their caterpillars. Therefore, the number of milkweed plants in a field is a good indicator of the habitat quality for monarch butterflies.
There are two fields we wish to assess for habitat quality, but we have limited time and resources so we cannot count every plant in the field. We have contracted with your students to find an accurate estimate of the population size of milkweed in each habitat.
Procedure:
1) Hand out a field photo, a sheet of grid paper, and some kind of cutting tool.
2) Explain the background above, and that what they see before them is the field they are going to survey. They know nothing about the population of plants in that field.
3) Explain that they will have 10 minutes to decide how they want to estimate the population of milkweed plants in their field. You can assume that (after appropriate training) two students will be able to sample one grid cell during an average field trip session.
4) Instruct students to cut out the areas on the grid paper that they intend to sample
5) Instructor will overlay their sampling design on their real population and hand them back to the students.
6) Instruct students to estimate the size of the milkweed population (this will involve calculating the average of the number found per grid cell and then multiplying that by the total number of cells, but let’s let them figure that out?)
7) For each population, compare the results of student with the actual population to see how accurate their estimate is. a.
Discussion point – in actual scientific studies you would never know what the real populations size is so, how would you determine your accuracy?
(i.e. repeated measures, performance curves)
8) Compare the success of different sampling designs within each population.
9) Contrast how the distribution of the organism affected their ability to estimate the population using various sampling methods.
Follow-up Discussion:
1) The Essential Questions above
Extension Exercise:
By plotting calculating and plotting the cumulative average, student can see how the accuracy of the average increases with the number of plot/amount area sampled. This can also give an indication of when you have collected enough plots to have an accurate average.

20
21
22
23
24
25
11
12
13
14
15
16
17
18
19
5
6
7
8
9
10
Plot
1
2
3
4
# of
Organisms
45
46
47
48
49
50
36
37
38
39
40
41
42
43
44
30
31
32
33
34
35
Plot
26
27
28
29
Calculate the average based on plots (or samples):
1 – 5
1 – 10
1 – 25
1 – 50
1 – 100
Plot these numbers on the graph to the right.
After how many samples does the line begin to level?
How many samples is enough?
# of
Organisms Plot
# of
Organisms
70
71
72
73
74
75
61
62
63
64
65
66
67
68
69
55
56
57
58
59
60
51
52
53
54
0 2
0
4
0
60 80
# of Samples
95
96
97
98
99
100
86
87
88
89
90
91
92
93
94
80
81
82
83
84
85
Plot
76
77
78
79
# of
Organisms
100