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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 population’s size? 2) Are most living things evenly spread across space? 3) When you cannot count every individual in a population, what measure do you use to estimate it? 4) How can you estimate the accuracy of a population estimate? 5) 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): Other Evidence: After going through the exercise, students 1) Level of engagement and participation of will be able to more accurately estimate the students in activities and discussion. size of a new unknown population. 2) 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. Plot 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 # of Organisms Plot 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 How many samples is enough? # of # of Organisms Plot Organisms 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 # of Organisms Plot 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Calculate the average based on plots (or samples): 1 – 10 1 – 25 1 – 50 Density Estimate 1–5 1 – 100 Plot these numbers on the graph to the right. After how many samples does the line begin to level? 0 2 0 4 0 60 # of Samples 80 100