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12/29/2003 - Kathleen Damonte
You have probably participated in or seen a contest where you had to guess the number of jelly beans in a jar to win. Because you couldn’t count all the jelly beans, you might have tried counting a small number and working out a reasonable guess or estimate from that number. You unknowingly used a technique common to mathematicians and scientists called sampling. Scientists use sampling to get an estimate of things they cannot easily count.
A population is made up of all the organisms of one species living together in one place at the same time. All of the people living together in one town are considered a population. All of the grasshoppers living in a field are a population. Scientists keep track of the change (increase or decrease) of population numbers to make decisions about issues that affect that population. For example, marine biologists count the number of different fish species to see what effect fishing might be having on them. Fishery managers use this data to determine how many fish can be caught without damaging a population.
It is often not practical or even possible to count all the members of a population. A population can be so large that counting it would be like trying to count the number of grains of sand on a beach. Animals can be difficult to count because they live underwater, move around a lot, or are only active at night. To get around these counting problems, scientists take data from just a small portion of the population called a sample. They take several samples and then use the average size of those samples to calculate an estimate of the entire population size.
How Sampling Works
A forest ranger wants to know how many oak trees there are in a forest because the oak trees provide food for deer, wild turkeys, and other wildlife. She divides the area of the forest into 10 equal areas and then counts the number of oak trees in 3 of those 10 areas. She then finds the average of the three samples and multiplies it by 10 to get an estimate of how many oak trees are in the forest. If she finds an average of six trees per sample she would calculate that there were 60 oak trees in the forest.
How Many Grasshoppers?
Use the directions below to do a sampling activity using pasta to represent the number of grasshoppers in a field.
Materials:
Time needed:20 minutes
Directions:1. Using the pen or pencil and ruler, divide the paper into four columns across and five rows down so that you have 20 equal squares on the paper.
2. Measure 1 teaspoon (5 mL) of pasta and scatter the pasta as evenly as possible over the entire paper. Make sure some pasta gets in each box on the page.
3. Randomly choose one square on the page. Count the number of pieces of pasta in one square and record below.
4. Count the number of pieces in a second, different square and record it on the chart.
5. Count the number of pieces in a third square and record.
6. Find the mean (average) number of pieces of pasta for the three squares. (Find the total for your three squares and divide the total by three.)
7. Multiply the mean (average) you got by the number of squares on the paper (20). This will give you an estimate of the number of pieces of pasta on the whole paper.
Population Sampling Chart
Questions:
For Younger Students
Primary students will not have the mathematics skills necessary for this activity. Have students divide their paper into four equal parts and scatter one-half cup (125 mL) of larger elbow macaroni evenly over the paper. Next, have students count the macaroni in two of the squares and then double it. This will give an estimate of the number of pieces of pasta on the whole paper. Although the final estimate may differ from the actual, young students can benefit from modeling the process of sampling.Kathleen Damonte teaches seventh-grade science at Julius West Middle School in Rockville, Maryland.
I've posted links to OK Go's music videos before, and I still think they are amazing. Here's a chance to use their song "One Moment" to show a connection between music, science, engineering, and mathematics. To make events happen at exactly the right time in the video, and to link them perfectly to the beats of the song, takes a major spreadsheet and a good understanding of math an physics. Damian Kulash does a great job explaining his process here. YouTube link | Archive