Prepare: Print the provided ‘Data for printing’ sheet. You will need one per group—each page is one full set of data.
For each set (page) of data – 1) Cut out the data (one number/site per slip of paper) and group all data for each site. There are thin vertical gray boxes between the site name and the Enterococcus count; there are broad vertical gray boxes separating different columns of data. 2) Place the data for each site into a separate cup labeled for that site (e.g. “Battery – mid Hudson”).
Engage: Ask students: Is the Hudson River healthier in Manhattan or in Albany? Why? How do we decide whether water is healthy or not?
Explore: Students should assemble themselves or be assigned into groups of three. Pass out worksheets (one per student), graphs (one per group), and colored pencils.
Students then complete the sampling activity, as described in the worksheet. They will complete four rounds of sampling. In the first round, they will sample only 3 times from each site, using yellow pencils. They will then make an estimate of what they think the next sample would be (i.e. if they were to take another sample tomorrow). They decide which site they think has the most variability in the data and discuss and document their confidence in these answers.
The students then complete three more rounds of sampling, following the same steps above, but adding samples each time [Round 2 – draw 5 more samples (total 8); Round 3 – draw 7 more samples (total 15); Round 4 – draw 10 more samples (total 25)].
Finally, students answer the reflection questions on pages 3-4 of the sampling Activity worksheet. By the end of this process, students should develop an improved understanding of how science is conducted, the importance of replication for understanding variation in a system, and how this variation impacts the sorts of conclusions we can make.
Explain: Often, our estimates of ‘averages’ and ‘modes’ change as we collect more samples. Similarly, our confidence changes too. If we consistently sample a site and find very low variability in the sample values, we may quickly become confident that our next sampled value will be similar to those previously sampled. However, if we find a lot of variation in our samples, we may not feel very confident about what we think will be the value of the next sample drawn. Yet, as we collect more and more samples, we may gain confidence that the next value drawn will be within a certain range.
- Low variability in data = more quickly become confident in our estimates of ‘average’ and ‘mode’
- High variability in data = not as confident in our estimates, and we often need to collect many more samples to achieve a similar level of confidence in our estimates of ‘average’ and ‘mode’
Understanding the scientific process and how much confidence we ‘should’ have given a certain sample size and variation in the data is important when we use data as evidence for claims we make. The students are asked to make claims about whether any of the sites differ in their Enterococcus counts, or whether they have similar counts. The student should use the sample variation as evidence for their answers.
Extend: Students can create a bar graph of their data (using data averages), and compare and contrast the information provided by each type of data representation. This is a good opportunity to introduce the concept of error bars to the students. Error bars can help us gain a better understanding of the variability in bar graph data. You can go more in-depth into this topic if desired (math courses, AP, etc).
Evaluate: Use student answers to the worksheet questions to assess student understanding.