Capture-Recapture

Imagine that a city employee is given the task of counting the number of fish in a city pond in a park. The “capture-recapture” method may be used to approximate the number of fish in the pond. The employee could capture a number of fish, say 20, and tag them and release them back into the pond. Waiting until the fish have a chance to become mixed with the other fish in the pond, the employee can capture more fish. If the number of fish captured is 25 and 4 of them are tagged, we can use proportional reasoning to estimate the number of fish in the pond.

SRS vs. Convenience Sample in the Gettysburg Address

Students have an interesting view of what a random sample looks like. They often feel that just closing their eyes and picking “haphazardly” will be enough to achieve randomness. This lesson should remove this misconception. Students will be allowed to pick words with their personal definition of random and then forced to pick a true simple random sample and compare the results.

The Forest Problem

Students want to know why they would ever use a sampling method other than a simple random sample. This lesson visually illustrates the effect of using a simple random sample (SRS) vs. a stratified random sample. Students will create a SRS from a population of apple trees and use the mean of the SRS to estimate the mean yield of the trees. Students will then create a stratified random sample from the same population to again estimate the yield of the trees. The use of the stratified random sample is to control for a known source of variation in the yield of the crop, a nearby forest.

Flintstone's Writing Project - Sampling

This writing project was written as a letter from Fred Flintstone to the students asking for their advice on proper sampling techniques that requires their mathematical “expertise”. This clearly defines the target audience for the paper and gives the students an idea of the mathematical background that they should assume of the reader. The plot lines in the project is a little bit goofy, although not imprecise, which helps relax the students and gives them the opportunity to be creative when writing their papers.

Sampling Techniques - Jelly Blubbers

This activity introduces the Simple Random Sample (SRS) to students, and shows why this process helps to get an unbiased sample statistic. Relying on our perceptions can often be deceiving. In this exercisestudents are asked to determine the average length of a jellyblubber (a hypothetically recently discovered marine species) using a variety of techniques. The student will learn that a Simple Random Sample (SRS) is the most accurate method of determining this parameter, and that intuition can be deceptive. 

M & M Variablility

Central Tendency and Measures of Dispersion

Goal: The goal of this activity is to allow students the ability to practice data collection and find measures of central tendency and dispersion. Wrap up questions will also allow for an insight into how each of these calculations are related to one another. Materials needed: 12 small bags of M & M’s (they can be the fun size or regular packs), calculator and the M & M worksheet and answer sheet.

Inferences about two populations

Goal: The goal of this activity is for students to compare to samples from two different populations. They will make inferences based on what they find from their dot plot.

Estimating the Mean

Goal: The goal of this activity is for students to randomly draw words from an excerpt to estimate the mean length word count of the entire document.