Skittles Statistics: A 10

th

Grade Geometry Lesson

1

Carol Clinton

1

, Rebecca Richmond

2

Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati OH;

2

Hughes Center, Cincinnati, OH

Abstract

Students will environmental use testing Skittles results, candy to analyze simulate statistical properties of the data set, plot the data, then interpret it to predict simulated health outcomes.

This lesson links math to the science of toxicology, which is used by environmental engineers and public health officials routinely to assess risks and apply technologies to protect the public health.

Goals

Students should understand basic statistical concepts and how to analyze and graph data sets.

Students will also be exposed to environmental engineering use of statistics concepts to protect health and the environment.

Objectives

Students will calculate mean, median, mode, lower quartile and upper quartile for a data set representing environmental testing data; construct a histogam and a box & whiskers plot; then interpret the data against “toxicity data” to predict health outcomes of exposures to levels of a “pollutant” represented by the data set.

State Standards

Data Analysis and Probability Standard A.

Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.

D. Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.

E. Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.

F. Construct convincing arguments based on analysis of data and interpretation of graphs.

K.

Make predictions based on theoretical probabilities and experimental results.

Activity

Environmental engineers also use statistics to assess likelihood of harm from environmental exposures. Mention punnet square, use of statistics in biology – likelihood of traits being passed along.

Gregor Mendel got his basic data from growing peas. We use data that toxicologists get from killing creatures. They figure out what dose/concentration of a substance it takes to cause harm (how much in the air, how much in the water). Engineers take air & water samples to figure out what the concentration is, then they make predictions about what might happen.

some Today we’re going to use “tox” data and some concentration data and use it to predict who will die.

Attention Getting: You may be thinking these Skittles on your table are just delicious candy – but today they will tell us who will die.

Content: We’ll be using the math concepts of mean, median and mode to explore the meaning behind numbers.

We’ll discuss the definitions of these terms, and practice calculating the mean, median and mode of sets of numbers.

Most importantly, we’ll discuss what those numbers mean.

Mean, median and mode are important because you’ll be seeing problems involving them on the proficiency test; but more importantly because they can help you understand the significance of numbers (data) that people may give you to describe health risks.

Activity: Toxic Exposures?

The skittles represent air samples that were analyzed for dimethyl chickenwire (DCW) level.

and it was found that: DCW has been through toxicity testing

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The IDLH (immediately dangerous to life and health) value is 15 parts per million (ppm)

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The LD50 (level that causes death to half of the population) is 7 ppm - There are 2 ways to die:

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Acute – any one at the IDLH (15)

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Chronic – mean above the LD50 (7) Coding system:

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Green skittles represent samples that had no detectable DCW

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Yellow had 3 ppm

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Orange had 5 ppm

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Red had 10 ppm

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Purple had 15 ppm Results for air quality in your community are shown in the bag of skittles for your table.

Don’t eat the skittles (at least right away), let’s use them to figure out who will die by calculating the mean, median, mode, range and using the data to plot histograms and box and whiskers plots.

Compute sample space (how many possible data sets are there? How many possible combinations?)

Conclusions Average class improvement in scores comparing pre and post test was 134%.

For individual students who took both the pre and post test, improvement averaged 174%.

Improvement in Scores

800 600 400 200 0 -200 0 5 10 15

Student ID

20 25 30 Series3

The average score on classwork was 84%.

Classwork Scores

120 100 80 60 40 20 0 0 5 10 15

Student ID

20 25 30

References

Series2 •

Bass, Laurie E. and Johnson, Art; Prentice Hall Mathematics Geometry, Pearson Education, Inc.; Saddle River, New Jersey; 2004

•

Andres, Richard J. and Bernstein, Joyce; Preparing for the OGT in Mathematics; Amsco School Publications, Inc.; 2004

Acknowledgments

Project STEP is funded through NSF Grant # DGE058532 Appreciation is particularly given to the following for their assistance in development and implementation of this lesson: Ms. Rebecca Richmond – Hughes High School Dr. Richard Miller – University of Cincinnati Andrea Burrows – University of Cincinnati