Skittles Statistics:A 10th Grade Geometry Lesson

Carol Clinton1, Rebecca Richmond21 Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati OH; 2 Hughes Center, Cincinnati, OH

Abstract Activity Conclusions

Goals

References

Objectives

State Standards

AcknowledgmentsProject 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 SchoolDr. Richard Miller – University of CincinnatiAndrea Burrows – University of Cincinnati

Students will use Skittles candy to simulate environmental testing results, analyze 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.

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.

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.

Data Analysis and Probability StandardA. 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.

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. Today we’re going to use some “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. DCW has been through toxicity testing and it was found that:-The IDLH (immediately dangerous to life and health) value is 15 parts per million (ppm)- The LD50 (level that causes death to half of the population) is 7 ppm - There are 2 ways to die:

• Acute – any one at the IDLH (15)• Chronic – mean above the LD50 (7)

Coding system:-Green skittles represent samples that had no detectable DCW- Yellow had 3 ppm- Orange had 5 ppm- Red had 10 ppm- 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?)

The average score on classwork was 84%.

• 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

Improvement in Scores

-200

0

200

400

600

800

0 5 10 15 20 25 30

Student ID

% Im

prov

emen

t

Series3

Classwork Scores

020

406080

100120

0 5 10 15 20 25 30

Student ID

Scor

e (%

of 1

00)

Series2

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%.