CAN YOU SEE THE DATA?
ESTIMATED TIME TO COMPLETE: 75 minutes
MODULE OBJECTIVES:
Students will understand the role of visualization tools to enhance quantitative understanding.
CONCEPT(S) LEARNED IN THIS MODULE:
Box and whisker plots and environmental measures
STANDARDS ADDRESSED BY UNIT MODULES:
 Praxis(0016):
 Curriculum components  Appropriate materials and technology
 Problem solving
 Investigate and understand content
 Formulate problems for everyday situations
 Verify and interpret results
 Build student confidence
 Solve problems that are developmentally appropriate
 Probability and Statistics
 Counting
 Organizing
 Representing
 Interpreting data
 Handheld calculators and computers  Computer based interactive software and graphing calculators in problem solving and concept development
 Classroom management and motivation
 Problem solving
 Experimentation
 Small group instruction
 Whole group construction
 Efficient instruction
 Analysis of students’ work  Use of rubrics
 Use of manipulatives and developmentally appropriate materials  Variety and reliability
 Contentspecific pedagogy  Theories necessary for implementing sound representations of numeric and algebraic concepts
 Science as inquiry  Development of ability to ask questions, investigate, observe, construct explanations and communicate results
 Praxis(0069):
 Organize data into an appropriate presentation  Use of interactive software and graphing calculators for organizing and evaluation of data.
 Read and analyze data presented in various forms
 Solve problems involving average
 Draw conclusions from data
 MSPAP 58:
 Environmental Science  Students will use scientific skills and process to explain the interactions of environmental factors (living and nonliving) and analyze their impact from a local to a global perspective.
 Life Science  Students will use scientific skills and processes to explain the dynamic nature of living things, their interactions, and the results from the interactions that occur over time.
 Algebra, Patterns, and Functions  Students will algebraically represent, model, analyze, and solve mathematical and realworld problems involving patterns and functional relationships.
 Statistics and Probability  Students will collect, organize, display, analyze and interpret data to make decisions and predictions and will use experimental methods and theoretical reasoning to determine probabilities to make predictions.
 Number Relationships and Computation  Students will describe, represent and apply numbers and their relationships and will estimate and compute using mental strategies and paper/pencil.
 Processes of Mathematics  Students will use reasoning to solve problems in mathematics, be able to communicate the processes used and the solution(s) while making connections within mathematics, to other disciplines, and to the real world.
TECHNOLOGY  ENHANCED INSTRUCTIONAL STRATEGIES UTILIZED IN THIS MODULE:
Computer and graphing calculator based visualization investigations
Component 
Brief Description of Module Activities 
Student Grouping 
Materials/Technology 
Engagement 
Students will be given two sets of data (See Teacher Notes) and asked to determine the mean, mode and median. The mean and median values will be equal in both sets of data and there will not be a mode; thus through discussion, the need for other ways to draw conclusions about the data will be noted.

Whole class 
Calculators appropriate but not required 
Exploration 
Students will be instructed in the five number summary for data and how to display it in a box and whisker plot. Students will visit the Interactivate site at www.shodor.org and see the applications of box and whisker plots. 
Whole class and pairs 
Web access 
Explanation 
Students will receive instruction on completing a box and whisker plot on the graphing calculator. Students then analyze data given in the engagement using box and whisker display. 
Whole class 
Graphing calculators 
Extension 
Students construct comparative box and whisker plots to evaluate a data set. 
Individual 
Graphing calculators 
Evaluation 
Students are given real world data and are asked to make an informed decision from information derived in their construction of comparative box and whisker plots. 
Individual 
N/A 
EXPECTED MODULE OUTCOMES:
Students will be able to:
 Construct Box and Whisker plots
 Use the box and whisker plot as a tool in analyzing the data and drawing conclusions.
PERFORMANCE BASED ASSESSMENT OF MODULE OUTCOMES:
Students construct comparative box and whisker plots of three of the five selected water sites at the web sites indicated below.
SCORING RUBRIC:

Data Analysis 
Display 
2 
 At least three comparative statements regarding water quality
 Correct five number summaries for each data set

 Appropriate title and correct labels
 Correctly scaled
 All five number summaries on each plot are labeled

1 
 Only two comparative statements
 Minor errors in five number summaries

 Appropriate title and correct labels
 Correctly scaled
 Five number summary label are incomplete

0 
 Incorrect comparative statements
 Five number summaries have major errors

 Incorrect scaled line or missing labels

TEACHER NOTES:
Teachers should find (webbased) background reading on dissolved oxygen as a measure of water quality
(e.g. www.dnr.state.md.us/bay/monitoring/water/index.html)
 Engagement Activity:
The following data exemplifies dissolved oxygen readings and yields nearly equal mean and median values thus necessitating a need for an alternative method to analyze the data. Have the students compute these central tendency measures and then lead a discussion of what they know about other ways to "show" the data.
 Dissolved oxygen levels at Site 1:
12.21, 10.78, 10.29, 9.28, 8.72, 8.47, 7.53, 6.22 (ppm)
 Dissolved oxygen levels at Site 2:
10.25, 9.5, 9.05, 8.98, 8.75, 8.5, 8.47 (ppm)
 Exploration:
As a part of the teacher explanation of the five number summaries and what a box and whisker plot is we recommend a "human" box and whisker based on heights of students in the class. Students are then ready to explore the Box Plots tool at Interactivate.
 Evaluation:
Maryland environmental water quality data available at
www.chesapeakebay.net/data/index.htm
Unit Description
Module 1 2 3 4