WHICH MEASURE?
ESTIMATED TIME TO COMPLETE: 75 minutes
MODULE OBJECTIVES:
Students will successfully use interactive tools  hand manipulatives and computer software  to construct meaning for the measures of central tendency.
CONCEPT(S) LEARNED IN THIS MODULE:
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  Use of computer based interactive software 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 computer based interactive tools for organizing data
 Read and analyze data presented in various forms
 Solve problems involving average
 Draw conclusions from data
 MSPAP 68:
 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 based estimation, computation, and the measures of central tendency
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Component 
Brief Description of Module Activities 
Student Grouping 
Materials/Technology 
Engagement 
Students will brainstorm to complete a list of mathematical concepts that could be taught using attribute blocks. (See Teacher Notes) This is intended to lead to an exploration of mean, median and mode.

Whole Class 
Overhead and class sets of attribute blocks 
Exploration 
Using a teacher designed worksheet, students will use the Interactivate software tool Plop It, accessed at www.Shodor.org to develop a)definitions of mean, median and mode, b) an understanding of the effects of changing values on the central tendencies of a set of data, and c) a working definition of mean. 
Individual 
Computer with web access, student worksheet 
Explanation 
Students will create/find data sets that meet instructorset criteria regarding the measures of central tendency. Students will be able to justify why a particular measure of central tendency is the best descriptor of a set of data 
Individual 
Web access, calculators 
Extension 
Students will share with class a recent news article that uses one of the measures of central tendency in its explanation. They will explain why the chosen measure is or is not the best representation of the data. 
Individual Whole 
Access to reading materialnewspapers, magazines etc. 
Evaluation 
Student poster demonstrating knowledge of mean and median utilizing attribute blocks. 
Individual 
General poster supplies 
EXPECTED MODULE OUTCOMES:
Students will be able to:
 Access and Apply Shodor’s Interactivate software
 Define (not just calculate) mean and median
PERFORMANCE BASED ASSESSMENT OF MODULE OUTCOMES:
Students will construct a visual display containing at least 5 different attribute blocks with a mean value equal to a teacherdefined number. Each student will also display the median value of his or her data.
SCORING RUBRIC:

Understanding of Math Concepts 
Presentation 
2 
 Mean equals teacher defined value and meets criteria for data values
 Median is correctly stated

 Poster is neat
 Organized
 Correctly colored and labeled

1 
 Mean is calculated correctly but data values don not meet criteria
 Median is correct

 Values and shapes shown but no color
 Work is neat

0 

 Incomplete work or no labels

TEACHER NOTES:
 Engagement Activity:
Teacher places a collection of attribute blocks on the overhead (Do not include circles). Ask students to contribute to a brainstorm list of concepts that could be taught using these manipulatives. (For example, perimeter, area, quantity, size, more than, less than, graphing) Next distribute collections of attribute blocks in a manner so that each student/group receives a variety of shapes, sizes and colors. Assign values to the different shapes and continue the brainstormed list by asking what further concepts could be discussed when numeric values are added. Teacher then asks, “If these blocks were payoffs in a game, how could we decide who could be called the winner?” This discussion should lead to an introductory discussion of mode and mean and provide a transition to the Exploration Component of lesson.
 Exploration:
Teacher first introduces students to Shodor site and Plop It! Tool. Teacher distributes the attached worksheet as a guided discovery lesson on mean and median. These questions are developed from questions provided in the activities section of Interactivate.
 Explanation:
The instructorset criteria will vary depending on the ability of students. These criteria may only establish a range for mean and mode, or the criteria may be a statement of the exact number of elements in the set, and a specific mode, median and mean.
Unit Description
Module 1 2 3 4