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:

• Mean
• Median
• Mode

• 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
• Hand-held 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
• Content-specific pedagogy - Theories necessary for implementing sound representations of numeric and algebraic concepts
• Science as inquiry - Development of ability to:
• 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 6-8:
• Algebra, Patterns, and Functions - Students will algebraically represent, model, analyze, and solve mathematical and real-world 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

(Go to the Adobe Acrobat® website for a free software download if you do not have the plug-in.)

 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 instructor-set 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 material-newspapers, 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 teacher-defined 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 Mean or Median incorrect 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 pay-offs 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 instructor-set 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