All materials, with the exception of a few worksheets, all assessments, and rubrics, have been provided by the Shodor Foundation.

 

Abstract

The unit is designed to introduce middle school students to statistical data and methods of representing data derived from the statistics. It is a 20 hour module (5 hours instruction and 15 hours of lab work) which allows the student to model life situations through the use of the graphs to include circle graphs, histograms, bar graphs and stem and leaf graphs. The primary lab tool being presented will be Project Interactivate. As a result of this module, the student will have a firm grasp of the subject and have improved understanding of statistics and how it correlates to the world around them.

 

Objectives

 

Upon completion of this unit, students will:

·        understand three different measures of  “center”

·        have been exposed to multiple ways of expressing sets of numbers

·        have practiced their arithmetic skills

·        have been introduced to histograms and bar graphs

·        have understood the difference between bar graphs and histograms

·        have seen examples of how data can be represented in a variety of graphical forms

·        have been introduced to the notion of stem-and-leaf plots have learned the terminology used with stem-and-leaf plots

·        have used stem-and-leaf plots to calculate mean, median, and mode of a set of data

·        communicate knowledge and understanding in everyday and mathematical language

·        understand concepts and procedures from statistics

·        define and solve problems

·        use mathematical reasoning

·        formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

·        select and use appropriate statistical methods to analyze data

·        develop and evaluate inferences and predictions based on data

 

Student Prerequisites

 

To complete this module, students should have a general understanding of arithmetic operations including: addition, subtraction, multiplication, and division of whole numbers and decimals (with or without calculator use). Students will need the ability to use a mouse and browser.

 

Teacher Preparation

 

• Students need access to a Java-capable browser and appropriate software
• Students will need pencil, paper, and/or calculators

 

Unit Outline

 

• What are statistics and data?
• Measures of center.
• Graphing (frequency table, histogram, bar graph, stem-and-leaf plot, pie chart)

 

References and Resources

           

Project Interactivate

            Washington State Essential Academic Learning Requirements   

            National Council of Teacher of Mathematics Standards

 

Activities

 

• Measures activity
• Sample problems on mean, median, and mode
• Discussion on mean, median, and mode
• Measures exploration questions
• Histogram exploration questions
• Sample problems on histogram scales and impressions
• Class interval discussion: scale and impression
• Plop It activity
• Sample problems on bar graph scales
• Vertical scale discussion: increase or decrease
• Sample problems on bar graph class intervals
• Histogram vs. bar graphs discussion
• Sample problems on comparing histograms and bar graphs
• Stem and leaf plot discussion
• Worksheet to accompany the stem and leaf plot lesson
• Circle Graph (pie chart) exploration questions
• Pie chart recording work sheet
• Activity Rubrics

 

 

 

 

 

 

Standards Addressed

           

Probability and Data Analysis (National Council of Teachers of Mathematics)(NCTM)

Geometry (National Council of Teachers of Mathematics)(NCTM)

Probability and Statistics (Washington State Essential Academic Learning

Requirements)(EALR’s)

Number Sense (Washington State Essential Academic Learning

Requirements)(EALR’s)

Geometric Sense (Washington State Essential Academic Learning

Requirements) (EALR’s)

 

Cross Curricular Connections

           

This module covers skills that are used in all core academic and technology areas.

 

Assessment Techniques

           

Journal recording

            Performance assessment using paper and pencil

            Student assessment

            Assigning grades to journals

           

Glossary

           

Average

Chart   

Class Interval

Data

Dependent Set

Distribution

Frequency Table

Graph

Histogram

Horizontal Axis

Independent Set

Mean

Measure of Center

Median

Mode

Multi-modal

Outlier

Plot

Quadrant

Qualitative Data

Quotient

Range

Sector

Sequential

Statistics

Sum

Vertical Axis

 

 

 

 

 

 

 

 

 

 

 

 

 

Procedures For Mean, Median, Mode Lessons

 

• Instructor will model the applet “Measures Activity” using plant height data.
• Leading Questions-----                        

• Q: What do you think the mean is?
• Q: Why do you think there is no mode?
• Q: What do you think median means?

• Students will read “What”, “How”, and “Why” for the “Measures Activity”, recording the definitions of mean, median, mode, and range in their journal notebook.
• Students will explore what happens to data as it pertains to mean, median, and mode through the “Measures Exploration Questions” (Measures Activity).
• Instructor and students will discuss the results of the “Measures Activity”.
• “Mean, Median, Mode Discussion”.
• Students individually complete “Sample Problems on Mean, Median, and Mode” using paper and pencil.
• In groups of four, students will discuss their answers to the sample problems and decide which measure of center is most appropriate for the given data set.
• Individual groups will share their findings with large group.
• Determine, by group discussion, why a certain measure of center is chosen for a particular data set.
• Students describe measures of center and their relationship to statistics in their journal.
• Paper and pencil assessment.

  A web version is also available here.

    

 

Assessment: In Journals----

• Students will be asked to describe, in their own words, what statistics, data, mean, median, and mode are as they pertain to data collection.

• Students will be asked how mean, median, mode, and range relate to each other?
• Students will be asked to described measures of center and their relationships to statistics.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Procedures For Histograms and Bar Graph   

 

Bar Graphs                                                                

 

• Instructor will model the applet “Plop It” by soliciting students’ birthday month/date.
• Leading Questions-----                        
• Q: What can you say about what the graph is telling you?
• Q: If you change the numbers on the vertical scale, what will that do to the appearance of the graph?

• Students will explore the mean, median, mode relationship to bar graphs through “Plop It Exploration Questions”.
• In groups of four, students will discuss and share with large group their solutions to the exploration questions.
• Students use graph paper and pencil to solve “Sample Problems on Bar Graph Scales”.
• In groups of four, students will discuss and share with large group their solutions to the sample problems and decide which vertical scale is most appropriate for the given data sets.
• Determine, by large group discussion, why a vertical scale is best for a particular data set using “Vertical Scale Discussion: Increase or Decrease?”.
• In journals, students define bar graph and communicate the purpose of increasing or decreasing the vertical scale on a bar graph.

 

Assessment: In Journals----

• Students will define bar graph and vertical scale.
• Students will describe the purpose of increasing or decreasing the vertical scale on a bar graph.

Paper and pencil quiz.

A web version is also available here.

 

 

 

 

 

 

 

Histograms                                        

 

• Instructor will model the applet, “Histogram Activity” using data sets in the activity.
• Leading Questions-----

• Q: Look at the word histogram. What do you think it means? (history) (something written or drawn)
• Q: What is happening to the picture of the graph as it is being changed (teacher is changing class interval in the activity)?

§         Q: Is the data itself changing or is it the appearance of the data changing?

• Students will read “What?”, “How?”, and Why?” for the “Histogram Activity”, and record the definitions of range, histogram, frequency, and class interval in their journal notebook.
• Students will explore given data as they solve the “Histogram Exploration Questions” within the “Histogram Activity”.

• Instructor and students will discuss the results of the “Histogram Exploration Questions”.
• Class discussion: “Class Interval Discussion: Scale and Impression”.
• Students individually using paper and pencil solve “Sample Problems on Histogram Scales and Impressions”.
• In groups of four, students will discuss their answers to the sample problems, deciding which interval is most appropriate for the given data sets.
• Individual groups will share their findings with large group.
• Determine, by large group discussion, why a certain interval is best for a particular data set.

• Students describe class interval and its usage with histograms in their journal.
• Large group discussion, “Histograms vs. Bar Graphs Discussion”.
• Assessment: Using graph paper and pencil, individually, the students will complete, “Sample Problems on Comparing Histograms and Bar Graphs”.

Paper and pencil assessment.

A web version is also available here.

 

Assessment: In Journals----

• Students will define class interval, range, histogram, frequency, and class interval.
• Students will describe class interval usage and its relationship with histograms

 

 

 

Lesson on Stem and Leaf Plots                  

 

• Students need to read the “What?” page in the “ Stem-and-Leaf Plotter Activity”.
• In small groups students discuss the definition and usage of stem-and-leaf plots.
• In large group students will share small group results.
• Instructor and students will debrief using the “Stem-and-Leaf Plots Discussion”.
• Instructor models how to use the “Stem-and-Leaf Plotter Activity”.
• Students will complete problems 1 and 2 using the “Stem-and-Leaf Plotter Activity”.
• Review results of problems 1 and 2 with the students.
• Using graph paper and pencil, students construct stem-and-leaf plots for problems 3 and 4. 

Paper and pencil assessment.

A web version is also available here.

 

Assessment: In Journals----

• Students will record the definition and purpose of stem-and-leaf graphs and their relationship to mean, median, and mode of a data set.
• Students will describe the relationship between stem-and-leaf graphs and measures of center.

Lesson on Pie Charts                                                        

 

• Instructor models the applet, “Pie Chart Activity:” using data generated by asking students which of these 5 candy bars they prefer: Snickers, Kit Kat, Butterfinger, Big Hunk, Baby Ruth. Data will be converted from numbers to percentages to degrees.
• Students record activities on the >““Pie Chart Recording Worksheet” for a 24-hour period following  the modeling lesson.
• Students complete the pie chart data sheet and use “Pie Chart” applet to compare results.
• Students will explain any variations from their graph to the applet comparison graph in their journals.

 

Assessment: In Journals----

• Students will record any variations from their graph to the applet comparison graph.