Numbers a la Mode - Author(s): Jeff St. Crouix - Grade Level: 7-9 - Subject Area: Mathematics - In small groups students will be asked to organize assorted report card grades to demonstrate which report card is the best of the group. The grades can be organized in any way the group feels best to rank the cards from best student to worst student.

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LU Title: Numbers a la Mode	Author(s): Jeff St. Crouix
Grade Level: 7-9	School Address: General Brown
Subject Area: Mathematics	School Phone/Fax:

CONTENT KNOWLEDGE

Declarative	Procedural
Measures of Central Tendency-mean, median, mode, range, midrange, quartile.	Steps in making a graph by hand-bar, line, pie, picto.
Types of graphs-bar, line, pie, pictograph.	Steps involved in organizing statistics.
Collection and organization of statistical data.	Organizing statistics to create a spreadsheet on the computer and printing out bar, line, pie and pictographs.
Setup and use of a spreadsheet on a computer.	Calculation of Measures of Central Tendency.
Organization of a graph on graph paper.	Analysis of Statistical Data.
	Draw Conclusions.

ESSENTIAL QUESTIONS

In what ways can statistical data be organized?
How can you use statistics to demonstrate a particular point of view?
What makes statistics valid and reliable?

INITIATING ACTIVITY

In small groups students will be asked to organize assorted report card grades to demonstrate which report card is the best of the group. The grades can be organized in any way the group feels best to rank the cards from best student to worst student.

Connection to State Learning Standards

Content Area: Mathematics

Level: 7-9

Standard: 1: Analysis, Inquiry, and Design: Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

Standard: 2: Information Systems: Students will access, generate, process, and transfer information using appropriate technologies.

Unit Theme:

Statistics

Standard: 3: Mathematics: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Standard: 5: Technology: Students will apply technological knowledge and skills to designs, construct, use, and evaluate products and systems to satisfy human and environmental needs.

Learning Experiences

Declarative Knowledge

What declarative knowledge should e in the process of acquiring & integrating? As a result of the unit, the student will know or understand…

What experiences or activities will be used to help students acquire & integrate this knowledge?

What strategies will be used to help students construct meaning, organize and/or store the knowledge?

Describe what will be done.

Concept: Measures of Central Tendency (meaning of) - mean, median, mode, range, midrange, quartile

Concept: Ways to collect statistics - survey, observation, questionnaire, research, random sample, stratified random sample

Concept: Basic knowledge of different kinds of graphs - bar, histogram, line, pie, pictograph

Concept: Use of a spreadsheet on a computer

Textbook p.

Workbook p.

Handouts

Textbook p.

Workbook p.

Handouts

Textbook and other classroom resources

Current newspaper and magazines

Class will be held in the computer lab

Handouts

Brainstorming

Notetaking

KWL

Cooperative learning-small groups

Notetaking

Cooperative learning-small groups

Class discussion

Notetaking strategies

Brainstorming

Instructor lecture

Individual independent student work

Students will be given sets of data and asked to calculate measures of central tendency.

Instructor will present different methods of collecting statistics to the class. Discussion of when each method is appropriate. In small groups, students will be asked to match appropriate method to use for various groups of stats.

Students will be presented with a variety of sample graphs from various samples. They will be asked to evaluate the graphs for their effectiveness, looking at the scales and other parts of the graph.

Students will be given a group of statistics to be made into a spreadsheet to print out various graphs. Instructor will guide the students through the process step by step.

Learning Experiences

Procedural Knowledge

What procedural knowledge will students be in the process of acquiring & integrating? As a result of this unit, students will be able to:

What will be done to help students construct models, shape & internalize the knowledge?

Describe what will be done.

Calculate the following measures of central tendency: mean, median, mode, range, midrange.

Create the following graphs using graph paper and a ruler from a set of statistics-bar, line, pie, and pictograph.

*Changing the scalle of a graph is important to the point of view that a graph will show.

Create graphs from a spreadsheet on the computer: Bar, line, pie, pictograph.

Collect data from a specific source that is valid, reliable and accurate. Analyze and evaluate statistics for validity, reliability, and accuracy.

Textbook, workbook, and other classroom strategies. Visual examples. Demonstrate and have students practice variations.

Textbook, workbook, and other classroom strategies. Demonstrate and have students practice variations. Practice with different sets of numbers.

Class will be held in the computer lab. Students will be given steps needed to construct spreadsheet.

Textbook p.

Workbook p.

Visual examples

Demonstrate and have students practice.

Students will be given a variety of worksheets, examples and other samples of data with which to figure out all measures of central tendency. Some work will be done in groups and some individually. Students will also evaluate which measure is the best indicator for each set of numbers.

Students will construct graphs given a set of data. The students will learn how to change the scale of a graph to illustrate a certain point of view and also which graph is most appropriate for each set of data.

Students will construct a spreadsheet from statistics that they have collected on a topic of their choice. By the end of the class, student should print out desired graphs.

Students will be asked to analyze sets of data for validity, reliability and accuracy. They will then analyze the statistics that they collected in the same manner.

Learning Experiences

Extending and Refining

What knowledge will students be extending and refining? Specifically, they will be extending and refining their understanding of…

What reasoning process will they be using?

Describe what will be done.

Bar and line graphs

Comparing

Classifying
Inductive Reasoning

Deductive Reasoning

Error Analysis
Analyzing Perspectives
Constructing Support
Abstracting
Other:

Students will be creating bar and line graphs on graph paper and changing the scales.

Rubric:

Key Questions:

What are the key elements, traits, or dimensions that will be evaluated?

Are the identified elements of equal importance or will they be weighed differently?

CULMINATING PERFORMANCE RUBRICS

You are to collect and organize information and statistics on a topic of your choosing. You are to put it in a booklet or folder form. In this project, I want you to have the following items:

1. A paragraph or paragraphs describing how you collected your statistics. Specifically tell me where you got your information from, what steps you took to collect it and what were the total numbers from your sample. If you used a frequency table or a line plot, include it here. (11 points)

2. You are to make your own bar, line, pie, and pictograph using your statistics. You must use graph paper and a ruler. (36 points)

3. You are to use a computer to make a bar, line, and pie graph. (21 points).

4. Using your statistics, figure out the following measures of Central Tendency: mean, median, mode, range, and midrange. (20 points)

5. Collect sample graphs cut out of newspapers or magazines. You must have at least one example of each of the following graphs: bar, line, pie, and pictograph. (12 points)

SCORING GUIDE FOR CULMINATING PERFORMANCE

1. Paragraph describing how statistics were collected (11 points total)

________Steps taken to collect and organize statistics (2)

________Total number of all statistics (1)

________Individual numbers for each group of statistics (2)

________Description of data collected including random, population, sample, stratified (2)

________At least one conclusion that can be made from the statistics (2)

________Statement about reliability and validity of the data (2)

________Bonus points for line plot/frequency table (2)

________TOTAL POINTS PART 1

2. Hand made graphs (36 points total)

Bar, line, pie, pictograph-each graph is worth 9 points.

________Clear, accurate, and appropriate scales (3)

________X and Y-axis labeled (2)

________Straight lines drawn with a ruler (1)

________Title (1)

________Well organized and easy to read (2)

________Bonus points for coloring or extra graphs (2)

________TOTAL POINTS PART 2

3. Computer generated graphs (21 points total)

Bar, line, and pie graphs-each graph is worth 7 points.

________Clear, accurate, and appropriate scales (2)

________X and Y-axis labeled (2)

________Title (1)

________Well organized and easy to read (2)

________Bonus points for extra graph (2)

________TOTAL POINTS PART 3

4. Measures of Central Tendency (20 points total)

Mean, median, mode, range, midrange-each measure is worth 4 points.

________Explanation and work shown of how measure was arrived at (2)

________Measure is correct mathematically (2)

________Bonus points for upper and lower quartile (2)

________TOTAL POINTS PART 4

5. Sample graphs (12 points total)

One example of a bar, line, pie, and pictograph-each graph is worth 3 points.

________Appropriate example of each kind of graph (3)

________Bonus point for extra graphs (2)

________TOTAL POINTS PART 5

It is possible to score a maximum of 2 bonus points on each part of the project.

NOTE: Rubric or other performance assessment instruments may be used.

Have You Considered These Yet?

Learn to Learn Skills:

Assessment Modifications:

Unit Schedule/Time Plan:

SEQUENTIAL TIME LINE OF LESSONS

DAY 1: Initiating activity with measures of central tendency. Define each measure: mean, median, mode, range, midrange, upper quartile, lower quartile, line plot, frequency table. Briefly introduce project.

DAY 2: Discuss project in depth, give deadlines for topic, statistics collected, and final project. Review measures of central tendency.

DAY 3: Steps in making a line graph. Short quiz on central tendency.

DAY 4: Steps in making a bar graph. Difference between a bar graph and a histogram.

DAY 5: First day in computer lab. Show students how to construct a spreadsheet to use to print out graphs.

DAY 6: Steps in making a pie graph and a pictograph.

DAY 7: Representing a point of view. Students learn how changing a scale on a bar and line graph will change the perspective.

DAY 8: Methods of gathering statistics-inquiry, survey, counting, observation, research. Terms to define and discuss-population, sample, random sample, stratified random sample, reliable statistics (fair, reasonable, valid). What makes statistics valid and reliable.

DAY 9: Library activity-analyzing sample graphs cut out of newspapers or magazines.

DAY 10: Second day in computer lab. Students spend entire period printing out graphs and other parts of project.

DAY 11: Projects due. Test on unit.

*extra days may be added to review or to give an extra day to type, depending on calendar and activities at school.