LU Title: Analyze This!

Author(s): Nancy Nowicki

Grade Level: 9

School Address: Holland Patent Central School

Subject Area: Applied Math

School Phone/Fax: (315) 865-8154

Declarative

Procedural

• Definitions Topic I

• Calculating probabilities

• Probability-number of ways an event can occur divided by the total outcomes.

• Drawing tree diagrams

• Sample-random selection

• Calculating permutations

• Sample Space-set of all possible outcomes for an activity

• Use of counting principle

• Probability of Events-sure to happen equals 1, never to happen equals 0.

• Construct frequency and cumulative frequency tables

• Tree Diagrams-a diagram that provides the total number of choices and the details for each sequence of choices.

• Construct frequency and cumulative frequency histograms

• Permutations-an ordered arrangement of objects.
• Counting Principle -helps in counting the number of elements in a sample space by using multiplication.
• Definitions Topic II
• Frequency -the number of times a data value appears in a list.
• Cumulative Frequency -the sum of all frequencies from a given data point up to and including the next data point.
• Histograms -a vertical bar graph whose bars are adjacent to each other.
• Mean-average
• Median-the middle value when a set of numbers is arranged in size order.
• Mode-data value that occurs most frequently in a given set of data.

• Calculate mean, median and mode

Benchmarks: Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.

Benchmarks: Students use measurement to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.

Standard: MST 3-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:

What declarative knowledge should studentsbe 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.

1. Definitions and general background information for probability, sample, sample space, probability of events, counting principle, permutations and tree diagrams.
2. Definitions and general background information for frequency, cumulative frequency, histograms, mean, median and mode. (The same process will be done with the statistics portion of this unit but at a later date.)

Students will individually on the computer using Riverdeep CD-ROM instructional software. 

Riverdeep, Inc.

17304 Preston Rd.

Suite 605

Dallas Texas 75252

FAX: (972) 381-4655

E-mail: info@riverdeep.com

Tel: (800)854-1259

Provide students with a graphic organizer and questions which will help lead them to the correct answers. 

To develop a working vocabulary, students will use Riverdeep CD-ROM. They will watch it one time through given the organizer questions (students will know what to look for). The students will then watch the segment again as they fill out the graphic organizer. We will then discuss the terms in class. 

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.

1. Calculate probabilities

Think-aloud process

Guided practice of problems

Point out common errors 

Review vocabulary as related to probabilities.

In collaborative groups, have students figure out probabilities given one bowl of pennies and one bowl of mixed coins

Additional practice problems will be given, we will do some together and the students will do others on their own.

 Quiz and Unit Test - multiple choice and performance lab related Part II.

• Draw tree diagrams

• Calculate permutations

• Use counting principle

• Construct frequency and cumulative frequency tables and histograms. Calculate mean, median and mode.

6. Unit Learning Log

LONG RANGE - After each chapter test, randomly put class scores on the board. Students will calculate mean, median and mode. Make histogram and tables of that information. Continue throughout the year with each unit test. Store data on computer, at the end of each semester extend to calculate percentiles, quartiles, etc. Graph all data on the computer.

Construct a graphic representation of the skill

Think-aloud process

Guided practice

Compare skill of tree diagrams to permutations

Practice problems with little variation

Have students write down the steps they used in their own words and create a graphic organizer.

Compare permutations and counting principle using a Venn Diagram

Construct a graphic representation of the skill

Provide students with graphic organizer

Guided practice

Point out errors and pitfalls

Discuss when and why you would use a tree diagram.

Practice examples together and on their own or in collaborative pairs.

Have students create their own tree diagrams based on their interests for example, cars - color, options, etc).

Discuss when and why you would use permutations

Use students to physically show different ways of lining up

Do other problems together and individually

Using the tree diagrams the students have created, have them calculate different combinations using permutations.

Discuss differences between permutations and the counting principle

Use students to physically show different possibilities when electing officials to a club

Practice problems together then individually

Discuss declarative knowledge

Practice problems in pairs - write out steps in students words

Throwing dice lab

Every 2-3 days students will do a self-reflection and self-evaluation log of their learning experiences. An analysis must be included throughout the unit.

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.

1. Tree diagrams, permutations and counting principle

• Frequency, cumulative frequency histograms

• Statistics and probability

• Comparing*
• Classifying
• Inductive Reasoning
• Deductive Reasoning*
• Error Analysis*
• Analyzing Perspectives
• Constructing Support
• Abstracting
• Other:

 Create a graphic organizer comparing tree diagrams, permutations and counting principle - list the similarities and differences, when each should be used and why.

Students will fill out a deductive reasoning matrix based on statistical information. (DOL Handbook, p. 107)

Students will be given completed problems. Using their graphic organizers and previous examples they will find errors and make corrections in the given problems.

Step 1

Step 2

Step 3

What knowledge will students be using meaningfully? Specifically, they will be demonstrating their understanding of and ability to...........

What reasoning process will they be using?

Describe student's products and performances and the criteria for evaluation.

Construct and interpret frequency and cumulative frequency tables and histograms. Construct and interpret tree diagrams as related to probabilities.

[ X] Decision Making
(selecting from seemingly equal alternatives or examining the decisions of others)
[) Problem Solving
(seeking to achieve a goal by overcoming constraints or limiting conditions)
[] Invention
(creating something to meet a need or improve on a situation)
[ ] Experimental Inquiry
(generating an explanation for a phenomenon and testing the explanation)
[ ] Investigation
(resolving confusions or contradictions related to a historical event, a hypothetical past or future event, or to the defining characteristics of something)
[ Systems Analysis
(analyzing the parts of a system and how they interact)
[ ] Other:

Products/Performances

Criteria for evaluation

In groups of 3:

1. Students will choose and research a product (with at least 3 options) that they may want to purchase (car - stereo, color, air-conditioning, etc)
2. Students will create a tree diagram and list the sample space based on the researched product and the options available.
3. Students will create and distribute a survey to the school population asking their opinions on their researched product. Students will then calculate and interpret the data received and create frequency tables and histograms on the computer using a program such as Microsoft Excel.
4. Students will write a report presenting their findings and results. The written report will include tables and histograms that were produced on the computer. The document must be done using Microsoft Word, importing the graphs from Microsoft Excel.
5. Students will give an oral presentation to the class using Microsoft Powerpoint. All students must speak. The students must use visuals such as posters, graphs and diagrams to help explain their project.
6. Students will keep a self-reflection and self-evaluation log of their learning experiences. An analysis must be included of the problems encountered through the project and improvements they would make if given the project again.

Element #1

Element #2

Element #3

Element #4

Elements

Scale

 Written Report

(Using Microsoft Word)

 Oral Presentation/Powerpoint Criteria

 Posters, Graphs and Diagrams/Excel Criteria

Self-evaluation and reflection log 

Decision Making

Weights

 50%

 30%

 10%

 10%

4

 The written report and computer components were fully developed, detailed and easy to follow. The report was handed in on time.

 Equal use of speaking distribution, excellent transitions. Exemplary dress and appearance. Exemplary use of vocabulary.

Exemplary use of Powerpoint.

 Neatly done and precise. Exemplary accuracy displayed. Exemplary use of color and graphics.

Exemplary use of Excel.

 Full development and detail of learning experiences. Fully addresses analysis of problems and improvements.

The student presents a comprehensive list of the most important possible alternatives and describes each in detail.

3

 The written report and computer components were well-organized and easy to follow. The report was handed in on time.

 Reasonable use of speaking distribution, smooth transitions. Appropriate dress and appearance. Consistent and precise use of vocabulary.

Reasonable use of Powerpoint.

 Neatly done, clear and precise. Reasonable accuracy displayed. Reasonable use of color and graphics.

Reasonable use of Excel.

 Reasonable development and detail of learning experiences. Reasonably addresses analysis of problems and improvements.

The student identifies alternatives that represent most of the important possible alternatives.

2

The written report and computer components were organized but somewhat confusing. The report was handed in 1-2 days late. 

 Moderate use of speaking distribution, moderate transitions. Moderate dress and appearance. Moderate use of vocabulary.

Moderate use of Powerpoint.

 Moderate neatness, somewhat confusing. Moderate accuracy displayed. Moderate use of color and graphics.

Moderate use of Excel.

 Moderate development and detail of learning experiences. Moderately addresses analysis of problems and improvements.

The student identifies some alternatives that are important and others that are not.

1

 The written report and computer components lacked organization and were difficult to follow. The report was handed in 3-4 days late.

 Speaking unequally distributed, awkward transitions. Inappropriate dress and appearance. Misuse of vocabulary.

Powerpoint not used effectively.

 Somewhat neat, difficult to follow. Some accuracy displayed. Little use of color and graphics.

Excel not used effectively.

 Lacked development and detail of learning experiences. Analysis of problems and improvements not addressed.

The student selects alternatives that are clearly not relevant to the decision.