Teacher: Ms. Fountain

School:  Oromocto High School

Subject: Geometry & Applications

Grade Level:  112

Content/Theme: Probability       

From: October 4, 2005

To: November 3, 2005

No. of  days/minutes: 20 classes

Daily Outline:

September 26 – ½ Class: Probability Diagnostic Test 

October 4: Introduction to Probability and Quantifying Outcomes => Focus A and Probability Games (Card Game from text), Animal Game)

October 5: Probability and Quantifying Outcomes => Optional Investigation and Questions - Modeling The Driver’s Test, and Utilizing a Graphing Calculator - The “Meeting Problem”

October 6: Chapter Project and Practice Questions for Unit Assignment

October 7: Introduction to Tree Diagrams and The Fundamental Counting Principle=>, Investigation 3, When A    Loss Could Have Been A Win Activity, and Questions

October 11: Applying the Fundamental Counting Principle to Probability and Dependent and Independent Events    => Did You Know? Riddle (from text), Focus B, Investigation 4, and Game Show: Drawing a Tree Activity

October 12: Applying the Words “And” and “Or” using Venn Diagrams => Investigation 5, Investigation 6, The Union of Intersections Activity

October 13: The Addition Principle => Focus C, A Fair Deal for the Carrier Activity, and Questions

October 17: Area Models and Probability => Focus D, Investigation 7

October 18: Chapter Project and Practice Questions

October 19: Enhancements (Calculating Conditional Probability, Focus E) or Review of Missed Concepts, and Quiz (5.1 & 5.2)

October 20: Combinations and Permutations => Investigation 10 and Questions

October 21: Factorial Notation => Focus F, Using a Graphing Calculator, and Questions

October 24: Writing an Expression for Permutations => Investigation 11, Definitions, Practice with Permutations and Combinations Worksheet, and Use of Graphing Calculator

October 25: Determining the Number of Possible Combinations => Focus G, Compound Event Activity and Chapter Project

October 26: Applications to Probability => Focus H, Lotto & Gambling Activity, Review or Enhancement Questions

October 27: Applications to Probability => Practice/Review Questions and Quiz (5.3 & 5.4)

October 31 - ½ Class: Constructing Pascal’s Triangle => Investigation 12

November 1: Pascal’s Triangle with Combinations and Expansion => Investigation 13, Investigation 14, and Pascal’s Triangle Activity

November 2: Raising Polynomials to Any Power => Focus I, Chapter Project and Practice Questions

November 3: Final Unit Quiz/Test, then Portfolio Projects due November 7

Objectives:

Students will learn to:

1. use the Fundamental Counting Principle to calculate probabilities.

2. use area diagrams and tree diagrams and simulations to solve problems involving probabilities of
    dependent and independent events.

3. define combinations and permutations and use them to find probabilities.

4. relate combinations, Pascal’s triangle, and coefficients of binomial expansions.

Curricular Outcomes: 

A6 develop an understanding of factorial notation and apply it to calculating permutations and
        combinations

B8 determine probabilities using permutations and combinations

G13 develop and apply simulations to solve problems

G23 demonstrate an understanding that determining probability requires the quantifying of outcomes

G33 demonstrate an understanding of the fundamental counting principle and apply it to calculate probabilities of
        dependent and independent events

G4 apply area and tree diagrams to interpret and determine probabilities

G7 distinguish between situations that involve permutations and combinations

G8 develop and apply formulas to evaluate permutations and combinations

G9 demonstrate an understanding of binomial expansion and its connection to combinations

G10 connect Pascal’s Triangle with combinatorial coefficients

Possible Enhancements:

G5(111) determine conditional probabilities

G11(111) connect binomial expansions, combinations, and the probability of binomial trials

G12(111) demonstrate an understanding of and solve problems using random variables and binomial
                  distributions

Skills:

 Students will be able to:

1. demonstrate an understanding of the Fundamental counting Principle and apply the principle to find        
     probabilities,

2. apply area diagrams and tree diagrams to determine probabilities of dependent and independent events,

3. use simulations to solve problems involving probabilities,

4. define and calculate combinations and permutations,

5. calculate probabilities using permutations and combinations, and

6. explain the connection between combinations, Pascal’s triangle, and coefficients of binomial expansions.

Products / Assessment Methods:

Group Work Assessments (Formal and Informal)

Quizzes – 2

Quiz/Test – 1

Portfolio Project

• Chapter Project

• Practice Questions (assigned)

• Other Questions

• Journal Entries

Performance Assessments (on Portfolio Project)

Process/ Teaching Strategies:

**Lecture
**Demonstration
    Guest Speaker
**Co-operative Learning
**Discussion
    Debate
    Learning/Interest Centers
**Independent Study
**Small Group Study
**Peer Tutoring
    Role Play
    Field Trip
**Note Taking
**Experiment
**Learning Games
 

 Multiple Intelligences: 

Linguistic intelligence – through word problems and through journal writing as a component of their portfolios

Logical-mathematical intelligence – through activities and logical mathematicalquestions and concepts

Bodily-kinesthetic intelligence – through activities class activities that involve movement

Spatial intelligence – through pictorial activities and visual probability problems

Interpersonal intelligence – through group work in activities

Intrapersonal intelligence – through individual work and self-reflections as a component of their portfolios

Learning Styles: 

Visual – through use of print, pictures, charts in the text and on activity sheets

Auditory – through group discussion and whole class discussion of activities, as well as small lectures

Kinesthetic – through use of active group activities that include movement around the room

 Bloom’s Taxonomy: 

Knowledge – Define probability and probability notation.

Comprehension – Distinguish between dependent and independent events with respect to probability.

Application – Apply the Fundamental Counting Principle to Probability

Analysis – Determine the number of possible combinations in a situation

Synthesis – Predict final results in the expansion of a generalized expression for polynomials.

Evaluation – Evaluate lottery odds and the results of gambling in North America or Canada.

Resources & Materials: 

Blackline Masters, Activity Sheet Handouts, Cards, Dice, Spinners, Graphing
Calculators, Instruction Task Sheets, Portfolio Guidelines (one overview or in
pieces), quizzes, test, overhead projector, and overheads for various activities
and topics.

Differentiation of Curriculum:

There are varying activities from basic to difficult level already incorporated throughout the course to appeal to students at all levels. There is also time allowed for enhancement activities that would allow for more investigation.

For learners having a hard time, have provided resources with a slower introduction and easier practice questions to allow them to learn at their level and gradually improve.

For learners looking for or needing more of a challenge, have provided enhancement activities (primarily from the textbook) that allow them to explore probability in more depth.