Syllabus

Course Syllabus for First Quarter

#343 Probability and Statistics  (5 credits)

Text:  Tannenbaum and Arnold, Excursions in Modern Mathematics (1998)

Required Materials:  text, notebook and pen/pencil

Course Outline:

 

First Quarter – Collection of Statistical Data, Descriptive Statistics

 

Topics:

Topic 1:         Population/Sample and Parameter/Statistic (10.D.3)

Topic 2:         Random Sampling, Sampling Error, Selection bias, and Non-response bias (12.D.1)

Topic 3:         Graphical descriptions of data (10.D.1)

Topic 4:         Quantitative and Qualitative variables (12.D.1)

Topic 5:         Numerical Summaries of Data

Student Objectives:

  • Find or create study and describe population, sample, parameter, and statistic
  • Draw conclusions about a study using numerical statistics and graphs
  • Define variables used in a study
  • Take standard deviation, range, mean, median, five number summary for a data set 

 

Assessments:

  • Collins on Creating a Survey
  • Project on Five Number Summary

 

Grading:

  • Each test counts as 1 major grade (2-3 per quarter)
  • Every 2-3 quizzes count as 1 major grade
  • Notebook counts as 1 major grade
  • Homework counts as 2 major grades
  • Collins assignment counts as 1 major grade

 

Course Syllabus for Second Quarter

#343 Probability and Statistics (5 credits)

Text:  Tannenbaum and Arnold, Excursions in Modern Mathematics (1998)

Required Materials:  text, notebook and pen/pencil

Course Outline:

 

Second Quarter – Chances, Probability, and Odds, Distributions

 

Topics: 

Topic 1:         Random experiments and sample spaces (12.D.7)

Topic 2:         Counting and the Multiplication Rule (12.D.6)

Topic 3:         Permutations and Combinations (12.D.6)

Topic 4:         Probability Spaces, Odds, Independent Events

Topic 5:         Normal Curve and approximately normal distributions (12.D.4)

Student Objectives:

  • Calculate probability by: 
    • Sample spaces 
    • Counting 
    • Multiplication Rule 
    • Permutations and Combinations
  • Find probability spaces for experiments
  • Calculate odds using probability and vice versa
  • Use the normal curve to approximate values in set
  • Relate real-world problems to normal distribution

 

Assessments:

  • Collins on Normal Curve with Roulette
  • Project on Permutations and Combinations

 

Grading:

  • Each test counts as 1 major grade (2-3 per quarter)
  • Every 2-3 quizzes count as 1 major grade
  • Notebook counts as 1 major grade
  • Homework counts as 2 major grades
  • Collins assignment counts as 1 major grade

 

 

Course Syllabus for Third Quarter

#342 Discrete Math  (5 credits)

Text:  Tannenbaum and Arnold, Excursions in Modern Mathematics (1998)

Required Materials:  text, notebook and pen/pencil

Course Outline:

 

Third Quarter – Mathematics of voting, Fair Division, Euler Circuits

Topics: 

Topic 1:         Plurality, Plurality with Elimination, Borda Count, and Pairwise Comparisons

Topic 2:         Extended and Recursive Rankings

Topic 3:         Division of Continuous sets

Topic 4:         Division of Discrete sets

Topic 5:         Graphs and real life application

Topic 6:         Finding Euler Circuits and Euler Paths

Student Objectives:

  • Decide a winner of an election using voting methods
    • Plurality
    • Plurality with Elimination
    • Borda Count
    • Pairwise Comparisons
  • Use extended and recursive rankings to describe an election
  • Divide a set of goods among a set of players using methods
    • Divider-Chooser
    • Lone Divider
    • Lone Chooser
    • Last Diminisher
    • Sealed Bids
    • Method of Markers
  • Create a graph from a real-life problem
  • Find Euler Circuits and Euler Paths using Eulerization and semi-Eulerization

 

Assessments:

  • Collins on Finding Euler Circuit in Neighborhood
  • Project on Borda Count and Heisman

 

Grading:

  • Each test counts as 1 major grade (2-3 per quarter)
  • Every 2-3 quizzes count as 1 major grade
  • Notebook counts as 1 major grade
  • Homework counts as 2 major grades
  • Collins assignment counts as 1 major grade

 

Course Syllabus for Fourth Quarter

#342 Discrete Math  (5 credits)

Text:  Tannenbaum and Arnold, Excursions in Modern Mathematics (1998)

Required Materials:  text, notebook and pen/pencil

Course Outline:

 

Fourth Quarter – Hamilton Circuits, Networks, Mathematics of Scheduling

 

Topics: 

Topic 1:         Weighted graphs

Topic 2:         Hamilton Circuits and Paths

Topic 3:         Networks and trees

Topic 4:         Minimum Spanning Trees

Topic 5:         Scheduling

 

Student Objectives:

  • Find Hamilton Circuits by:
    • Brute-Force Algorithm
    • Nearest-Neighbor Algorithm
    • Repetitive Nearest-Neighbor Algorithm
    • Cheapest Link Algorithm
  • Find the Minimum Spanning Tree using Kruskal’s Algorithm given a weighted graph
  • Schedule several tasks using several processors using:
    • Decreasing-Time Algorithm
    • Backflow Algorithm
    • Critical-Path Algorithm
    • Using independent tasks

 

Assessments:

  • Collins on Hamilton Circuits
  • Project on Minimum Spanning Trees

 

Grading:

  • Each test counts as 1 major grade (2-3 per quarter)
  • Every 2-3 quizzes count as 1 major grade
  • Notebook counts as 1 major grade
  • Homework counts as 2 major grades
  • Collins assignment counts as 1 major grade


Learning Standards for Grades 9–10[1]

 

Data Analysis, Statistics, and Probability

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 that are based on data

Understand and apply basic concepts of probability

 
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

10.D.1            Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.

10.D.2            Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.

10.D.3            Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data. 

 

 

Learning Standards for Grades 11–12

Data Analysis, Statistics, and Probability

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 that are based on data

Understand and apply basic concepts of probability

 
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

12.D.1            Design surveys and apply random sampling tech­niques to avoid bias in the data collection.

12.D.2            Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data.

12.D.3            Apply regression results and curve fitting to make predictions from data.

12.D.4            Apply uniform, normal, and binomial distributions to the solutions of problems.

12.D.5            Describe a set of frequency distribution data by spread (i.e., variance and standard deviation), skewness, symmetry, number of modes, or other characteristics. Use these concepts in everyday applications.

12.D.6            Use combinatorics (e.g., “fundamental counting principle,” permutations, and combinations) to solve problems, in particular, to compute probabilities of compound events. Use technology as appropriate.

12.D.7            Compare the results of simulations (e.g., ran­dom number tables, random functions, and area models) with predicted probabilities.

 

 

[1] Massachusetts Department of Education, Mathematics Curriculum Frameworks 2000, Malden, MA.

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