Problem Solving Syllabus

Course Syllabus & Guidelines – Qualitative Analysis – Mr. Beretsky – Room B-230

Course Description and Expectations

Qualitative Mathematical Analysis (also known as Problem Solving) is a course for upper classmen who are serious about developing skills in problem solving, critical thinking, written communication and oral communication.  If you approach this course seriously, you will grow a great deal in these areas and have a good time doing it.  The Problem Solving Course reflects the belief that the Belchertown High School educational community fosters academic excellence and responsible citizenship in a positive, safe and respectful environment in order to develop productive contributors to society.  Algebra II is a pre-requisite.  It is a half year course (2 1/2 – graduation credits)

Problem Solving students are expected to:

  • Read mathematical problems actively and critically.
  • Write effective solutions to problems and projects
  • Present solutions to problems effectively
  • Use a variety of appropriate resources including the computer and calculator to solve mathematical problems
  • Employ multiple critical and creative thinking strategies in reasoning and problem solving
  • Demonstrate a knowledge and appreciation of how mathematics can be used outside the mathematics classroom
  • And meet all of the course objectives listed below

Topics will include the following Problem Solving Strategies:

  • Draw a Diagram
  • Systematic Lists
  • Eliminate Possibilities
  • Matrix Logic
  • Look for a Pattern
  • Guess and Check
  • Sub Problems
  • Unit Analysis
  • Solve An Easier Related Problem
  • Physical Representations
  • Work Backwards
  • Venn Diagrams
  • Algebra
  • Finite Differences
  • Organizing Information
  • Changing your Point of View

Emphasis is placed on developing problem solving strategies that can be applied in real life situations.

Course Objectives

The Student will be able to:

  • Work together with a group of students to solve a problem
  • Write detailed descriptions of solutions to problems
  • Present solutions to problems orally to groups of people
  • Demonstrate an understanding (orally and in writing) of a given problem
  • Choose an appropriate problem solving strategy (listed above) to solve a problem
  • Implement an appropriate problem solving strategy used to solve a problem
  • Get a correct answer to a problem and label the answer appropriately
  • Give a clear coherent and complete explanation of a given problem, the strategy used to solve that problems and the solution to that problem
  • Describe ways problem solving strategies are used in real world applications


Problem Solving Strategies -2nd Edition – Ken Johnson and Ted Herr – Key Curriculum Press – 2001

Internet Access

I have a homepage on the Internet.

This page will contain a course specific section on which I hope to put all homework assignments, projects, a copy of the course syllabus and links that will be helpful and interesting to you.  Be sure to visit this page regularly.  Email can be sent to me at

You are expected to bring the following materials to class every day:

Notebook (discussed in detail below)

– A binder with sections is recommended

– Lined paper

– Graph paper

Ruler – scaled in centimeters

Pens, pencils and erasers

Textbook – covered – at all times

A Calculator – Scientific or Graphing

General Classroom Behavior

  • You are expected to respect and value yourself, your school environment and the diversity of the BHS community.
  • You are expected to contribute to classes and work cooperatively whenever the situation requires.
  • You are expected to come to class prepared and you are responsible for all missing work
  • You are expected to use pencil and show work for all mathematics on homework, class work, projects, tests and quizzes
  • You are to be in your assigned seat when the bell rings.  Otherwise you are late which may result in a detention.
  • You are expected not to talk while I am speaking or interrupt while other people are speaking.
  • There will be no getting out of your seat or speaking without permission.  If you want to speak or get of your seat during class, raise your hand and wait to be recognized.
  • There will be no leaving the room except for emergencies, which should not occur often.
  • If you need to leave the room, just take the pass and leave as quietly as possible.
  • Books should be covered at all times.  If you lose your book, report it to me immediately.
  • The bell does not dismiss the class.
  • No eating or drinking in the classroom.
  • The Pass is to be used only in an emergency

Quarter Grading Policy

Your grade comes from point values assigned to tests, homework, cooperative group activities and Internet projects.  Quarter grades will be calculated by dividing the total number of points that you have earned by the maximum number of points that you could have earned and calculating a percent.  For example if you earned 600 points out of a possible 800 points, then you get 600/800  = 75%.

Graded Problem Sets will account for about 45% of your grade; Quizzes 10%; Homework 20%; Journal Writings 5%; Oral Presentations 10% and Cooperative Class Activities 10%

Semester Grading Policy

Quarter 1 – 40%                                                          A 90-100

Quarter 2 – 40%                                                          B 80-89

Final Exam – 20%                                                       C 70-79

D 65-69

F 0-64


You should have an organized notebook with four sections:

Section 1 – Class Notes

Section 2 – Problem Set – B’s

Section 3 – Homework Problems

Section 4 – Journal Entries

All materials should be neat and dated and each section of your notebook should be in chronological order.


Reading is required. Reading is an extremely important component of this course and will help you to learn the basic material you need to have a useful understanding of problem solving techniques.  There will often be reading assignments for homework, which you are required to complete.  Homework assignments, some quizzes and journal entries will be based on the reading.

Cooperative Group Activities

Cooperative group work will be encouraged and take place often.  Students will be part of a four or five person groups. Group members will change often. Cooperative activities will begin in class, but will often require work outside of the classroom in order to be completed.  There will be cooperative work almost every day of class.  Your participation in these activities will be observed and count for 10% of your grade.  In addition your cooperative work will help you with graded problem sets and homework. You must use a pencil to receive full credit.

Grading of Problem Solutions

All problems that are graded, whether they on a graded problem set, quiz, or final examination will be graded on the following criteria:

  • Understanding the Problem
  • Choosing a Solution Strategy
  • Implementing the Strategy
  • Getting the Answer
  • Explaining your Solution

(A complete assessment rubric will be given to you in a few weeks.)  You must use a pencil to receive full credit.  It is important for you to show all work and use words in all of your solutions!

Graded Problem Sets

Most of the credit in this class will come from graded problem sets.  These sets will be assigned weekly, beginning the third week of class.  There will be about 12-14 sets.  They are referred in your book as Problem Set B – They generally consist on 5 problems and are worth 50 points (each problem is worth 10 points and is graded according to the criteria outlined above.)  You will be given about a week to submit your solutions.  This will always include one class session in which you and your group will work on these problems together.


Half period / about 2 per quarter / Initially tests will be about reading, after that they will be on the current problem solving strategy.  Quizzes will have a maximum score of 50 points each.  You must use a pencil to receive full credit.


Homework assignments (posted on my homepage) will be given often and will often be graded.  Homework will consist of reading assignments and problems sets and journal entries.  Maximum grades will be 5 or 10 points.  A maximum grade indicates that you attempted all problems (work shown) and got most of them correct. 0 indicates you did not do your assignment, missed an assignment and did make it up, or made very little attempt.  Homework may be turned in one day late at reduced credit. You must use a pencil to receive full credit.

Oral Presentations

Each Day, students will be selected to present solutions to homework or group work projects.  You will be asked to do about 10 to 15 brief presentations during the semester.  Don’t worry about extra preparation for these presentations; just do your assigned work. Think of them as being asked to do a homework problem on the board.  Presentations are worth 10 points each.

Journal Entries

Throughout the semester you will be asked to reflect upon what you have learned or what you are working on in this class.  These entries are open-ended and give me a chance to have a dialog with you during the semester.  They are generally worth 5-10 points each and are usually assigned for homework.

Final Exam or Project

There will be a Final Exam or Final Project due.  The class will decide at the start of the third quarter, exactly which option to choose.  If a final exam is chosen it will consist of Problems, similar to ones you have done throughout the semester.

Make-up Work

If you miss a test, a project, a group activity or a homework assignment (posted on my homepage) for any reason, you are expected to make it up. Generally, you will be given up to one week from the day you return to make up that assignment.  For example, if you are out of school on Monday and return on Tuesday, you have until the following Tuesday to make up your work.  Incomplete work, for any reason, will count as a 0. Quizzes may be made up, before school, after school or during my study periods.

Extra Help

If you are having trouble with any material, you are expected to seek extra help from me.  I will be available after school in room B-230 from Monday to Thursday and before school by appointment on any school day.