Mathematics at Watershed

Emphasis on Projects, Challenge Sets and Logical Thinking.
 
Throughout the math program there is an emphasis on using projects and challenge sets to develop logical thinking, problem solving skills and an understanding of math concepts that is grounded in real world examples. A strong relationship with their teachers and classmates helps students feel free take risks, and to challenge themselves to think and communicate with clarity.  Every student has the ability to master the mathematics that will be interesting and useful in his or her life and career.
 
The first two years of math at Watershed provide a solid foundation in Algebra and Geometry. Some of the problems with math education stem from the “one size fits all” pacing that often occurs in schools. Students who take longer to grasp mathematical concepts get lost when the pace is too fast for them. Because they are swept along before they have mastered a skill, they are frustrated and develop an “I hate math” mindset . On the other end of the scale, are students who can progress rapidly and get bored waiting for the class to move on.  At Watershed, particularly in the first year, students can often work at their own pace, while still having a teacher in the room to help them overcome obstacles and to provide coaching.  The ALEKS system is a thoughtfully designed web-based program that requires students to work on problems with pencil and paper, and to enter their answers, not just choose among multiple choice answers. If their answer is incorrect, they will get immediate feedback and can try again. Using ALEKS helps us individualize our math program.
 
The second two years of math at Watershed allow students to prepare for different levels of postsecondary mathematics.  Watershed is able to provide appropriate math skills for every level of need. Some students complete Algebra II and Trigonometry, while others finish PreCalculus or Calculus. Our math teachers adjust the program to the needs of each year’s group and create interesting, rigorous and engaging math curricula for all Watershed students.
 
 

Math

Integrated Math 1

Integrated Math I

Instructor: Mary L. Smyth, MD

Fall 2017

Watershed School


Course Description:  This course will be using a problem-based, exploratory approach. The course is taught by assigning a challenge problem set  that the student first attempts on his/her own, followed by classroom discussion and then creation of written summaries.   Sample topics include linear models, slope, quadratic functions, factoring, dimensional analysis, number theory, triangle theorems, sequences and more.


Course Materials:


Phillips Exeter Academy Math curriculum (July 2013)

Many other online resources


Foundational Skills addressed:


The  Skills covered in this course include

NUMERACY  

Interpret and create graphs


Use abstract symbols in

quantitative reasoning


Solve quantitative problems with

the use of logic-based sequential

thinking


Recognize and describe how

relationships such as functions can

relate two quantities--an input and an

output


DIGITAL TOOL USE

Student can use handheld and/or online graphing technology to make and modify graphs.



PERSONAL GROWTH


A. study/life skills (organization, Cornell notes, time management, planning and setting goals)

B. persistence/attitude

C. basic social skills

D. listening and providing feedback

E. ethical decision-making

F. stress management

G. generic skills of the valued employee

Algebra 2

 

Algebra 2
Instructor: Sherry Frazer
Fall 2017
Watershed School


Course Description:  

Algebra 2 reviews and expands on some topics from Algebra 1. It makes use of students’ increasing ability with solving equations so that they can push farther.  Topics include absolute value, systems of equations, quadratic equations, variation, rational and radical expressions and the unit circle in trigonometry. My emphasis is on helping students understand where formulas come from and why they work.  Occasionally formulas need to be to memorized, however it is more satisfying to be able to derive new formulas from what you already know. I had a colleague who said, “Algebra makes numbers dance.”  Algebra 2 makes them dance the tango.

Expectations for Credit

Assessment will be through topic tests, a cumulative midterm and cumulative final. Tests are given at the end of each topic to give feedback on what was understood and where more clarification is needed. Effectively studying for and taking tests is a skill that needs5tthyh practice. For example, you should be able to complete a test in the given time. Memorization will be tested separately from application. All topic tests must be completed with at least an 80% or retaken during a lunch the following week. There will be no retakes on the midterm and final exams. You will, however, have some choice of topics.

Before taking a test you need to complete and hand in a problem set that makes sure you are aware of and have mastered the topics for that test.  These completed problems will be handed in as a ticket to allow you to take the test.  You can’t take the test without a ticket. 

A complete and well-organized notebook is your primary resource for studying. At the end of each class, please file your notes, dated and titled, and any handouts or returned work into your 3 ring notebook. Your notebook will be collected without warning and handed back with suggestions to make it even more useful. Please communicate your understanding of a topic with neatly presented and logically organized pages. If you are absent, you are responsible for work missed. Please get notes from classmates and handouts from me.

You have four hour-long Algebra II classes each week for a total of  about 144 hours a year. I will start class on time and expect you to be ready with all your materials. You will need your own calculator, which should include trig functions and square roots. Please stay focused for the entire class. Engage with the material. Ask questions. Don’t give up. Tenacity in pursuit is what I am looking for.  In class you are expected to check your own work to see if the answer is correct. If  not you should try to find what mistakes were made and fix them.   Showing respect for yourself and your ability to learn challenging material, for your classmates and their need to focus and for me is a basic expectation of this class. That kind of respect will ensure that everything else falls into place.

Foundation Skills Objectives

11B Demonstrate persistence in problem-solving and maintaining focus.

3A use basic mathematical concepts such as multiplication, exponents, orders of magnitude, percentage,    proportions

            3E Use abstract symbols in quantitative reasoning

            3F Solve quantitative problems with the use of logic-based sequential thinking

            3D interpret and create graphs

3G recognize and describe how relationships such as functions can relate two quantities--an input and     an output

 

Advanced Geometry

 

Advanced Geometry

Instructor: Mary L. Smyth, MD

Fall 2017

Watershed School


Course Description:  This course will be using a problem-based, exploratory approach to investigate advanced concepts of high school mathematics using an integrated curriculum.  Sample topics include vectors, parametric equations, optimum path, translations, coordinate geometry, triangle, polygon, and circle theorems.


Course Materials:


Phillips Exeter Academy Math curriculum (July 2013)

Projects for PreCalculus, Harcourt and Brace, 1997

and many other online resources


Foundational Skills addressed:


The  Skills covered in this course include

NUMERACY  

Interpret and create graphs


Use abstract symbols in

quantitative reasoning


Solve quantitative problems with

the use of logic-based sequential

thinking


Recognize and describe how

relationships such as functions can

relate two quantities--an input and an

output


DIGITAL TOOL USE


PERSONAL GROWTH

PreCalculus

 

Pre-Calculus
Instructor: Sherry Frazer
Fall 2017
Watershed School

Course Description

Although this course explores many topics not touched on in previous algebra classes, it depends on a student’s fluency in solving for variables,  and understanding of parent graphs and how they can be transformed.  Students should be completely comfortable moving from one form of an equation to another.

After a review of systems of linear equations, properties of exponents  (including rational exponents) and complex numbers we will begin looking at new topics.

Some of the topics covered in the class are:

                                Functions and graphs                                     Polynomial functions

                                Rational Functions                                          Exponential and Logarithmic functions

                                Trigonometric functions                                Trigonometric Identities

                                Applications of Trigonometry                        Sequences Series and Probability

                                Conic sections

Expectations for Credit

Assessment will be through topic tests, and cumulative midterms and finals. Tests are given at the end of each topic as feedback on what was understood and where more clarification is needed. Effectively studying for and taking tests is a skill that  will be  practiced. For example, you should be able to complete a test in the given time. Memorization will be tested separately from application. All topic tests must be completed with at least an 80% or retaken during a lunch the following week. There will be no retakes on the midterm and final exams. You will, however, have some choice of topics.

Before taking a test you need to complete and hand in a problem set that makes sure you are aware of and have mastered the topics for that test.  These completed problems will be handed in as a ticket to allow you to take the test.  You can’t take the test without a completed ticket. 

A complete and well-organized notebook is your primary resource for studying. At the end of each class, please file your notes, dated and titled, and any handouts or returned work into your 3 ring notebook. Your notebook will be collected without warning and handed back with suggestions to make it even more useful. Please communicate your understanding of a topic with neatly presented and logically organized pages. If you are absent, you are responsible for any work missed. Please get notes and hand outs from a classmate.

You have four hour-long Pre Calculus classes each week - a total of  about 144 hours a year. I will start class on time and expect you to be ready with all your materials. You will need your own calculator, which should include trig functions and square roots. Please stay focused for the entire class. Engage with the material. Ask questions. Don’t give up. Tenacity in pursuit is what I am looking for.  In class you are expected to check your own work to see if the answer is correct. If  not you should try to find what mistakes were made and fix them.   Showing respect for yourself and your ability to learn challenging material, for your classmates and their need to focus and for me is a basic expectation of this class. That kind of respect will ensure that everything else falls into place.

Foundation Skills Objectives

11B Demonstrate persistence in problem-solving and maintaining focus.

3A Use basic mathematical concepts such as multiplication, exponents, orders of magnitude, percentage, proportions

3D. Interpret and create graphs

           3E Use abstract symbols in quantitative reasoning

           3F Solve quantitative problems with the use of logic-based sequential thinking

           3G. Recognize and describe how relationships such as functions can relate two quantities—

               an input and an output

 

Calculus

 

Calculus

Mary L. Smyth, M.D.

Fall 2017

Watershed School


Course Description:


This course is an extension of the math curriculum beyond the core high school content.  It is intended to be an introduction to the concepts of Calculus, and would be appropriate as preparation for the study of Calculus I in college.  


Course Materials:


The syllabus for this course follows the suggested outline of AP Calculus AB.  Some topics will be abbreviated.  

Calculus Explorations, Paul Foerster, Key Curriculum Press

AP modules, such as the study of motion of a particle, and AP practice questions will be used.  

We will read Calculus Made Easy, by Silvanus Thompson and Martin Gardner, fourth ed. (originally written in 1911)


Foundational Skills addressed:


The  Skills covered in this course include

NUMERACY  

Interpret and create graphs


Use abstract symbols in

quantitative reasoning


Solve quantitative problems with

the use of logic-based sequential

thinking


Recognize and describe how

relationships such as functions can

relate two quantities--an input and an

output


DIGITAL TOOL USE


PERSONAL GROWTH