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

2018-19

Watershed School

 

Course Description: This course uses 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

  • study/life skills (organization, Cornell notes, time management, planning and setting goals)
  • persistence/attitude
  • basic social skills
  • listening and providing feedback
  • ethical decision-making
  • stress management
  • generic skills of the valued employee

Geometry

 

Geometry

Instructor: Sherry Frazer

2018-19

Watershed School


Course Description:

 

In Geometry we look at the way lines, points, angles and planes behave and interact. Tools used for this study are compasses, protractors, Euclid’s theorems and postulates, spatial imagination, logic, and Algebra,. We move between real objects in all their imperfection and the formulas that represent those objects idealized. Students become increasingly adept at using Algebra as they derive new formulas from patterns and from pre-existing formulas and learn how formulas were derived.


Through projects in reflection, displacement, volume, and architecture, students grapple with some of the difficulties in analyzing 2 and 3 dimensional shapes. We begin the year with exercises to improve the ability to imagine shapes. Students are encouraged to reason inductively, moving from an observation to a hypothesis that would hold true for all similar shapes.


Course Materials:

 

Students generate their own manual for this class in the form of their notebook. I collect the notebooks monthly to make sure they are complete, organized and useful.


Class Expectations :

 

Arrive in class ready to participate. This means putting your cell phone away and having all materials available, being awake and well fed. Please eat outside of class.


You have four hour-long Geometry classes each week - a total of  about 144 hours a year. I will start class on time and expect you to be ready. 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 will ensure that everything else falls into place.


Expectations for credit :

 

There will sometimes be pk彩票work assigned on Monday which will be  collected on Wednesday.  The main reason for pk彩票work is to give you an opportunity to work independently and practice perseverance.  If there is a test that week’s pk彩票work will be to complete a “test ticket” .


Before taking a test you need to complete and hand in a problem set that assures that 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.


Assessment will be through topic tests. 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 75% or retaken the following week.


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 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 from a classmate and handouts from me.


Foundational Skills associated with Geometry:

 

11A  Study skills (organization, note-taking, memorization)

Keeps an organized notebook and materials, adequate note-taking. Is able to memorize information consistently. Makes up missed work


3B Make use of measurement tools, incorporating significant figures-

Use of protractor, ruler and compass


3E Use abstract symbols in quantitative reasoning   

Representing  2 and 3 dimensional shapes algebraically

 

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

Geometric Proofs


7 Design.

A project creating a model of a building with limited surface area, maximizing usable space.


 

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
2018-19
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
Instructor: Mary L. Smyth, M.D
2018-19
Watershed School

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Course Course Description:

This course is an extension of the math curriculum beyond the core high school content. Content will include limits, derivatives and integrals. It will be taught with an AP Calculus AB syllabus.

Course Materials:

The syllabus for this course follows the suggested outline of AP Calculus AB. Some topics will be expanded. Calculus, 2nd edition, Finney, Thomas, et al 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.

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