Mathematics at Watershed
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
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 homework assigned on Monday which will be collected on Wednesday. The main reason for homework is to give you an opportunity to work independently and practice perseverance. If there is a test that week’s homework 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
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
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
Instructor: Mary L. Smyth, M.D
2018-19
Watershed School
Cou
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