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

ALEKS Math

 


Course Description:


Since each student begins and ends at a different level, specific content expectations vary for each learner.  In general, it takes about a year to complete a class (i.e. Algebra 1 or Algebra 2) on ALEKS.  A class is considered complete at Watershed and credit can be awarded if the student has demonstrated mastery of 75% of the material and has been exposed to an additional 15% in ‘learning mode,’ meaning those topics are not yet fully mastered.  Advancement to the next higher class is possible after attaining 90% but requires discussion with the instructor about the remaining unfinished topics.


Course Materials:


ALEKS:

Assessment and LEarning in Knowledge Spaces is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. (http://www.aleks.com/about_aleks)

Foundational Skills addressed:


3. Numeracy:


A. use basic mathematical concepts such as multiplication, exponents, orders of

magnitude,percentage, proportions.make use of measurement tools, incorporating significant figures

D. interpret and create graphs

E. use abstract symbols in quantitative reasoning

F. solve quantitative problems with the use of logic based sequential thinking.

G.recognize and describe how relationships such as functions can relate two

quantities--as input and output.


Assessment of a student’s success in these objectives will be measured by asking the student to describe his/her math reasoning, the steps taken and the thinking behind them.  Persistence will be assessed by analyzing the statistics from the ALEKS program.  Some of the items ALEKS tracks include time spent on a topic, number of attempts, total rate of progress, retention of gained skills, and number of topics mastered.  ALEKS also provides drills on QuickTables to test competence/speed of recall of basic math facts.

 


9. Digital Tool Use and Literacy:


B. Graphing


There will be specific assignments asking students to explain a pattern or concept in writing.  Students will also be asked to solve a Question of the Day, taken from the SAT math section.  These are open-ended questions and they test the ability of a student to reason out a solution using all the tools at his/her disposal—knowledge of algebra, pattern recognition, logical elimination, or testing of solutions. Even though these questions are normally given to high school juniors, younger students can learn, with practice, to think flexibly and creatively to find solutions.


11. Personal Strength and Resilience:


B. Persistence

C. attitude

G. stress management





 

Geometry

 

Course Description:


In Geometry we look at the way lines, points, angles and planes behave and interact. Tools used for this study are Euclid’s theorems and postulates, logic, coordinate Geometry, Algebra, drawing and compasses. We move back and forth between real objects in all their imperfection and the formula that represents that object idealized. Students become increasingly adept at using Algebra as they derive new formulas from patterns and from pre-existing formulas.

 

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 frequently to make sure they are complete, organized and useful. Some of the course material is in the form physical objects such as buckets of water, tall buildings, oranges, and laser pointers and tools such as compasses and protracters.

 

Foundational Skills addressed:


3. Numeracy


B. Make use of measurement tools, incorporating significant figures-Use of protractor, ruler and compass

E. Use abstract symbols in quantitative reasoning. Algebraic Translation of Real Life Situations

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

Geometric Proofs, Number Theory, Probability


Protractors, compasses, rulers, and scale drawings  are used in this class.  We also practice creating algebraic formulas from figures and patterns. Identifying the difference between inductive and deductive reasoning, Proving statements true using logical, justifiable steps  written as a two column geometric proof.




7. Design process.


Design a house that meets certain surface area requirements. Make well crafted scaled models in two and three dimensions.


11. Personal Strength and resilience


A.Study skills (organization, note-taking e.g. Cornell notes, memorization) Keeps an organized notebook and personal materials, adequate note-taking. Is able to memorize information consistently. Makes up missed work. Challenges self to make connections between concepts.


Keep an organized notebook (collected once a month) that contains all notes, handouts and tests. Use this to study. There is not a textbook in this class.






.

 

 

Advanced Geometry

 

Course Description:


This course is an integrated math course.  The content includes both Algebra and Geometry ABOVE the levels of introductory Geometry and Algebra II.  This course is only available to advanced students on the recommendation of the teacher.

 

Course Materials:

The course will use the Math 2 curriculum from Philips Exeter Academy, (July 2013).


Foundational Skills addressed:


3.  Numeracy:


B.  make use of measurement tools, incorporating significant figures

C. find or check relations among physical quantities using dimensional analysis

F. solve quantitative problems with the use of logic-based sequential thinking


Students will keep a detailed notebook of all problems worked.  A first attempt will be required prior to class meetings.  After in-class discussion and questions, a further effort will be required to complete the problem.  Brief answers will be posted online by the teacher for students to check.  Hints for solutions may be offered if students get stuck.  Final presentation of the solutions will be written up in the student’s notebook, along with explanations of process, and a full annotation including similarities to other problems or techniques learned.  Notebook checks will be the main grading mechanism.



9. Digital Tool Use and Literacy:

B. Graphing


Sketches of all graphs generated will be part of the solution presentation.  Graphing will be done on TI 83 calculators and also on Desmos, a Google graphing program available online.


11. Personal Strength and Resilience:


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

B. persistence

C. attitude

D.basic social skills

E. listening and providing feedback


The teacher will provide coaching and feedback on habits of work.

PreCalculus

 

Course Description:


This course is an extension of the math curriculum beyond the core high school content.  Students will spend this year “putting together” all they have learned in previous study of algebra and geometry.  The course includes Trigonometry in the second semester.  


Course Materials:


The course is based on a sequential progress through topics in the ALEKS PreCalculus course.  We also use worksheets generated on line, SAT practice problems,  and challenge problems from Projects for Precalculus, published by Harcourt Brace, 1997.


Foundational Skills addressed:


3.  Numeracy:


  1. interpret and create graphs

  2. use abstract symbols in quantitative reasoning

      F. solve quantitative problems with the use of logic-based sequential thinking

  1. Recognize and describe how relationships such as functions can relate two quantities--an input and an output


There will be a mixture of classroom time with traditional lectures, group work, quizzes and tests, projects, and individual time spent on ALEKS, our computer math tutorial system.



9. Digital Tool Use


  1. graphing


We use TI 83 and 84 graphing calculators and Desmos, the Google graphing program online.


11. Personal Strength and Resilience:


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

B. persistence

C. attitude

D.basic social skills

E. listening and providing feedback


The teacher will provide coaching and feedback on habits of work.

Calculus

 

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.  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 for background ideas.


Foundational Skills addressed:


3. Numeracy


This course is beyond the Foundational level in Numeracy.


9. Digital Tool Use and Literacy:


B. Graphing


Sketches of all graphs generated will be required for projects and tests.  Graphing will be done on TI 83 calculators and also on Desmos, a Google graphing program available online.



11. Personal Strength and Resilience:


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

B. persistence

C. attitude

D.basic social skills

E. listening and providing feedback



The teacher will provide coaching and feedback on habits of work.