Advanced Algebra
(Mathematics Cluster)
COURSE DESCRIPTION
This integrated, collaboratively taught Advanced Algebra Core class will provide all students an opportunity to study functions, graphs, matrices, trigonometry, and other related subjects, so they
will know about, understand, and better appreciate mathematical facts, concepts,
and applications through textbook lessons, logic exercises, mental arithmetic, and
technology laboratories. By satisfying requirements of this study, all students will become more informed,
skilled, productive, employable, and socially responsible citizens.
SWRSD OUTCOMES
Outcome
6:
Students exhibit a positive attitude and self-initiative.
Outcome 7:
Students use a variety of ways to think and to reason when solving problems and making
thoughtful decisions.
Outcome 9:
Students use technology for adapting to and initiating productive change.
Outcome 11:
Students demonstrate skills and attitudes that will enable them to achieve post high
school education.
COURSE OUTLINE
CONTENT
(Essential course facts, concepts, and basic skills; assessed
with
teacher
-made
tests
and
rubrics
)
Major Components of Study
A. Textbook Lessons
Alaska Content Standard(s):
Standard B: Mathematics
(A student should understand and be able to select and use a variety of problem solving
strategies.)
Key Elements:
Students will know about, understand, and demonstrate the ability to
use computational methods and appropriate technology as problem-solving tools;
Students will:
write an equation or inequality in an equivalent simplest form
will use slope-intercept, point-slope, and standard forms of linear equations
use problem solving to investigate and understand mathematical content;
Students will:
solve equations by factoring, completing the square, and using the quadratic formula
determine ordered pairs in solution sets of relations and functions
find the vertex, maximum, and minimum of relations and functions
identify the domain and range of relations and functions
recognize relations and functions and develop equations from graphs and data points
identify the sine, cosine, and tangent relationships of right triangles
solve for missing parts of right triangles
use the methods of solving simple logarithmic and exponential equations
simplify radicals and express as equivalent rational exponents
formulate mathematical problems that arise from everyday situations;
develop and apply strategies to solve a variety of problems;
Students will:
use ordered pairs in graphs and in solution sets
identify the types of solutions
identify the attributes of families of functions
solve equations with complex solutions
use the four basic operations of radicals
solve quadratic equations with radical equations
use common sense to help interpret results;
Students will:
identify the types of solutions
apply what was learned to new situations;
Students will:
identify the relationship between ordered pairs,graphs, and equations
relate ordered pairs, graphs, and equations
identify and apply the laws of sine and cosin
identify the relationship between exponential and logarithmic functions
identify the basic properties logarithms and use them to solve problems
apply the basic operations with radicals
solve linear equations with radical solutions
use mathematics with confidence.
Standard C: Mathematics
(A student should understand and be able to form and use appropriate methods to define
and explain mathematical relationships.)
Key Elements:
Students will know about, understand, and demonstrate the ability to
express and represent mathematical ideas using oral and written presentations, physical
materials, pictures graphs, charts, and algebraic expressions;
Students will:
use ordered pairs in graphs and in solution sets
solve by graphing, substitution, linear combination, and the use of matrices
use functional notation and graph solutions of functions
relate mathematical terms to everyday language;
Students will:
define functions
define complex numbers
use the relationship between rational exponents and their radical form to rewrite
and solve solutions
develop, test, and defend mathematical hypotheses; and
clarify mathematical ideas through discussion with others.
B. Logic Exercises
Alaska Content Standard(s):
Standard D: Mathematics
(A student should be able to use logic and reason to solve mathematical problems.)
Key Elements:
Students will know about, understand, and demonstrate the ability to
recognize and use the language of formal logic;
Students will:
understand true and false terminology
recognize and understand propositions, premises, and conclusions
understand and use IF...THEN, AND, OR, and NOT terminology
understand hypothesis/antecedent and conclusion/consequence clauses
recognize symbolic logic and be skilled in the algebra of propositions
draw logical conclusions;
use models, known facts, and relationships to draw logical conclusions and explain
the student's reasoning
Students will:
understand, produce, and use truth tables
will recognize, understand, and use converse, inverse, and contrapositive variations
and use them to manipulate logical statements
use deductive and inductive reasoning to verify conclusions, judge the validity of
arguments, and construct valid arguments;
Students will:
perform deductive reasoning in mathematical systems
understand indirect deduction and the phenomena of paradoxes
perform inductive reasoning in mathematical systems
understand incomplete and complete inductive reasoning
C. Mental Arithmetic
Alaska Content Standards: Standard A: Mathematics
(A student should understand mathematical facts, concepts, principles, and theories.)
Key Elements:
Students will know about, understand, and demonstrate the ability to
understand and use numbers, number systems, counting numbers, whole numbers, integers,
fractions, decimals, and percents;
Students will:
define, recognize, and use imaginary and complex numbers
select and use appropriate systems, units, and tools of measurement, including estimation;
perform basic arithmetic functions, make reasoned estimates, and select and use appropriate
methods or tools for computation or estimation including mental arithmetic, paper
and pencil, a calculator, and a computer.
Students will:
solve equations with complex solutions
D. Calculator/Computer Laboratories
Alaska Content Standard(s):
Standard B: Mathematics
(A student should understand and be able to select and use a variety of problem solving
strategies.)
Key Elements:
Students will know about, understand, and demonstrate the ability to
use computational methods and appropriate technology as problem-solving tools;
use problem solving to investigate and understand mathematical content
Students will:
produce meaningful data
effectively record and organize data
formulate mathematical problems that arise from everyday situations;
develop and apply strategies to solve a variety of problems;
Students will:
present data in usable numeric or graphical form (lists, tables, charts, graphs)
choose appropriate tools and methods to accurately and precisely measure experimental
phenomena
select appropriate technology to record, display and analyze data (graphing calculator,
spreadsheet, mathematical software)
select appropriate technology to build relationship models (Geometer's Sketchpad
, Stella
)
effectively use software to model relationships
use common sense to help interpret results;
Students will:
analyze data using appropriate pencil and paper or electronic methods
apply what was learned to new situations;
use mathematics with confidence.
Students will:
develop mathematical models for experimental phenomena
use models to predict behavior of experimental phenomena
test models through experimentation
develop and manipulate models to demonstrate mathematical truths and investigate mathematical
relationships
Standard E: Mathematics
(A student should be able to apply mathematical concepts and processes to situations
within and outside of school.)
Key Elements:
Student will know about, understand, and demonstrate the ability to
explore problems and describe results using graphical, numerical, physical, algebraic,
and verbal mathematical models or representations;
use mathematics in daily life;
use mathematics in other curriculum areas.
Standard C: Technology
(A student should be able to use technology to explore ideas, solve problems, and
derive meaning.)
Key Elements:
Students will know about, understand, and demonstrate the ability to
use technology to observe, analyze, interpret, and draw conclusions.
use technology to solve problems both individually and with others.
use technology to create new knowledge by evaluating, combining, or extending information.
SKILLS
(Essential processes or skills, universally taught by all teachers in all courses;
assessed
with
teacher
-made
rubrics
and/or
tests
)
Major Categories of Skills
A. Cross-curricular and/or Integrative Skills
Key Elements:
Student will know about, understand, and demonstrate the ability to
effectively communicate (listen, observe, read, write, discuss, present, explain,
persuade, defend)
apply a variety of mathematical concepts and skills (logic, statistical interpretation,
plotting and analyzing graphs, concluding, predicting trends) to solve common day-to-day
problems
use a variety of higher order thinking skills (hypothesizing, estimating, analyzing,
classifying, synthesizing, evaluating,inferring, generalizing) to solve common
day-to-day problems
set and achieve goals (brainstorm, envision, plan, research, manage time, persist,
complete)
produce quality products (plan, organize, draft, evaluate, revise, improve, persist,
complete)
B. Technological Skills
Key Elements:
Student will know about, understand, and demonstrate the ability to
- use modern technology (computers, scanners, copiers, printers, calculators, audio/visual
tools, telephones, fax machines, calculators) to solve common, day-to-day problems
- apply basic computer applications (word processing, spreadsheet, database, graphics,
desktop publishing, Internet, e-mail) to produce quality products, including
- multimedia presentations (speeches, demonstrations, lectures)
- reports, bids, proposals, instructions, manuals
- research polls, surveys, checklists
- graphs, tables, charts, maps, illustrations, photographs
- letters (complaints, requests, replies, recommendations, applications, resumes)
- expository essays, research papers, literary works related to Advanced Algebra
C. Life and/or Employability Skills
Key Elements:
Student will know about, understand, and demonstrate the ability to
- behave responsibly and produce quality products related to Advanced Algebra
- attend, be punctual, follow directions, manage time, stay on task, meet deadlines
safely, effectively, efficiently, accurately use the work area, materials,
tools, & technology
- set short and long-term goals, plan, use higher order thinking skills, seek help,
persist
- work well with others (cooperate, develop group unity, determine leadership roles,
contribute to group success, allow others to contribute, resolve group conflicts,
make group decisions)
- relate Advanced Algebra
content and skills to your personal life and the lives of others
respect and treat others equally, from the perspective of the needs and rights
of all people
- responsibly examine (be aware, know resources, research, consider, discuss) current
Advanced Algebra
issues and/or events that personally affect you or others
- effectively support opinions in productive ways (preplan, research, logically organize,
give specific examples, illustrate, recommend)
- use new knowledge, understanding, skills and tools to solve real life problems, make
decisions or choices , and predict logical consequences or possibilities
- . acquire career knowledge and skills related to employment opportunities in math/science
related organizations
- compare colleges, technical, or business schools (locations, size, costs, special
programs)
- apply for admission, complete applications for scholarships or other financial aids
- develop a four-year schedule of classes, including alternatives for those not available 6. present oneself in an employable manner
- wear appropriate dress and be physically well-groomed demonstrate good
speaking and/or interviewing skills
- complete all written forms (letter of application, resume, required forms, legal
documents) provide a portfolio that shows special products, skills, experiences,
achievements, awards
D. Cultural Relevance:
Alaska Content Standards for Culturally Responsive Schools: Student Standards A-E
Key Elements:
Student will know about, understand, and demonstrate the ability to
- respect ones own cultural heritage, traditions, and language
- interview elders in order to compile personal genealogies and/or a local history
- identify local cultural values and traditional responsibilities to the environment
- respect and live in tune with local cultural values and traditions
- build on local knowledge and skills to achieve future success in the world at large
by
- using methods from ones own traditions to learn about the world beyond ones village understanding
how the local culture relates to others in the area, state, nation, and world
- making appropriate choices regarding the long-term consequences of ones own actions
- participate in a variety of traditional activities related to the local culture,
including
- subsistence activities, arts and crafts, dance and music, sports and recreation
- community government, tribal, and church affairs
- total wellness programs (drug and alcohol free programs, parenting, nutrition, exercise)
- engage in family-related activities based on traditional ways of knowing and learning,
including
- consistent, respectful, loving interactions with Parents and Elders that show appreciation of
their roles as providers and care givers, culture bearers, and educators in the community
- self-assess ones own strengths and needs in order to make appropriate life choice
- explain the processes, forces, and interactions of the world and its varied cultures,
including the
- interrelationships of the spiritual, natural, and human world
- geographical and ecological resources of the local environment
- impact of the environment on the origins of culture and ones personal cultural perspective
- the nature of diversity and the need for change over time
- cross-cultural influences, interactions, conflicts, communications, and resolutions
INSTRUCTIONAL RESOURCES AND MATERIALS
A. Community Resources Related to Course
Each individual and/or team of instructors, with the help of long time staff, students,
parents and other concerned community members should cooperatively compile and periodically
update a list of village elders, parents, local government leaders, business persons, and other concerned, active members of the community willing to share their
wealth of experiences, knowledge and skills. If available, specific examples should be included now.
B.
Major Internet Web Site Addresses Related to Course
(a tiny sample)
Free Federal Resources for Academic Excellence: www.ed.gov/free/subject
ITO Interdisciplinary Projects: www.fred.net/nhhs/html/ito
PBS Mathline www.pbs.org/learn/mathline
National Council of Teachers of Mathematics www.nctm.org
Mega-Mathematics www.c3.lanl.gov/mega-math/
Math games,toys, puzzles www.sal.cs.uiuc.edu/~Jeffe/mathgames
Appetizers and lessons for math and reason www.cam.org/~aselbui/lesson
Geometry forum forum.swarthmore.edu
AIMS education foundation 204.161.33.100/aims
Project mathematics www.projmath.caltech.edu
Annenburg/CPB math/science project www.learner.org
Geometry center www.geom.umn.edu
C. Media Center: Southwest Region School District
Contact Roz Goodman, the Southwest Region Media Specialist, for help. She has
lists of materials related to specific subject areas and will help you find Internet
resources or other materials
- The Alaska State Framework for Mathematics Content Standards (This resource is full of
suggestions for activities, teaching/assessment strategies, lesson plans, web site
addresses etc.
)
- Teaching Study Skills & Strategies in High School (includes activities); Active
Learning: 101 Strategies to Teach Any Subject (includes activities)
- Reconnecting Youth: A Peer Group Approach to Building Life Skills; Teaching Social
Studies With the Internet (booklet and CD ROM);
- Lion's Quest: Skills for Adolescence (instructional manual/student activities)
D. Itinerant Travel Kits and/or Permanent Core Skills Instructors' Materials
Donald in Mathemagics Land; Stand and Deliver; Life by the Numbers.
- Simulations and/or Activity Packets Related to Course
- CD ROMs/Software Related to Course
- Text and/or Supplemental Books Related to Course
A History of Mathematics; Journey through Genius; A Brief History of Time; An Old
Man's Toy; Science for All Americans.
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(Assessment Guidelines and Grading still "under construction" and awaiting additional
in-put)
Teacher-made tests of content units will be required: pretests, quizzes, Unit Tests,
Final Exams
Processes/Skills will be assessed Rubrics, checklists, et.al.
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(The Following Still Needs Input, Thought, and Work)
ASSESSMENT GUIDELINES AND GRADING
The primary goal of this class is to give all
students an opportunity to gain essential new knowledge, comprehension, and skills.
To determine if all
students are actually attaining this goal, regular, in-progress
assessment
of student progress will be part of daily in-progress activities and final student
projects.
- cooperatively develop traditional teacher-made daily/weekly quizzes, unit tests,
and final trimester exams
designed to measure student knowledge and comprehension of basic course content.
- cooperatively plan and consistently apply a variety of student performance assessments
(rubrics,
check-lists) to evaluate in-progress and summary student skill development.
CONTENT KNOWLEDGE TESTS
Minimum Requirements
: At the very least, course Content
will be regularly assessed with traditional
Teacher-made Tests
(multiple choice, completion, true/false, matching, short essay).
- daily or weekly Quizzes
should be given as part of normal, on-going classroom procedures.
- periodic reviews and subsequent summary Unit Exams
will be given in every course.
- comprehensive reviews and summary Trimester Final Exams
will be given in every course. Unit and Trimester Final Exams should measure
student retention and comprehension of the most
important
factual content (who, what, where, when, why, how) and
improvement of basic
skills (recall, reading, thinking, writing, calculating).
Suggestions:
- Pretest
or use the test-study-test
method
rather than simply study-test
. Pretesting at the start of a unit helps both students and teachers discover
What They Already Know
and What They Need to Learn
.
- Wh en necessary develop individualized tests to account for individual learning styles
and/or special learning difficulties. Consult Special Education teachers and
counselors for help.
- Reteach
and Retest
when needed to improve and/or reinforce student knowledge and comprehension.
- Promptly grade and review results of all quizzes, tests, or exams. Students want,
need, and have the right to quickly know how they have done on tests.
- Use tests as a teaching tool: require students to correct all factual errors and/or
process mistakes.
- Teach students How to Take Tests
. Important skills are involved and students need to learn them.
CRITERION-REFERENCED TESTS (CRT's)
- Core Skills
Language Arts and Mathematics teachers at the secondary level still have the duty
of teaching, testing, and accurately recording student progress on the district's
standardized CRT Tests
and are accountable for accurately recording student progress on these tests.
- Note:
Because all
secondary teachers are members of collaborative teams, all
secondary teachers are expected to assist their team partners help all
students successfully complete, at the very least, Banks 7 and 8
of the CRT's
.
STUDENT PERFORMANCE RUBRICS
- Rubrics
will be used to better teach and assess the development
of essential Skills
(listening, reading, speaking, critical thinking,writing, research, cooperative
group work, discussion, problem solving, decision-making, use of technology, social
behavior, employability, social behavior/citizenship, cultural relevance) and
to determine the quality
of final products
- Rubrics
must include clearly stated, easily understood directions, and specific information
about what students will be expected to do and learn. Quality standards and deadlines
should be included.
- Rubrics
will be assigned at the beginning of any activity whose major objective is the acquisition
and application of essential Skills. Carefully explain exactly how a particular
rubric will be used.
- Use rubrics as a teaching tool. Teach all
students how to use rubrics to self-assess the quality of their own work and/or
that of their classmates--and their teachers.
EXTRA CREDIT WORK
In order to encourage students to pursue high level performances and quality products,
all
students who have completed required work, including any expected revisions, should
be given an opportunity and encouraged to do Extra Credit
work that might increase the depth and/or breadth of their understanding.
- Note that extra
does not
mean in place of
; rather, extra
means in addition to
. Students should thus be allowed and encouraged to voluntarily complete additional,
challenging tasks that might broaden or deepen their understanding.
- Assessment of Extra Credit
work should follow the same systematic guidelines and/or utilize the same type of
assessment rubrics
, tests, or other techniques used to evaluate required work.
GRADING
All
students will be held accountable for meeting the minimum requirements of all courses
and will earn grades based on their ability to demonstrate the acquisition of basic
content knowledge and comprehension, and their ability to apply specific essential
skills to produce quality finished products. Final Grades in all courses will follow
on a traditional "A", "B", "C", "D", "F", "I", system.
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