Deerfield Beach High Mathematics
Instructor: T. Lambert
E-mail: Therese.Lambert@Browardschools.com
Parent Conferences: Schedule via Guidance Dept.
UPDATED AUGUST 10, 2018
WHITE BOARD MARKERS are required as you will be presenting work in class on the Boards.
Your work will also be placed under the document camera at various times during the course.
The teacher reserves the right to alter the curriculum to meet the standards of the State of Florida as well as the students.
Calculus AP:AB/BC All trig. identities are considered previous knowledge and will be reviewed as well as relationships to the unit circle. Students are required to keep up to date with all assignments. The instructor expects the students to work out the problems themselves and not COPY from internet sources or other students the steps in solving the problems.
Honors Geometry All trig. identities will be taught in relationship to the unit circle so that DBHS can meet the precision and standards of Common Core, EOC , IB and AP curriculums. SInce all test requirer short answers students must demonstrate all math in a vertical format. All exit exams have non calculator sections hence the student will be required to work without calculators and formula packets throughout the year.
The instructor expects the students to work out the problems themselves and not COPY from internet sources or other students the steps in solving the problems.
Keep in mind that certain university math classes adhere to the above conditions as well.
Standards can be found at FLDOE and CPALMS.
Student:
You the student should actively practice by doing the problems assigned in pen or pencil.
You the student should actively practice by redoing the problem done in class and supported by the textbook site.
Individually review journal entries, internet practice , and exams (from textbook and internet sites).
Make your own practice test from examples in the text, problems done in class and problems that have their answers in the back of the text.
Teacher available usually:
7 A.M. to 7:20 A.M. general questions on a first come first serve with instructor unless instructor is assigned other duties
Bring with you all of your attempts so that the instructor can get a better feel for your potential errors.
Prepare your question(s) for open question times during the class period usually at the end of the period as part of classroom strategies or ask the instructor while she is on hall duty.
Mu Alpha Theta competitions provide great practice test that cover common core and AP style questions.
Mu Alpha Theta after school practices
Honor Society tutoring
YMCA potential programs
Technology Assignments: Students will be assigned readings, videos , research and evaluations on the internet. Please be reminded that you must allow your broswer to
allow cookies/pop ups. Computers are available at the media center before school, during lunch and after school.
Courses: Honors Geometry / IB/CBA/Urban Teacher Academy, Pre-Capstone ....
Calculus AP/AB , AP/BC , IB/SL, IB/HL
Instructor: T Lambert
Description: Each course above will meet the criteria for the State of Florida
Standards , AP curriculum and all Pre-IB/ IB courses will cover the requirements of the IB curriculum as well. A list of topics can be found in your course curriculum guide.
Grading Policy: In accordance with the Broward County Public School System the following grading scale is in effect.
A 90-100 C+ 77-79 D+ 67-69
B+ 87-89 C 70 - 76 F 0 - 59
B 80-86 D 67 - 69
Points are awarded to each activity based upon teacher discretion.
If an activity carries a weight higher point value then usual students are notified verbally.
All Students: Explorations/Portfolios:Students are required to complete special individual math portfolios/explorations as assigned by the instructor. These portfolios/explorations will follow the MYP areas of interactions as well as the diploma requirements and must be turned in in multiple copies 2 for testing year in the Diploma Program. All work is to be done in non erasable black ink. Each portfolio must be in story format with graphs and/or pictures included with the worded reference. All calculator / math programs must be documented by printing the screen(s). Only math notation is acceptable!! No programming language is allowed. All work must be done by the student and turned in on the assigned day/time. There are no redo’s for portfolios/projects!!! Your MYP/Pre capstone program forms the foundation for your external evaluation.
Criteria for MYP/Pre Capstone explorations /portfolios will be given during each assigned task.
Exploration Rubric Mathematics IB students only
IN CLASS POSTED DUE DATES OVERRIDE LISTINGS BELOW IF DIFFERENT.
Testing year SL 2019 HL 2019/2020 due dates : Final draft of non Calculus based info with downloads of modeling photos from growth of math Algebra 1 through Pre-Calculus/Statistics required in typed form with bibliography , some early reflection and citations
1)Topic choice, intro, photo, 3 math concepts from Law of Sines /Cosines by Aug 24
2) Regression development with area under curve approximations with modeling by Sept 28
3) Final upload and submission of document Nov. 14, 15 or 16 , 2018
See Handout from first week of school in Journal Entry
Final exploration with Calculus and a serious MATH reflection December 2 or 3, 2016 . Two copies are required.
Higher Level Candidates your papers are due April 20, 2017 your junior year. This allows you to explore topics that are in the BC curriculum and beyond to show your individual eagerness to go beyond the classroom. In the event you attend a special summer program you are allowed to request a change in what was submitted in April.
WARNING TO ALL IB STUDENTS : You may also need to upload your final internal assessment to a site yet to be determined if IB changes format.
The mathematics you explore should be part of the syllabus and beyond the level of the course.
The mathematics involved should not be completely based on mathematics listed in prior learning.
If the level of the mathematics is not commensurate with the level of the course you can only get a maximum of two marks for criterion E. ( If you have taken Algebra II you can not base your work on arithmetic and algebraI only. You need to reach into both Pre-Calculus , Statistics and simple Calculus.)
You need to demonstrate within your exploration that you fully understand the mathematics used.
You can demonstrate sophistication of mathematics in your explanation by
Showing that you understand and can use challenging mathematical concepts.
Showing that you can extend the application of mathematics beyond that which you learned in class (from above .. You need to reach into both Pre-Calculus , Statistics and simple Calculus.).
Looking at a problem from different mathematical perspectives.
Identifying structures to link different areas of mathematics.
Rigor involves clarify of logic and language when making arguments and calculations.
Precise mathematics is error-free and uses an appropriate level of accuracy all the time.
The actual rubric will be listed in class / found in the IB textbook and be presented as a handout.
Student Rights and Responsibilities
1.To be given the opportunity to learn and receive a full period of meaningful instruction.
2.To be treated with respect by all individuals within the teaching environment.
3.To respect self and others through action, words and deeds.
4.To be willing to try and try again until the task meets the set criteria.
5.To abide by all rules as set down in the Student Conduct Code.
6.To try all assignments and document their efforts in writing / tape recording.
7. To obtain at least two phone numbers from his/her classmates so as to keep abreast of materials and topics that were covered during an absence.
How to Study for a Math Test
1.Rewrite your notes each day.
2.Complete all portions of your notebook. Write down the definitions and formulas.
3.Attempt the examples that are related to your assigned work that appear in your textbook.
4.Try out the problems in the book that have answers.
5.As you gain confidence attempt the homework problems. Making sure not to erase your attempts ( unless you know it is absolutely wrong). This will enable your tutor to see how you were thinking at the time of a potential error.
7.If a formula or vocabulary word is not easily remembered then make a flash card out of it. Use an index card
Side one: A = (1/2)ap then
Side two would be: Area of an equilateral triangle where a is the apothem and p is the perimeter of the triangle
8. Review the stack of flash cards every two days making two piles the ones you study every day and the ones you study every week. Parents please work the flash cards with your student, so that you can be made aware of their progress.
9.As you do problems either from the textbook or other correct assignments generate your own test questions and practice problems each day. So before a major test you will have a practice test with the correct methods within your grasp.
Major Tests: Must be made up.
Quizzes and some test are both written and oral
Extra Credit: Earned by 1. Winning a Math Bee Competition in class
or
2. A classroom activity deemed appropriate by the teacher.
Writing Skills across the curriculum ( Journal and Explorations)
Journal: Calculus students must make a journal entry six days a week. ENTRIES WILL RELATE A MATHEMATICAL CONCEPT APPROPRIATE TO THE LEVEL. Journals will be collected at any time. Students are therefore required to bring their journal to class every day.
Geometry Journals
Two journals will be required by the student at various times during the year.
Journal #1 The student will write at the top of every other page the question
What are you grateful for learning in math today?
The response should include a theorem , diagram and example. Entries may also include a vocabulary word with the definition and example.
NOTE NOTE: The grateful journal is not a notebook. This composition book will be used for reviewing for the EOC. Better to look at 50-100 pages rather then flipping through 300 - 400 pages.
Journal #2 Common core...SAT .... ACT ...NGSSS... focus is on circular and the connections to lines and segments
Week One : Day 1 or 2 How round is round?
Show how round can be applied to your hand ?
First weekend : Where is round within your environment outside of school ?
What is one Algebra concept applied to round in your environment ?
Assignments will be given at random times and will require taping and stapling of objects.
Students will be required to write and be graded according the MYP/IB rubrics and /or writing across the curriculum mandates.
All Algebra Presentations will be vertically presented!!!!!!!
Example: 3x + 6 - 2( x+1 ) = 9
3x + 6 -2x -2 = 9
3x - 2x + 6 -2 = 9
x + 4 = 9
x = 9 - 4
x = 5
All Classes Special Projects are assigned at various times during the year. If students are working within a group they are responsible to get their part of the project to a group member prior to the time that the project is due. If a student is unable to do this please post mark their material to
T. Lambert
Deerfield Beach High
910 SW 15 Street
Deerfield Beach, FL.
Teacher rights and responsibilities:
1.To work in an environment conducive to teaching , learning and discovering.
2.To be provided with a safe teaching environment. ( Book bags out of aisles.)
3.To work in an environment where all individuals are treated with respect.
4.To teach students proper classroom and small group behavior.
5.To provide a complete period of meaningful instruction each day with respect to the subject matter and the relationship it has across the curriculum.
6.To be a good role model by adhering to school board policy.
2016-2017 CALCULUS
Calculus IB is to be incorporated into the AP curriculum as well as Statistics. The AP curriculum will be presented Semester I with spiralling Semester II. Hence the pace is quick and to the point.
Non IB Calculus students will be required to do all IB related math topics since these topics will improve your math foundation!!!! AT times non IB students will have alternate assignments that allign to CBA, Urban TEeacher Academy and/or Capstone.
Calculus Students will be tested on the unit circle, Pre-Calculus formulas and derivatives within the first three days of the course. This evaluation will be both oral and written.
Midterm exam will be an actual AP test and will be scaled according to material that has been presented.
Essays and multiple choice problems both calculator and non calculator will be administered.
Midterm Exam Report Card Grade
AP grade of 5 will be recorded as an A on the report card.
AP grade of 4 will be recorded as a B on the report card.
AP grade of 3 will be recorded as a C on the report card.
AP grade of 2 will be recorded as a D on the report card.
AP grade of 1 will result in an F appearing on the report card.
Final Exam will be a crochet exam that allows the student to demonstrate the application of change to real world and document their work with Calculus based math.
Final Exam Report Card Grade Calculators are allowed
Missing 1 problem will be recorded as an A on the report card.
Missing 2 problem will be recorded as a B on the report card.
Missing 3 problem will be recorded as a C on the report card.
Missing 4 problem will be recorded as a D on the report card.
Missing 5 problem will result in an F appearing on the report card.
Labs and Portfolios : Story format, two copies, typed or black ink all five areas of interaction with technology unless otherwise instructed.
Higher Level students must decide upon their paper three option of Statistics or Analysis by the start of October.
The instructor reserves the right to alter this syllabus.
Course: AP/BC AND AB CALCULUS
AB STUDENTS You Start At This Point
Journals are required to be continued : Students answer each day :” What are you grateful for learning in math today? This journal acts as a review book of the AP syllabus just prior to them sitting to take the test.
Notebooks are recommended and will be continued from AP/AB: Each notebook must contain a formula , vocabulary, homework, example, essays and practice problem section. Additional section appropriate with school board policy are allowed .
Textbooks and Supplements:
New Calculus TExt Calculus for AP by Larson and Battaglia with Calcchat and calcview
Calculus Larson Hostetler Edwards from Houghton Mifflin
Calculus and Analytic Geometry Thomas/Finney from Addison Wesley
Calculus Concepts and Application Foerster by Key Curriculum
Calculus Problems for a New Century from MAA editor Fraga
Mathematics Vertical Teams Toolkit College Board
Old AP released exams from 1987 to present
Investigating Change by Barnes from Curriculum Corporation
Advance Placement Mathematics by Best & Lux from Venture Publishing
Multiple Choice & Free Response Question by Lederman from D & S Marketing
AP College Board Calculus internet site
MAPLE software
ELMO document camera
Mathematics Teacher
[NOTE BC Students Only: Students have all had AP/AB the first term of the previous year Aug. - Dec.
Thus it is necessary to review all of AP/AB material as soon as possible. The first 1-5 weeks is spent doing this. Time is strictly determined on student recall and is not limited to a specific section. The instructor keeps the syllabus handy and marks off topics covered and needing additional review. As we journey into BC material infinite series are introduced slowly to develop more theory and work on remediating those silly algebra errors.
Students are usually 12 graders taking either the Methods or Higher Level test of the IB program. Since students are in the AP/BC class the instructor still must meet their in depth theory questions that exceed the boundaries of College Board.]
Midterm Exam: An actual AP test is administered with the AP grade calculated.
Report card exam column has a modified scaling as not all concepts may have been presented.
Final Exam is based upon a complete AP test graded according to AP standards
5- A , 4- B, 3-C, 2-D, 1-F
AB Calculus and BC calculus: General topics and not limited to the list
The rate of Change of a Function
Introduction
Coordinates
Increments: notation and graphical interpretations
Slopes of a straight line
Equations of a straight line : Standard , Point Slope, Slope Intercept and Double Intercept.
Functions and graphs
Domain, Range, Intercepts, Concavity,Increasing , decreasing, zeros, maximum and minimum values of domain and range,
slopes at points from a Calculator aspect for discovery of info for next chapter. Continuity from the “Driving on the Road” aspect.
Derivative of a function both formal and short cut using simple polynomials and rational functions
Velocity and rates
Properties of Limits
Formal Differentiation
“Litany” Graphing functions using Calculus concepts involving limits/formulas and interpreting by naming the y’ line, y” line, Summarizing what each one does. Confirm by the second derivative test.
Continuation of limit First Principles” into epsilon delta definition
Rational and polynomials functions with irrational and rational coefficients and their derivatives
Inverse functions and their derivatives
The increment of a function ( intro to Riemann sums from an algebraic Perspective)
Newton’s Method for solving Equations
Trig functions Review with appropriate identities
Derivatives of Sine and Cosine
Composite functions and their derivatives
L’Hopitals Rule for limits using differentiation formulas
Derivatives of Secant, Cosecant , Tangent and Cotangent
Formal Continuity
Differentials
Use of various derivative notation of for differentiation
Euler's Method via a lab activity
Application
Sign of the first derivative as it compares to the graph of the function
Implicit Differentiation
(Two methods dy/dx versus ( dy and dx).
Related Rates
Sign change of the second derivative as it relates to the graph of f(x) and f’(x)
Curve plotting from both an algebraic standpoint and calculator. Emphasis on when to use Calculator and when to rely on algebra skills
Average Rate of Change
Slope Fields
Rolle’s Theorem
Mean Value Theorem
L’Hopital’s Rule from a formal presentation and its indeterminate forms.
Extension of the Mean Value Theorem
Applications of the Mean Value Theorem
Integration
Review of summation notation
Riemannian Sums Major Lab using both Technology Programs and simple Geometry/Algebra. Students are required to discover a relationship from the following areas under the curve of a quadratic and cubic:
Upper, Lower , Midpoint, Trapezoidal Rule, Simpson’s rule include an error analysis after third day of working with this topic.
The indefinite integral
Applications of indefinite integration
Integration of sine and cosine
Area under a curve by Calculus and technology
Area between curves using the definite integral
Application of the Definite Integral
Continue with area between curves involving trig functions and polynomials for use of the calculator.
Distance
Volumes
slices: Disk, isosceles right triangles, equilateral triangles
shell
washer
Length of a plane curve
Area of surface of revolution
Average value of a function
The Theorems of Pappus Donut Lab during FCAT testing of 10Th graders
Work Problems
Solving differential equations by separation of variables ( More growth and decay)
During the Application of the definite Integral include
Derivatives of inverse function and apply the “litany of graphing”
Derivatives of natural log and logarithmic functions and apply the “litany of graphing.”
Derivatives of exponential functions au and hyperbolic sine and apply the “ litany of graphing”
Note: The “Litany” is a comprehensive look at the function from domain through concavity using the second derivative test.
Compound interest
Exponential Growth
Logistics Equation
Methods of Integration with a constant spiral back into applications involving derivatives
Basic Formulas
Powers of Trig. Functions
Even powers of trig functions
Integrals involving radicals TRIG Substitution
Integrals involving ax2 + bx + c
Integration by partial fractions
Integration by Parts
Integration of rational functions and appropriate trig. functions
Improper Integrals
Polar Graphs
The polar coordinate system
Graphs of polar functions by hand and by calculator.
Polar equations of the conic sections and other curves
The angle between the radius vector and tangent line
Plane areas in polar graphs.
Vectors and Parametric Equations
Vector components and the unit vector
parametric equations in kinematics
Parametric equations in Analytic Geometry
The derivative of the vector function
Tangential vectors
Curvature and normal vectors
Tangential and normal components of the velocity and acceleration vectors
Polar Graphs
BC Curriculum
INFINITE SERIES Will be taught slowly and be intermixed with the AP/AB review through vectors. After this is completed we use another textbook and do the chapter on INFINITE SERIES from start to finish with no spiraling to AB/AP curriculum unless needed for one of the test for convergence or divergence.
Infinite Series
Introduction using graphing calculator and MAPLE software
limits that arise frequently
Infinite series ( arithmetic and geometric)
Test for convergence of series with nonnegative terms
Absolute convergence
Alternating series
Conditional convergence
Power Series for functions Taylor and Mac laurin
Taylor’s Theorem with Remainder
Sine, Cosine, ex
Binomial Series
Lagrange’s Form
Further computations
Logarithms, arctangent, π
Indeterminate forms
Convergence of power series
integration and differentiation
Solving differential equations
First order : Variables separable
First order : Homogeneous
First order : Linear
First order: Exact
Statistics using Calculus
Poisson Distribution
Roots of Unity and other Oxford Press topics meeting IB standards
........ other topics needing remediation such as Geometry will be presented
Complete old AP exams are administrated during the course.
Practice exams from various authors are also included.
Students need to recognize when to use the calculator appropriately.
All responses should be in story format with appropriate calculus documentation.
Complete old IB Exams
Pre- Calculus
PRE CALCULUS: You must have a scientific calculator or graphing calculator otherwise a comprehensive table of trig ratios!
WHITE BOARD MARKERS are required as you will be presenting work in class on the Boards.
Your work will also be placed under the document camera at various times during the course.
Textbook: PreCalculus with Limits Fifth Edition
Supplemental Text Advance M athematics in preparation for Calculus
Supplemental Text Calculus( Either Larson or Key Curriculum)
Day #1 Box project :Examines the responsibility of the student to analyze their math past and apply it to the present course via oral and written math application such as navigation. This project will allow the instructor to gain insight on the students needs.
System of equation involving: linear , cubic ,quartic , logarithmic , exponential ,trigonometric, etc.
The study of right triangles:
via Sine , cosine, tangent, cotangent, secant , cosecant
The relationship of Geometric shapes to right triangles
The “ internal “rules , vocabulary and theorems as they apply to the six trig. functions as well as the Pythagorean theorem. The relationship of these theorems and rules to the real world.
Sequence: Finite and infinite
Relationships of polynomials to patterns: Binomial theorem of expansion
Complex numbers : operations, graphing, roots of unity, relationship to other number systems, conjugates, DeMoivre and related theorems
Proofs involving trig. with polynomials
Graphing all types of functions
Teaching when to use or not use technology
Using Calculus to make graphing easier when technology is not available.
Learning what college professors want from the analysis of a function.
Domain, range, increasing interval, decreasing interval, concave up, concave down, critical points, points of inflection, vertical asymptotes, horizontal asymptotes etc.
Area under the curve via sums and polynomial Calculus
Vectors: operations, graphing, volumes, area, and 3 dimensional vectors
Statistics: Probability, combinations, normal distribution
Matrices: operations and connection to systems of equation
Writing equations of tangent lines , perpendicular lines, straight lines in 2-D and 3-D
Standard Equation of a line ( North America and the world)
Double Intercept form
Point slope form
Slope intercept form
Logarithms
Writing Equations of the Conic Sections and identifying foci, symmetry, eccentricity
Polar Equations with relationships to their cartesian form
Midterm exam : Comprehensive short answer format
Final Exam: National Pre Calculus test ( calculators allowed)and the Litany of a function(non calculator)
