|
Month |
Content/Topic |
Skills |
Assessment |
Standards |
|
September
9 days |
· Algebra II Review and Pre-Calculus Intro (Ch. 1 &2) |
· Graphing linear relations and functions
· Review of vocabulary
· Computations with matrices
· Solving systems of equations
· Graphing systems of equations and inequalities
· Written and oral communication of mathematical ideas |
· Class discussions about vocabulary
· Review packet
· Online self-quizzes
· Daily homework
· Online journal/forums |
· A.12.1-6, F.12.1-4 |
|
Sept.-Oct.
14 days |
· The Nature of Graphs (Ch. 3)
o Symmetry
o Families of Graphs
o Inverse Functions and relations
o Rational Functions and Aysmptotes
o Graphs of Inequalities
o Derivatives
o Polynomial Functions
o Continuity
o End Behavior |
· Graph relations and functions both by hand and using graphing utilities
· Analyze families of graphs
· Define and explore symmetry, continuity, and transformations of graphs
· Find inverses of functions
· Find asymptotes, intercepts, derivatives, and critical points of graphs
· Identify end behavior of graphs |
· Daily homework
· Graphing calculator explorations
· Quiz
· Student presentations
· Test
· Notebook |
· A.12.1, A.12.4-5, F.12.2, F.12.4 |
|
October
9 days
|
· Polynomial and Rational Functions (Ch. 4)
o Quadratic Equations and inequalities
o Roots and Critical points |
· Solve polynomial equations
· Solve inequalities
· Solve radical equations
· Use both symbolic and graphical methods to solve equations and inequalities
· Solve an application problem using either symbolic or graphical methods
· Write description of mathematical procedure and results |
· Daily homework
· Graphing calculator explorations
· Online self-quizzes
· Test
· Notebook
· Project: Open Box Problem |
A.12.1-6, B.12.4-6, D.12.3, F.12.1-4 |
|
Oct. – Nov.
14 days |
· The Trigonometric Functions (Ch. 5)
o Angle measure
o Central angles and arcs
o Circular Functions
o Trig functions of special angles
o Right triangles
o Law of Sines
o Law of Cosines
o Area of triangles |
· Define new vocabulary related to trigonometry
· Measure angles in radians and degrees
· Convert angles from radians to degrees and vice versa
· Find reference angles and coterminal angles
· Create and learn to use a unit circle
· Find arc lengths and areas of sectors
· Find the values of the six trigonometric functions
· Solve right triangles
· Solve oblique triangles
· Find the area of triangles using Hero’s formula and sin or cos
· Give a presentation to the class of a problem using trigonometry concepts |
· Daily homework
· Graphing calculator explorations
· Online self-quizzes
· Glossary terms defined (Moodle)
· Unit circle
· Student presentations
· Test
· Notebook |
A.12.1-6, C.12.1-5, D.12.3, F.12.2, F.12.4 |
|
Nov. – Dec.
14 days |
· Graphing Trig Functions (Ch. 6)
o Amplitude
o Period
o Phase shift
· Inverses of Trig Functions (Ch. 6)
o Principal values
o Graphs |
· Graph trig functions
· Find the amplitude, period, and phase shift of trig functions
· Write equations of trig functions
· Evaluate inverse trig functions and find principal values
· Write equations of inverse trig functions
· Graph the inverses of trig functions
· Solve problems involving simple harmonic motion |
· Daily homework
· Graphing calculator explorations
· Online self-quizzes
· Quiz
· Online journal
· Test
· Notebook |
A.12.1-2, A.12.6, C.12.5, F.12.1-2, F.12.4 |
|
December
9 days |
· Trigonometric Identities and Equations (Ch.7)
o Basic Trig Identities
o Sum and Difference Identities
o Half-angle identies
o Double angle identities
o Solving trig equations |
· Identify and use basic trig identities
· Verify trigonometric identities
· Use identities to find numerical values of trig functions
· Solve trig equations numerically, symbolically, and graphically |
· Daily homework
· Graphing calculator explorations
· Student presentations
· Notebook |
A.12.1-6, C.12.5, D.12.3, F.12.2, F.12.3 |
|
January
13 days |
· Vectors and Parametric Equations (Ch. 8)
o Geometric vectors
o Algebraic vectors
o Vectors in 3-D Space
o Perpendicular Vectors
o Applications with vectors |
· Define new vocabulary
· Use vector notation
· Find vector magnitude and direction
· Add, subtract, and multiply vectors
· Find the inner product and cross product of vectors
· Use parametric equations to model and solve problems with vectors |
· Daily homework
· Graphing calculator explorations
· Online journal
· Student presentations
· Test
· Notebook |
A.12.1-6, C.12.1-2, C.12.4-5, D.12.1, D.12.3, F.12.1-4 |
|
Jan. – Feb.
14 days |
· Exponential and Logarithmic Functions (Ch. 11)
o Rational exponents
o The number “e”
o Common logarithms
o Natural logarithms |
· Use the properities of exponents and logarithms to simplify expressions
· Solve exponential and logarithmic equations symbolically and graphically
· Evaluate exponents and logarithms using a calculator
· Solve application problems involving exponents and logarithms
· Create a spreadsheet to calculate compound interest |
· Daily homework
· Graphing calculator explorations
· Spreadsheet activity
· Online journal
· Quiz
· Notecard of properties
· Test
· Notebook |
A.12.1-6, B.12.2, B.12.4-6, F.12.1-4 |
|
Feb. – Mar.
15 days
|
· Sequences and Series (Ch.12)
o Arithmetic
o Geometric
o Infinite
o Convergent and divergent
o Sigma notation
o Pascal’s triangle and binomial expansion |
· Identify and extend arithmetic, geometric and infinite sequences
· Find sums of arithmetic, geometric and infinite series
· Use formulas for sequences and series
· Identify series as either convergent or divergent
· Use Signma notation to write series
· Expand binomials using Pascal’s triangle |
· Daily homework
· Quiz
· Student Presentations
· Test
· Notebook |
A.12.1-6, B.12.2, B.12.4, F.12.1, F.12.4 |
|
March
13 days |
· Iteration and Fractals (Ch. 13)
o Graphical iteration
o The logistic function
o Complex numbers
o Julia and Mandelbrot sets |
· Iterate functions numerically
· Perform graphical iteration on both linear and quadratic functions
· Develop an understanding of chaotic long-term behavior for some functions
· Learn how to enter and use programs in a graphing utility to analyze functions and their behavior
· Define fractals and examine various examples
· Identify fixed points and determine whether one is an attractor or repellor
· Iterate complex numbers
· Make decisions about points in the Julia set or Mandelbrot set
· Research and create a power point presentation about fractal geometry and the chaos theory |
· Daily homework
· Graphing calculator programs
o Logistic
o Julia
o Mandelbrot
· Online journal about fractals and chaos theory
· Power point presentation
· Test
· Notebook |
A.12.1-6, F.12.4 |
|
April
11 days |
· Combinatorics and Probability (Ch. 14)
o Permutations
o Repetitions
o Circular
o Combinations
o Odds
o Independent
o Dependent
o Mutually exclusive or inclusive |
· Solve problems using the basic counting principle, permutations, and combinations
· Distinguish between dependent or independent events
· Distinguish between mutally exclusive or inclusive events
· Find probabilities
· Find odds of success or failure of an event
· Use Venn diagrams to organize information |
· Daily homework
· Online self-quizzes
· Online forum/journal
· Test
· Notebook |
A.12.1-3, A.12.6, B.12.1, B.12.4-6, E.12.5 |
|
May
9 days |
· Statistics and Data Analysis (Ch. 15)
o Frequency distribution
o Measures of Central Tendency
o Measures of Variability
o Scatter Plots
o Curve fitting
o Regression equations |
· Make and use graphs and plots to analyze data
· Find measures of central tendency and variability
· Organize data into frequency distributions
· Fit curves to data
· Collect data on a country’s population and find a model to fit the data
· Prepare a power point of results of research and analysis of population data |
· Daily homework
· Power point presentation: Population data
· Notebook |
A.12.1-6, B.124-6, E.12.1-3 |
|
May – June
8 days |
· Introduction to Calculus (Ch. 17)
o Limits
o Derivatives
o Area under a curve
o Integrals
o Fundamental Theorem of Calculus |
· Define the limit of a function
· Use the definition of a limit to find the derivative of a function
· Find derivatives of functions using the properties of derivatives
· Find the area between a curve and the x-axis by using limits of the areas of rectangles
· Use integration formulas
· Evaluate definite integrals and find areas |
· Daily homework
· Online self-quizzes
· Online forum/journal
· Student presentations
· Notebook |
A.12.1-6, C.12.2, F.12.1-4
|
|
June
4 days |
· Graph theory (Ch. 16)
o Euler paths and circuits
o Shortest paths and minimal distances
o Adjacency matrices
o Spanning trees |
· Learn new vocabulary
· Find Euler paths and circuits
· Develop algorithms to find shortest paths and minimal distances
· Create adjacency matrices for connected graphs
· Find minimal spanning trees
· Use graph theory to solve application problems |
· Worksheet packet
· Class investigations
· Student presentations
· Quiz |
A.12.1-6, B.12.4, C.12.1-3 |
