Curriculum Map

Faisal, Yvonne / Pre Calculus Honor / High School
           

Unit Title

Chapter 1

Content

Linear and Quadratic Functions

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Student will:
- Find the intersection of two lines and to find the length and midpoints of a segment;
- Find the slope of a line and to determine whether two lines are parallel, perpendicular, or neither;
- Find an equation of a lines given certain geometric properties of the line.
- Model real-world situations by means of linear functions;
- Add, subtract, multiply, and divide complex numbers;
- Solve quadratic equations using different methods;
- Define and graph quadratic functions;
- Model real-world situations using quadratic functions.

Unit Title

Chapter 10

Content

Trigonometric Addition Formulas

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will be able to:
1. Derive and apply fomulas for the sine, cosine and tangent functions taken of two different angles
2. Derive and apply double-angle and half-angle formulas
3. Use these identities to solve trigonometric equations

Unit Title

Chapter 11

Content

Polar Coordinates and Complex Numbers

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will be able to:
1. Graph polar equations
2. Write complex numbers in polar form
3. Find products of polar numbers
4. Use De Moivre's theorem to find powers of complex numbers
5. Find roots of complex numbers

Unit Title

Chapter 12 and 14

Content

Vectors, Determinants and Matrices

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will be able to:
1. Perform basic operations of vectors, both algebraically and graphically
2. Use coordinates to perform vector operations
3. Use vector and parametric equations to describe motion in the plane
4. Define and apply the dot product
5. Extend understanding of vectors to three dimensions
6. Sketch planes and fine their equations
7. Use determinants to solve algebraic and geometric problems
8. Define and apply the cross product
9. Find the sum, difference or scalar multiples of matrices
10. Find the product of two matrices
11. Find the inverse of 2x2 matrix
12. Solve linear systems using matrices

Unit Title

Chapter 4

Content

Functions

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

1. HW
2. Daily participation
3. Tests
4. Test corrections
5. Group Work

Outcomes

Students will:
- Identify a function, to determine the domain, range, and zeros of a function, and to graph a function;
- Reflect graphs and to use symmetry to sketch graphs;
- Determine periodicity and amplitude from graphs, to stretch and shrink graphs both vertically and horizontally, and to translate graphs;
- Find the inverse of a function, if the inverse exists;
- Form a function of one variable from a verbal description and, when appropriate, to determine the minimum or maximum value of the function.

Unit Title

Chapter 13

Content

Sequences and Series

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will be able to:
1. Identify and arithmetic or geometric sequence and find a formula for its nth term
2. Sum finite arithmetic and geometric sequences
3. Find or estimate the limit of an infinite sequence or to determine that the limit does not exist
4. Find the sum of an infinite geometric series
5. Represent series using sigma notation

Unit Title

Chapter 15 (partial)

Content

Combinatorics

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will be able to:
1. Use Venn diagrams to solve counting problems involving intersections and unions of sets
2. Use addition, multiplication and complement principles to solve counting problems
3. Solve problems involving permutations and computations

Unit Title

Chapter 2

Content

Polynomial Functions

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will:
- Identify a polynomial function, to evaluate it using synthetic substitution, and to determine its zeros;
- Use synthetic division and to apply the remainder and factor theorems;
- Graph a polynomial function and to determine an equation for a polynomial graph;
- Write a polynomial function for a given situation and to find the maximum or minimum value of the function;
- Use technology to approximate the real roots of a polynomial equation;
- Solve polynomial equations by various methods of factoring, including the use of the rational root theorem;
-Apply general theorems about polynomial equations.

Unit Title

Chapter 3

Content

Inequalities

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will:
- Solve and graph linear inequalities;
- Solve and graph polynomial inequalities in one variable;
- Graph polynomial inequalities in two variables and to graph the solution set of a system of inequalities;
- Solve certain applied problems using linear programming;

Unit Title

Chapter 5

Content

Exponents and Logarithms

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will:
- Define and apply integral exponents;
- Define and apply rational exponents;
- Define and use exponential functions;
- Define and apply the natural exponential function;
- Define and apply logarithms;
- Prove and apply laws of logarithms;
- Solve exponential equations and to change logarithms from one base to another;

Unit Title

Chapter 7

Content

Trigonometric Functions

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will:
- Find the measure of an angle in either degrees or radians and to find coterminal angles;
- Find the arc length and area of a sector of a circle and to solve problems involving apparent size;
- Use the definitions of sine and cosine to find values of these functions and to solve simple trigonometric equations;
- Use reference angles, calculators, or special angles to find values of the sine and cosine functions and to sketch the graphs of these functions;
- Find values of the tangent, cotangent, secant, and cosecant functions and to sketch the functions' graphs;
- Find values of the inverse trigonometric functions.

Unit Title

Chapter 8

Content

Trigonometric Equations and Applications

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will:
- Solve simple trigonometric equations and to apply them;
-Find equations of different sine and cosine curves and to apply these equations;
- Use trigonometric functions to model periodic behavior;
- Simplify trigonometric expressions and to prove trigonometric identities;
- Use trigonometric identities or technology to solve more difficult trigonometric equations.

Unit Title

PreCalculus Mastery Topics

Content

Determinants
Mathematical Induction
Permutations
Binomial Theorem

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

1. HW
2 Tests

Outcomes

1. To use determinants to solve algebraic and geometric problems
2.To define and apply the cross product
3. To use mathematical induction to prove that a statement is true
4. To solve counting problems that involve permutations with repetition and circular permutations
5. To use the binomial theorem and Pascal's triangle

Unit Title

Chapter 9

Content

Trinagle Trigonometry

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will be able to:
1. Use right triangle trigonometry to calculate angle and side values
2. Find the area of a triangle given the lengths of two sides and the measure of an included angle
3. Use the law of sines and law of cosines to find unknown parts of a triangle
4. Use trigonometry to solve navigation and survey problems.

Unit Title

Chapters 19 and 20

Content

Limimts, Series, Iterated Functions and an Introduction to Calculus

Skills

- Problem solving skills and strategies
- Critical thinking skills and strategies
- Graphical analysis
- Word problem analysis
- Calculator manipulation
- Mathematical intuition
- Mathematical connections
- Mathematical Modeling
- Deductive Reasoning
- Applying fundamental problems solving steps and strategies

Resources

- Text book
- Graphing calculator
- Teacher's supplements
- Office hours/study hall
- Peer/NHS tutoring

Instructional Strategies

- Warm-up problem
- HW check
- Interactive lesson introduction
- Teacher-student and student-student interactions
- HW review - split between teacher and student-led
- Use of overhead instruction
- Use of graphing calculator for visual explanations;
- Review worksheets
- After-school test review sessions

Assessment

- HW
- Daily participation
-Tests
- Test corrections
- Group Work

Outcomes

Students will be able to:
1. Find the limit of a function or the quotient of two functions
2. Determine whether a function is continuous
3. Sketch the graph of a rational function by hand
4. Use technology to approximate the area under a curve
5. Find derivates of functions
6. Sketch the graphs of functions using derivates
7. Solve extreme value problems using derivates
8. Find instantaneous velocities and accelerations