Competency-Based Mathematics Program: Instruction

Students in the Competency-Based Mathematics program learn the course content by using the software they are provided for the course. If they are taking the course at a Model 1 school, students may also be taught course content during class by their high school math teacher. The math teachers at Model 1 schools are given the freedom to choose how they teach their high school class, but all students in the program, in both Model 1 and Model 2, must complete all of the sections on the software that are required for each course and must complete the designated number of exams (3 for College Algebra; 2 for Plane Trigonometry; 3 for Precalculus) successfully.

The software’s learn mode presents the concepts, definitions, and examples for each lesson similar to how a textbook would, but unlike a textbook, the software also has narration and videos.

The software’s practice mode offers unlimited practice problems with helpful feedback and an Interactive Tutor that lets students view a fully worked-out solution or complete a guided step-by-step process in order to find a solution.

The software’s certify mode is where students complete assigned homework problems. There is a table in the lower part of the screen that shows the number of problems, the number of strikes for incorrect answers, and the maximum number of strikes allowed to pass the certification.  If a student earns too many strikes, they must reattempt the certify for that lesson. Students are allowed an unlimited number of attempts to certify.

MATH 156 College Algebra

  • Test 1: Covers Hawkes sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, which include:
    • Real numbers (including integers, rational numbers, absolute values and interval notation)
    • Algebraic expressions
    • Integer Exponents (including properties of exponents and scientific notation)
    • Rational exponents
    • Radical Expressions
    • Polynomials (including simple factoring including difference of squares, sum and difference of cubes)
    • The imaginary unit I and its properties
    • The algebra of complex numbers
    • Roots and complex numbers
    • Linear equations in one variable (including absolute values, solving for a certain variable and simple story
      problems)
    • Linear inequalities in one variable (including absolute values and simple story problems)
    • Quadratic equations in one variable (including solutions by factoring and the quadratic formula)
    • Rational expressions (including simplification and work-rate problems)
    • Radical equations
  • Test 2: Covers Hawkes sections 2.1, 2.3, 2.6, 3.1, 3.2, 3.3, 3.5, and 3.6, which include:
    • The Cartesian Coordinate System (including plotting points and the distance and midpoint formulas)
    • Linear Equations in Two Variables (including slopes, the slope-intercept form and the standard form)
    • Slope and Forms of Linear Equations
    • Linear Inequalities in Two Variables
    • Relations and Functions (including domains, ranges and graphs)
    • Linear and quadratic functions and their graphs.
    • Inverse and direct variation
    • Multivariable Functions
    • Mathematical Models
  • Test 3: Covers Hawkes sections 4.1, 4.2, 4.3, 4.4, 5.1, 5.2, 5.4, and 5.5,  which include:
    • Transformations of functions (including shifts, reflections, stretches and even and odd functions)
    • Properties of Functions
    • Combining functions (including addition, subtraction, multiplication, composition, and decomposition)
    • Inverses of functions (definition and computing simple inverses)
    • Polynomial functions (including zeros and roots)
    • Polynomial inequalities
    • Polynomial division (including division algorithm, remainder theorem, zeros, linear factors, and long division)
    • The Fundamental Theorem of Algebra (including constructing polynomials with given zeros)
    • Rational functions (including asymptotes and graphing)
    • Rational Inequalities including (solving rational inequalities)
  • Test 4: Covers Hawkes sections 6.1, 6.2, 6.3, 6.4, 11.1, 11.2, 11.3, 11.4, 11.5, and 11.7, which include:
    • Exponential functions (including graphing and exponential growth and decay problems)
    • Exponential models
    • Logarithmic functions (including graphing, properties of logarithms and common logarithmic functions)
    • Logarithmic models
    • Solving systems of equations with two equations and two unknowns.
    • Matrix Notation and Gaussian Elimination including (Linear systems, matrices, augmented matrices, Gaussian elimination, row echelon form, and using matrices to solve systems of linear equations)
    • Determinants and Cramer’s Rule including (Determinants and their evaluation, using Cramer’s rule to solve linear systems, and using matrices to solve systems of linear equations)
    • Basic Matrix Operations including (Matrix addition, scalar multiplication, matrix multiplication, and performing matrix operations)
    • Inverses of Matrices including (The matrix form of a linear system, finding the inverse of a matrix, and using matrix inverses to solve linear systems)
    • Systems of Linear Inequalities and Linear Programming

MATH 157 Plane Trigonometry

  • Test 1: Covers Hawkes sections 7.1, 7.2, 7.3, 7.4, 7.5, and 7.6, which include:
    • Radian and Degree Measure of Angles
    • Trigonometric Functions and Right Triangles
    • Trigonometric Functions and the Unit Circle
    • Graphs of Sine and Cosine Functions
    • Graphs of Other Trigonometric Functions
    • Inverse Trigonometric Functions
  • Test 2: Covers Hawkes sections 8.1, 8.2, 8.3, 8.4, 9.1, 9.2, 9.6 and 9.7, which include:
    • Fundamental Trigonometric Identities
    • Sum and Difference Identities
    • Product-Sum Identities
    • Trigonometric Equations
    • The Law of Sines
    • The Law of Cosines
    • Vectors in the Cartesian Plane including (Vector terminology, basic vector operations, component form of a vector, finding the magnitude and direction for the vector given its initial point and its terminal point, finding the horizontal and vertical components of a vector given its magnitude and direction, performing vector operations, and representing vectors in polar form)
    • The Dot Product including (The dot product and performing vector operations)

MATH 186 Precalculus

  • Test 1: Covers Hawkes sections 2.1, 2.6, 3.1, 3.2, 3.3, 3.5, 3.6, which include:
    • Cartesian coordinates (including plotting points and the distance and midpoint formulas)
    • Graph systems of linear inequalities
    • Relations and Functions
    • Linear and Quadratic Functions
    • Variation and Multivariable Functions
    • Mathematical Models
  • Test 2: Covers Hawkes sections 4.1, 4.2, 4.3, 4.4, 5.1, 5.2, 5.4, 5.5, which include:
    • Transformations of Functions
    • Properties of Functions
    • Combining Functions
    • Inverses of Functions
    • Introduction to Polynomial Functions and Graphs
    • Polynomial Inequalities
    • Polynomial Division and the Division Algorithm
    • The Fundamental Theorem of Algebra
    • Rational functions (including asymptotes and graphing)
    • Rational Inequalities including (solving rational inequalities)
  • Test 3: Covers Hawkes sections 6.1, 6.2, 6.3, 6.4, 11.1, 11.2, 11.3, 11.4, 11.5, and 11.7, which include:
    • Exponential Functions and Their Graphs
    • Exponential Models
    • Logarithmic Functions and Their Graphs
    • Properties and Applications of Logarithms
    • Solving Systems of Equations
    • Matrix Notation and Gaussian Elimination including (Linear systems, matrices, augmented matrices, Gaussian elimination, row echelon form, and using matrices to solve systems of linear equations)
    • Determinants and Cramer’s Rule including (Determinants and their evaluation, using Cramer’s rule to solve linear systems, and using matrices to solve systems of linear equations)
    • Basic Matrix Operations including (Matrix addition, scalar multiplication, matrix multiplication, and performing matrix operations)
    • Inverses of Matrices including (The matrix form of a linear system, finding the inverse of a matrix, and using matrix inverses to solve linear systems)
    • Systems of Linear Inequalities and Linear Programming
  • Test 4: Covers Hawkes sections 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, which include:
    • Radian and Degree Measure of Angles
    • Trigonometric Functions and Right Triangles
    • Trigonometric Functions and the Unit Circle
    • Graphs of Sine and Cosine Functions
    • Graphs of Other Trigonometric Functions
    • Inverse Trigonometric Functions
  • Test 5: Covers Hawkes sections 8.1, 8.2, 8.3, 8.4, 9.1, 9.2, 9.6, and 9.7, which include:
    • Fundamental Trigonometric Identities
    • Sum and Difference Identities
    • Product-Sum Identities
    • Trigonometric Equations
    • The Law of Sines
    • The Law of Cosines
    • Vectors in the Cartesian Plane including (Vector terminology, basic vector operations, component form of a vector, finding the magnitude and direction for the vector given its initial point and its terminal point, finding the horizontal and vertical components of a vector given its magnitude and direction, performing vector operations, and representing vectors in polar form)
    • The Dot Product including (The dot product and performing vector operations)