| Week |
Sections |
Topics |
Prerequisite Skills |
Student Learning Outcomes
|
| Week 1
|
Fundamentals
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
|
Students will be able to correctly identify the algebraic properties:
- Additive & Multiplicative identity
- Additive & Multiplicative inverse
- Commutative property
- Associative property
- Distributive property
Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of:
- Solving mathematical equations
- Simplifying/evaluating mathematical expressions
|
| Week 2
|
Fundamentals
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Algebraic Properties
|
Students will be able to:
- Add and subtract fractions.
- Determine common denominators and equivalent fractions.
- Work with proper and improper fractions.
- Simplify to lowest terms.
- Multiply and divide fractions.
|
| Week 2
|
Fundamentals
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Algebraic Properties
|
Students will be able to:
- Identify factored vs non-factored forms of a polynomial.
- Successfully factor binomials & trinomials and difference of squares into two binomial terms.
- Factor out GCF.
- Multiply and/or distribute to check their factors are correct.
- Differentiate between factors and terms of a polynomial expression.
|
| Week 3
|
Module 1.1
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Algebraic Properties
- Understanding of the Cartesian coordinate system
|
Students will be able to:
- Solve linear equations in one variable.
- Determine a linear equation.
- Write and interpret a linear equation.
- Graph a linear equation.
|
| Week 3
|
Module 1.2
|
|
|
Students will be able to:
- Solve systems of equations by graphing.
- Solve systems of equations by substitution.
- Solve systems of equations by elimination.
- Identify inconsistent systems of equations containing two variables.
- Express the solution of a system of dependent equations containing two variables.
|
| Week 4
|
Module 2.1
|
|
|
Students will be able to:
- Determine whether a relation represents a function.
|
| Week 4
|
Module 2.2
|
|
- Basic understanding of Functions (Module 2.1)
|
Students will be able to:
- Find the value of Functions.
- Graph the functions listed in the library of functions.
- Determine whether a function is one-to-one.
- Use the vertical line test to identify functions.
|
| Week 4
|
Module 2.2
|
|
|
Students will be able to:
- Find the domain of a function defined by an equation.
|
| Week 4
|
Module 2.2
|
|
|
Students will be able to:
- Find the range of a function defined by an equation.
|
| Week 4
|
Module 2.2
|
|
- Basic understanding of Functions (Module 2.1)
|
Students will be able to:
- Identify the basic toolkit functions.
- Determine Domain and Range for the basic toolkit functions.
|
| Week 5
|
Module 3.1
|
|
|
Students will be able to:
- Combine functions using Algebraic Properties.
- Create a new function by composition of functions.
- Evaluate composite functions.
- Find the domain of a composite function.
- Decompose a composite function into its component functions.
|
| Week 5
|
Module 3.2
|
|
|
Students will be able to:
- Verify inverse functions using Algebraic Properties.
- Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one.
- Find or evaluate the inverse of a function.
- Use the graph of a one-to-one function to graph its inverse function on the same axes.
|
| Week 6
|
Module 4.1
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Algebraic Properties
|
Students will be able to:
- Use the product rule for exponents.
- Use the quotient rule for exponents.
- Use the power rule for exponents.
|
| Week 6
|
Module 4.2
|
|
|
Students will be able to:
- Determine the difference between Linear and Exponential Functions.
- Evaluate exponential functions.
- Find the equation of an exponential function.
- Evaluate exponential functions with base e.
- Evaluate exponential functions with base 10.
- Graph exponential functions.
|
| Week 7
|
Module 5.1
|
|
|
Students will be to able to:
- Rewrite from exponential form to logarithmic form and vice versa.
- Use the product rule for logarithms.
- Use the quotient rule for logarithms.
- Use the power rule for logarithms.
- Expand logarithmic expressions.
- Condense logarithmic expressions.
- Use the change-of-base formula for logarithms.
|
| Week 7
|
Module 5.2
|
|
|
Students will be able to:
- Evaluate logarithms.
- Use common logarithms.
- Use natural logarithms.
- Graph logarithmic functions.
|
| Week 8
|
Module 6.2
|
|
|
Students will be able to:
- Determine complex number solutions.
- Determine solutions of quadratic equations using factoring techniques.
- Determine solutions of quadratic equations using Quadratic Formula.
|
| Week 8
|
Module 6.2
|
|
|
Students will be able to:
- Understand a polynomial expression.
- Recognize characteristics of parabolas.
- Understand how the graph of a parabola is related to its quadratic function.
- Determine a quadratic function's minimum or maximum value.
- Solve problems involving a quadratic function's minimum or maximum value.
|
| Week 9
|
Module 7.1
|
|
|
Students will be able to:
- Identify polynomial functions.
- Identify the degree and leading coefficients of polynomial functions.
- Use long division to divide polynomials.
- Use synthetic division to divide polynomials.
|
| Week 9
|
Module 7.2
|
|
|
Students will be able to:
- Evaluate a polynomial using the Remainder Theorem.
- Use the Factor Theorem to solve a polynomial equation.
- Use the Rational Zero Theorem to find rational zeros.
- Find zeros of a polynomial function.
- Solve real-world applications of polynomial equations.
|
| Week 10
|
Module 8.1
|
|
|
Students will be able to:
- Find the average rate of change of a function.
- Use a graph to determine where a function is increasing, decreasing, or constant.
- Use a graph to locate local maxima and local minima.
- Use a graph to locate the absolute maximum and absolute minimum.
- Identify end behavior of power functions.
|
| Week 10
|
Module 8.2
|
|
|
Students will be able to:
- Recognize characteristics of graphs of polynomial functions.
- Use Factoring to find zeros of polynomial functions.
- Identify zeros and their multiplicities.
- Determine end behavior of polynomial functions.
- Understand the relationship between degree and turning points.
- Graph polynomial functions.
|
| Week 11
|
Module 9.1
|
|
- The student understands that zero in the denominator of a fraction is undefined.
- Basic understanding of Fractions (Fundamentals)
|
Students will be able to:
- Simplify rational expressions.
- Multiply rational expressions.
- Divide rational expressions.
- Add and subtract rational expressions.
|
| Week 11
|
Module 9.2
|
|
|
Students will be able to:
- Identify and graph vertical asymptotes.
- Identify and graph horizontal asymptotes.
- Determine behavior of rational functions around vertical asymptotes.
- Find the domains of rational functions.
- Graph rational functions.
|
| Week 12
|
Module 10.1
|
|
|
Students will be able to:
- Graph functions using vertical and horizontal shifts.
- Graph functions using reflections about the x-axis and the y-axis.
|
| Week 12
|
Module 10.2
|
|
|
Students will be able to:
- Determine whether a function is even, odd, or neither.
- Graph functions using compressions and stretches.
- Combine transformations.
|
