| 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, subtract fractions:
- Determine common denominators and equivalent fractions
- Work with proper and improper fractions
- Simplify to lowest terms
Students will be able to multiply, and divide fractions:
- Work with proper and improper fractions
- Simplify to lowest terms
|
| 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:
- Solving 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 a 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 (Module 2.2)
|
| 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 to 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 (Module 1.1)
- 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:
- Rewriting from exponential form to logarithmic form and vice versa
- -y=b^x\equiv\log_b(y)=x
- 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:
- Basic understanding of 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
|
