High School Algebra Curriculum

Below are the skills needed, with links to resources to help with that skill. We also enourage plenty of exercises and book work. Curriculum Home

Important: this is a guide only.
Check with your local education authority to find out their requirements.

High School Algebra | Numbers
☐ Simplify radical terms (no variable in the radicand)
Squares and Square Roots
nth Roots
☐ Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form
Simplify in Algebra
Squares and Square Roots in Algebra
☐ Understand and use scientific notation to compute products and quotients of large or small numbers.
Standard Form
Scientific Notation / Standard Form
Index Notation - Powers of 10
Definition of Scientific Notation
☐ Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s)
Laws of Exponents
Absolute Value
Absolute Value Function
Factorial Function !
Absolute Value in Algebra
Definition of Absolute Value
Definition of Factorial
☐ Understand that dividing by zero is undefined.
Reciprocal
Dividing by Zero
Reciprocal
Reciprocal of a Fraction
Zero Product Property
☐ Understand what is meant by a recurring decimal and how it is written.
Does 0.999... equal 1?
Convert Decimals to Fractions
☐ Know how to calculate n! for whole numbers n, and the relationship between n! and (n - 1)!
Factorial Function !
☐ Understand what is meant by an imaginary number and a complex number.
The Evolution of Numbers
Real Numbers
Imaginary Numbers
☐ Understand what is meant by infinity and that infinity is not a Real number.
What is Infinity?
Real Numbers
High School Algebra | Measurement
☐ Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail)
Definition of Speed
US Standard Speed (Velocity)
Metric Speed (Velocity)
Girl, Boy and Dog
Making the Average
The Fly and The Trains
Riding Against the Wind
☐ Solve problems involving conversions within measurement systems, given the relationship between the units
Conversion of Area
Conversion of Length
How to Safely Convert From One Unit to Another
Metric Numbers
Unit Conversion Tool
Conversion of Volume
Conversion of Temperature - Celsius to Fahrenheit
☐ Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure
Accuracy and Precision
High School Algebra | Algebra
☐ Translate a quantitative verbal phrase into an algebraic expression
Introduction to Algebra - Multiplication
Introduction to Algebra
☐ Find values of a variable for which an algebraic fraction is undefined.
Dividing by Zero
Algebra Mistakes
Solving Equations
Solving Rational Inequalities
☐ Add or subtract fractional expressions with monomial or like binomial denominators
Fractions in Algebra
☐ Multiply and divide algebraic fractions, and express the product or quotient in its simplest form
Fractions in Algebra
☐ Recognize and factor the difference of two perfect squares
Factoring in Algebra
Special Binomial Products
Definition of Difference of Squares
Zero Product Property
☐ Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)
Factoring in Algebra
Definition of Trinomial
Factoring Quadratics
☐ Solve equations involving fractional expressions. Note: Expressions which result in linear equations in one variable.
Fractions in Algebra
Solving Equations
☐ Distinguish the difference between an algebraic expression and an algebraic equation
Algebra - Definitions
☐ Understand Special Binomial Products
Special Binomial Products
☐ Solve complex equations of degree greater than two by making an appropriate change of variable.
Change of Variables
Degree (of an Expression)
☐ Identify and factor the difference of two cubes or the sum of two cubes.
Difference of Two Cubes
Factoring in Algebra
Solving Polynomials
☐ Understand the difference between an equation and a formula.
Equations and Formulas
☐ Know how to change the subject of a formula.
Equations and Formulas
Activity: Buffon's Needle
☐ Know the various meanings of the words 'Standard Form', including Scientific Notation.
Standard Form
Scientific Notation / Standard Form
Zero Product Property
Definition of Standard Form (Numbers)
High School Algebra | Exponents
☐ Analyze and solve verbal problems that involve exponential growth and decay
Exponential Growth and Decay
High School Algebra | Inequalities
☐ Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable
Solving Equations
Solving Inequalities
Substitution
☐ Solve linear inequalities in one variable
Solving Inequalities
☐ Graph linear inequalities
Solving Inequalities
Intervals
High School Algebra | Linear Equations
☐ Solve systems of two linear equations in two variables algebraically
Systems of Linear Equations
☐ Solve all types of linear equations in one variable
Balance when Adding and Subtracting
Solving Equations
☐ Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable
Solving Inequalities
Balance when Adding and Subtracting
☐ Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables
Systems of Linear Equations
Solving Systems of Linear Equations Using Matrices
High School Algebra | Quadratic Equations
☐ Solve a system of one linear and one quadratic equation in two variables, where only factoring is required. Note: The quadratic equation should represent a parabola and the solution(s) should be integers.
Factoring Quadratics
Definition of Quadratic Equation
Quadratic Equations
☐ Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots
Quadratic Equations
Factoring Quadratics
Quadratic Equation Solver
Solving Equations
Zero Product Property
☐ Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression
Factoring Quadratics
Quadratic Equations
Quadratic Equation Solver
High School Algebra | Polynomials
☐ Multiply and divide monomial expressions with a common base using the properties of exponents. Note: Use integral exponents only.
Definition of Monomial
Multiplying Polynomials
Variables with Exponents - How to Multiply and Divide them
Laws of Exponents
Using Exponents in Algebra
☐ Add, subtract, and multiply monomials and polynomials
Adding and Subtracting Polynomials
Polynomials - Long Multiplication
Multiplying Polynomials
Definition of Monomial
Definition of Polynomial
Like Terms
☐ Divide a polynomial by a monomial or binomial, where the quotient has no remainder. Use factoring with canceling, or Polynomial long division.
Dividing Polynomials
Polynomials - Long Division
Simplify in Algebra
☐ Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms
Rational Expressions
Polynomials - Long Division
Dividing Polynomials
☐ Determine the sum and product of the roots of a cubic and higher poynomials by examining its coefficients.
Polynomials: Sums and Products of Roots
High School Algebra | Sets
☐ Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form
Introduction to Sets
Set-Builder Notation
Intervals
☐ Find the complement of a subset of a given set, within a given universe
Introduction to Sets
Definition of Set
Sets and Venn Diagrams
☐ Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)
Definition of Set
Introduction to Sets
Sets and Venn Diagrams
Intervals
☐ Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) Note: Students do not need to identify groups and fields, but students should be engaged in the ideas.
Real Numbers
Introduction to Sets
Commutative, Associative and Distributive Laws
Inverse
Introduction to Groups
Definition of Real Numbers
Definition of Commutative Law
Definition of Associative Law
Definition of Distributive Law
Definition of Identity
Definition of Additive Identity
Definition of Multiplicative Identity
Definition of Inverse
Definition of Additive Inverse
Definition of Reciprocal
Definition of Set
☐ Express the union or intersection of sets of numbers in interval notation.
Introduction to Sets
Intervals
Introduction to Inequalities
Number Line
High School Algebra | Functions
☐ Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations
Domain, Range and Codomain
What is a Function
Definition of Function
Definition of Domain of a function
Definition of Range of a function
Injective, Surjective and Bijective
☐ Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions
Absolute Value
Parabola
Function Grapher and Calculator
Absolute Value in Algebra
Linear Equations
Square Function
Graphing Quadratic Equations
Explore the Quadratic Equation Graph
Absolute Value Function
Exponential Function Reference
☐ Investigate and generalize how changing the coefficients of a function affects its graph
Function Grapher and Calculator
Graphing Quadratic Equations
Explore the Quadratic Equation Graph
☐ Find the roots of a parabolic function graphically. Note: Only quadratic equations with integral solutions.
Parabola
Function Grapher and Calculator
Graphing Quadratic Equations
Explore the Quadratic Equation Graph
Quadratic Equations
☐ Define a relation and function
What is a Function
Definition of Function
Definition of Domain of a function
Definition of Range of a function
Injective, Surjective and Bijective
☐ Determine when a relation is a function
What is a Function
☐ Determine if a function is one-to-one, onto, or both
Injective, Surjective and Bijective
Increasing and Decreasing Functions
☐ Determine whether a function is injective, surjective or bijective.
Injective, Surjective and Bijective
Increasing and Decreasing Functions
High School Algebra | Graphs
☐ Graph the slope as a rate of change between dependent and independent variables
Definition of Slope
Equation of a Straight Line
Slope (Gradient) of a Straight Line
Linear Equations
Explore the properties of a straight line graph
Gradient (Slope) of a Straight Line
☐ Determine the slope of a line, given the coordinates of two points on the line
Explore the properties of a straight line graph
Equation of a Straight Line
Slope (Gradient) of a Straight Line
Gradient (Slope) of a Straight Line
Linear Equation Test
Calculate the Straight Line Graph
Equation of a Line from 2 Points
Linear Equations
☐ Write the equation of a line, given its slope and the coordinates of a point on the line
Slope (Gradient) of a Straight Line
Gradient (Slope) of a Straight Line
Explore the properties of a straight line graph
Equation of a Straight Line
Linear Equation Test
Point-Slope Equation of a Line
Equation of a Line from 2 Points
Calculate the Straight Line Graph
Linear Equations
☐ Write the equation of a line, given the coordinates of two points on the line
Calculate the Straight Line Graph
Equation of a Line from 2 Points
☐ Write the equation of a line parallel to the x-axis or the y-axis
Point-Slope Equation of a Line
Linear Equations
Finding Parallel and Perpendicular Lines
☐ Determine the slope of a line, given its equation in any form
Explore the properties of a straight line graph
Slope (Gradient) of a Straight Line
Gradient (Slope) of a Straight Line
Equation of a Straight Line
Linear Equation Test
Linear Equations
☐ Determine if two lines are parallel, given their equations in any form
Finding Parallel and Perpendicular Lines
☐ Determine the vertex and axis of symmetry of a parabola, given its equation.
Parabola
Definition of Parabola
Graphing Quadratic Equations
Explore the Quadratic Equation Graph
Square Function
☐ Determine the vertex and axis of symmetry of a parabola, given its graph. Note: The vertex will have an ordered pair of integers and the axis of symmetry will have an integral value.
Parabola
Graphing Quadratic Equations
Definition of Parabola
Explore the Quadratic Equation Graph
Square Function
☐ Graph and solve systems of linear equations and inequalities with rational coefficients in two variables.
Systems of Linear Equations
☐ Solve systems of linear and quadratic equations graphically. Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers.
Function Grapher and Calculator
☐ Find the slope of a perpendicular line, given the equation of a line
Definition of Perpendicular Lines
Definition of Slope
Finding Parallel and Perpendicular Lines
Calculate the Straight Line Graph
☐ Determine whether two lines are parallel, perpendicular, or neither, given their equations
Finding Parallel and Perpendicular Lines
Perpendicular and Parallel
☐ Find the equation of a line, given a point on the line and the equation of a line perpendicular to the given line
Finding Parallel and Perpendicular Lines
☐ Find the equation of a line, given a point on the line and the equation of a line parallel to the desired line
Finding Parallel and Perpendicular Lines
☐ Find the midpoint of a line segment, given its endpoints
Definition of Midpoint
Midpoint of a Line
☐ Find the length of a line segment, given its endpoints
Distance Between 2 Points
Activity: A Walk in the Desert
☐ Find the equation of a line that is the perpendicular bisector of a line segment, given the endpoints of the line segment
Finding Parallel and Perpendicular Lines
Midpoint of a Line
☐ Find a set of ordered pairs to satisfy a given polynomial equation or other simple function; then plot the ordered pairs and draw the curve.
Graph of an Equation
Activity: Soup Can
☐ Recognize the symmetry in equations and their graphs.
Symmetry in Equations
☐ Plot points using coordinates in three dimensions.
Cartesian Coordinates

 

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