Algebra 1 Curriculum

Below are skills needed, with links to resources to help with that skill. We also encourage 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.

Algebra 1 | Numbers
☐ Simplify radical terms (no variable in the radicand)
☐ Squares and Square Roots
☐ Surds
☐ Simplifying Square Roots
☐ Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form
☐ Squares and Square Roots in Algebra
☐ Simplifying Square Roots
☐ Rationalize the Denominator
☐ Understand and use scientific notation to compute products and quotients of large or small numbers.
☐ Standard Form
☐ Scientific Notation
☐ Index Notation - Powers of 10
☐ Definition of Scientific Notation
☐ Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation
☐ Solving Equations
☐ Real World Examples of Quadratic Equations
☐ Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s)
☐ Absolute Value
☐ Laws of Exponents
☐ 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
☐ Know how to calculate n! for whole numbers n, and the relationship between n! and (n - 1)!
☐ Full Precision Calculator
☐ Factorial Function !
☐ Understand what is meant by an imaginary number and a complex number.
☐ Complex Numbers
☐ The Evolution of Numbers
☐ Real Numbers
☐ Imaginary Numbers
☐ Definition of Imaginary Numbers
☐ Definition of Complex Number
☐ Understand what is meant by infinity and that infinity is not a Real number.
☐ What is Infinity?
☐ Real Numbers
☐ Represent a repeating decimal as a fraction.
☐ Does 0.999... equal 1?
☐ Understand the geometric mean, how to calculate it, and its relationship to mean proportionals.
☐ Mean Proportional
☐ Geometric Mean
☐ Understand the harmonic mean, and how to calculate it.
☐ Harmonic Mean
Algebra 1 | 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 the metric measurement system, given the relationship between the units
☐ Conversion of Area
☐ Conversion of Length
☐ How to Safely Convert From One Unit to Another
☐ Metric Numbers
☐ Unit Converter
☐ 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 (metric measurements)
☐ Accuracy and Precision
☐ Errors in Measurement
☐ Percentage Error
☐ Unit of Measurement
☐ Solve problems involving conversions within the US standard measurement system, given the relationship between the units
☐ How to Safely Convert From One Unit to Another
☐ Conversion of Length
☐ Conversion of Area
☐ Unit Converter
☐ 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 (US standard measurements)
☐ Accuracy and Precision
☐ Errors in Measurement
☐ Percentage Error
☐ Unit of Measurement
Algebra 1 | Algebra
☐ Translate a quantitative verbal phrase into an algebraic expression
☐ Introduction to Algebra - Multiplication
☐ Introduction to Algebra
☐ Solving Inequality Questions
☐ Solving Word Questions
☐ Find values of a variable for which an algebraic fraction is undefined.
☐ Dividing by Zero
☐ Algebra Mistakes
☐ Solving Equations
☐ Using Rational Expressions
☐ Add or subtract fractional expressions with monomial or like binomial denominators
☐ Fractions in Algebra
☐ Using Rational Expressions
☐ Multiply and divide algebraic fractions, and express the product or quotient in its simplest form
☐ Fractions in Algebra
☐ Using Rational Expressions
☐ Recognize and factor the difference of two perfect squares
☐ Factoring in Algebra
☐ Special Binomial Products
☐ Definition of Difference of Squares
☐ Write verbal expressions that match given mathematical expressions
☐ Order of Operations - PEMDAS
☐ Order of Operations - BODMAS
☐ The Language of Mathematics
☐ 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 literal equations for a given variable
☐ Equations and Formulas
☐ Solve equations involving fractional expressions. Note: Expressions which result in linear equations in one variable.
☐ Fractions in Algebra
☐ Solving Equations
☐ Rational Expressions
☐ Using Rational Expressions
☐ Solve algebraic proportions in one variable which result in linear or quadratic equations
☐ Solving Equations
☐ Distinguish the difference between an algebraic expression and an algebraic equation
☐ Algebra - Definitions
☐ Translate verbal sentences into mathematical equations or inequalities, and simplify them.
☐ Solving Word Questions
☐ Solving Inequality Questions
☐ Write algebraic equations or inequalities that represent a situation
☐ Solving Word Questions
☐ Solve complex equations of degree greater than two by making an appropriate change of variable.
☐ Change of Variables
☐ Degree
☐ 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.
☐ Definition of Standard Form
☐ Standard Form
☐ Scientific Notation
☐ Zero Product Property
☐ Definition of Standard Form (Numbers)
Algebra 1 | Exponents
☐ 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
Algebra 1 | 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
☐ Determine whether a given point is in the solution set of a system of linear inequalities
☐ Solving Inequalities
☐ Graphing Linear Inequalities
☐ Inequality Grapher
☐ Graph linear inequalities
☐ Solving Inequalities
☐ Intervals
☐ Inequality Grapher
☐ Graphing Linear Inequalities
Algebra 1 | Coordinates
☐ Plot points using coordinates in three dimensions.
☐ Cartesian Coordinates
Algebra 1 | Linear Equations
☐ Solve systems of two linear equations in two variables algebraically
☐ Systems of Linear Equations
☐ Puzzle - Pencils and Jars
☐ 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
☐ Solving Word Questions
☐ Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables
☐ Systems of Linear Equations
☐ Solving Word Questions
☐ Show that, given a system of two equations in two variables, the two equations can be combined in various ways to give other equations with the same solutions; thus justifying the elimination method.
☐ Systems of Linear Equations
Algebra 1 | 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
☐ Quadratic Equations
☐ Systems of Linear and 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
☐ Analyze and solve verbal problems that involve quadratic equations
☐ Real World Examples of Quadratic Equations
☐ Solving Word Questions
Algebra 1 | Polynomials
☐ 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
☐ Definition of Monomial
☐ Definition of Binomial
☐ Definition of Polynomial
☐ 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
☐ Understand Special Binomial Products
☐ Special Binomial Products
☐ Factoring in Algebra
Algebra 1 | 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
☐ Intervals
☐ Set-Builder Notation
☐ Find the complement of a subset of a given set, within a given universe
☐ Introduction to Sets
☐ Sets and Venn Diagrams
☐ Definition of Set
☐ Understand the following terms: Member (or element) of a set, subset, Universal set, Null (or empty) set, intersection of sets (no more than three sets), union of sets (no more than three sets), the difference between two sets, the complement of a set
☐ 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
☐ Commutative, Associative and Distributive Laws
☐ Inverse
☐ 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
☐ Closure
☐ Real Number Properties
☐ Express the union or intersection of sets of numbers in interval notation.
☐ Introduction to Sets
☐ Intervals
☐ Number Line
☐ Sets and Venn Diagrams
☐ Draw and interpret sets in Venn diagrams
☐ Sets and Venn Diagrams
Algebra 1 | 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
☐ Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions
☐ Parabola
☐ Function Grapher and Calculator
☐ Absolute Value in Algebra
☐ Linear Equations
☐ Square Function
☐ Graphing Quadratic Equations
☐ Explore the Quadratic Equation
☐ 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
☐ Parabola
☐ Function Transformations
☐ 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
☐ Quadratic Equations
☐ Graph of an Equation
☐ 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
☐ Domain, Range and Codomain
☐ What is a Function
☐ Definition of Range of a function
☐ Definition of Domain of a function
☐ Definition of 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
Algebra 1 | Graphs
☐ Graph the slope (gradient) as a rate of change between dependent and independent variables
☐ Definition of Gradient
☐ Definition of Slope
☐ Equation of a Straight Line
☐ Slope (Gradient) of a Straight Line
☐ Linear Equations
☐ Calculate the Straight Line Graph
☐ Gradient (Slope) of a Straight Line
☐ Determine the slope (gradient) of a line, given the coordinates of two points on the line
☐ Slope (Gradient) of a Straight Line
☐ Gradient (Slope) of a Straight Line
☐ Equation of a Straight Line
☐ Calculate the Straight Line Graph
☐ Equation of a Line from 2 Points
☐ Linear Equations
☐ Write the equation of a line, given its slope (gradient) and the coordinates of a point on the line
☐ Slope (Gradient) of a Straight Line
☐ Gradient (Slope) of a Straight Line
☐ Equation of a Straight Line
☐ Point-Slope Equation of a Line
☐ Equation of a Line from 2 Points
☐ 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
☐ Equation of a Straight Line
☐ Linear Equations
☐ 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
☐ Equation of a Straight Line
☐ Determine the slope (gradient) of a straight line, given its equation in any form
☐ Slope (Gradient) of a Straight Line
☐ Gradient (Slope) of a Straight Line
☐ Equation of a Straight Line
☐ General Form of Equation of a Line
☐ Linear Equations
☐ Determine if two lines are parallel, given their equations in any form
☐ Gradient (Slope) of a Straight Line
☐ Slope (Gradient) of a Straight Line
☐ Finding Parallel and Perpendicular Lines
☐ Definition of Parallel Lines
☐ Determine whether a given point is on a line, given the equation of the line
☐ Linear Equations
☐ Determine the vertex, axis of symmetry, focus and directrix of a parabola, given its equation.
☐ Square Function
☐ Parabola
☐ Definition of Parabola
☐ Graphing Quadratic Equations
☐ Explore the Quadratic Equation
☐ 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.
☐ Square Function
☐ Parabola
☐ Graphing Quadratic Equations
☐ Definition of Parabola
☐ Explore the Quadratic Equation
☐ Graph and solve systems of linear equations and inequalities with rational coefficients in two variables.
☐ Systems of Linear Equations
☐ Graphing Linear Inequalities
☐ Function Grapher and Calculator
☐ Inequality Grapher
☐ 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
☐ Systems of Linear and Quadratic Equations Solving Graphically
☐ Systems of Linear and Quadratic Equations
☐ Quadratic Equations
☐ Find the slope of a perpendicular line, given the equation of a line
☐ Slope (Gradient) of a Straight Line
☐ Gradient (Slope) of a Straight Line
☐ Definition of Perpendicular Lines
☐ Finding Parallel and Perpendicular Lines
☐ Determine whether two lines are parallel, perpendicular, or neither, given their equations
☐ Slope (Gradient) of a Straight Line
☐ Gradient (Slope) of a Straight Line
☐ 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
☐ Point-Slope Equation of a Line
☐ Slope (Gradient) of a Straight Line
☐ Gradient (Slope) of a Straight Line
☐ Perpendicular and Parallel
☐ Find the equation of a line, given a point on the line and the equation of a line parallel to the desired line
☐ Slope (Gradient) of a Straight Line
☐ Gradient (Slope) of a Straight Line
☐ Finding Parallel and Perpendicular Lines
☐ Perpendicular and Parallel
☐ Point-Slope Equation of a Line
☐ Find the midpoint of a line segment, given its endpoints
☐ Definition of Midpoint
☐ Midpoint of a Line Segment
☐ Find the length of a line segment, given its endpoints
☐ Distance Between 2 Points
☐ Activity: A Walk in the Desert
☐ Pythagoras Theorem
☐ 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 Segment
☐ Bisect
☐ Definition of Bisect
☐ Definition of Perpendicular
☐ Point-Slope Equation of a Line
☐ Investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope (gradient) formulas
☐ Triangles - Equilateral, Isosceles and Scalene
☐ Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram
☐ Slope (Gradient) of a Straight Line
☐ Distance Between 2 Points
☐ Midpoint of a Line Segment
☐ Finding Parallel and Perpendicular Lines
☐ Gradient (Slope) of a Straight 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
☐ Function Grapher and Calculator
☐ Determine the area of an ellipse from its Cartesian formula
☐ Ellipse
☐ Area Calculator
☐ Know how to convert the equation of a straight line between these types: Slope-intercept form, General form and point-slope form.
☐ Point-Slope Equation of a Line
☐ General Form of Equation of a Line
☐ Equation of a Straight Line
☐ Find the coordinates of the point that divides a line segment in a given ratio.
☐ Midpoint of a Line Segment