Our Curriculum › Math › 9th Grade
Algebra I
A full year of Algebra I: linear equations, inequalities and systems, functions, quadratics and factoring, exponential models, polynomials, radicals, statistics and probability, with personal-finance and modeling projects and a long review stretch at the end.
180 lessons
One a day for a school year
10 units
Each opens to its lessons
8 year-end projects
3 explainers, 5 real-world applications
Standards
Common Core high school math
What's taught, unit by unit
Equations, systems, functions & sequencesDays 1–20
Interpreting and creating equations and inequalities from word problems, solving literal equations, rational exponents, solving systems by substitution and elimination, function notation, domain and range, arithmetic and geometric sequences, and scatter plots.
- 1 · Welcome to Algebra I: Quantities and Units
- 2 · Interpreting Linear Expressions
- 3 · Interpreting Exponential Expressions
- 4 · Creating Linear Equations from Word Problems
- 6 · Creating Linear Inequalities
- 7 · Solving Equations as a Process of Reasoning
- 8 · Solving Literal Equations
- 9 · Introducing Rational Exponents
- 11 · Solving Systems of Linear Equations: Substitution
- 12 · Solving Systems of Linear Equations: Elimination
- 13 · Introducing Function Notation: f(x)
- 14 · Domain and Range of a Function
- 16 · Arithmetic Sequences as Linear Functions
- 17 · Geometric Sequences as Exponential Functions
- 18 · Vertical Shift Transformations of Functions
- 19 · Interpreting Scatter Plots
Plus 4 review days, not listed.
Quadratics & special functionsDays 21–35
Interpreting and factoring quadratic expressions, solving quadratics by factoring, square roots, completing the square and the quadratic formula, graphing parabolas, a linear-quadratic system, and absolute value, step and piecewise functions.
- 21 · Interpreting Quadratic Expressions
- 22 · Factoring Quadratic Expressions
- 23 · Solving Quadratic Equations by Factoring
- 24 · Solving Quadratic Equations by Taking Square Roots
- 26 · Completing the Square
- 27 · The Quadratic Formula
- 28 · The Discriminant and the Existence of Complex Solutions
- 29 · Graphing Quadratic Functions: Vertex and Zeros
- 31 · Systems of One Linear and One Quadratic Equation
- 32 · Introducing Absolute Value Functions
- 33 · Introducing Step Functions
- 34 · Introducing Piecewise Functions
Plus 3 review days, not listed.
Data models & exponential functionsDays 36–50
Lines of best fit, residuals and the correlation coefficient (and why correlation is not causation), exponential growth and decay, compound interest, comparing linear and exponential growth, and choosing a model for real data.
- 36 · Linear Regression and Line of Best Fit
- 37 · Understanding Residuals
- 38 · Interpreting the Correlation Coefficient
- 39 · Correlation Does Not Imply Causation
- 41 · Exponential Growth Models
- 42 · Exponential Decay Models
- 43 · Compound Interest
- 44 · Comparing Linear and Exponential Growth
- 46 · Solving Exponential Equations Graphically
- 47 · Interpreting Rate of Change in Different Function Types
- 48 · Modeling With Multiple Function Types
- 49 · Solving Multi-Step Real-World Problems
Plus 3 review days, not listed.
Polynomials, exponents & factoringDays 51–65
Adding, subtracting and multiplying polynomials, the laws of exponents including negative exponents, factoring (GCF, difference of squares, trinomials, grouping, perfect squares), types of linear systems, and graphing systems of inequalities.
- 51 · Adding and Subtracting Polynomials
- 52 · Multiplying Polynomials
- 53 · Applying the Laws of Exponents
- 54 · Simplifying Expressions With Negative Exponents
- 56 · Factoring Out the Greatest Common Factor
- 57 · Factoring the Difference of Squares
- 58 · Comparing Consistent, Inconsistent, and Dependent Systems
- 59 · Graphing Systems of Linear Inequalities
- 61 · Factoring Trinomials With a Leading Coefficient
- 62 · Factoring by Grouping
- 63 · Factoring Perfect Square Trinomials
- 64 · Choosing the Right Factoring Strategy
Plus 3 review days, not listed.
Quadratic applications & radicalsDays 66–80
Quadratics for area, projectile motion and maximizing area, then simplifying, adding, multiplying and rationalizing radical expressions, square root functions, the Pythagorean theorem in algebra, and radical versus rational-exponent notation.
- 66 · Solving Quadratic Applications: Area Problems
- 67 · Solving Quadratic Applications: Projectile Motion
- 68 · Maximizing Area With a Fixed Perimeter
- 69 · Interpreting the Vertex in Real-World Context
- 71 · Simplifying Radical Expressions
- 72 · Adding and Subtracting Radical Expressions
- 73 · Multiplying Radical Expressions
- 74 · Rationalizing Denominators
- 76 · Simplifying Radical Expressions With Variables
- 77 · Graphing Square Root Functions
- 78 · Applying the Pythagorean Theorem in Algebraic Contexts
- 79 · Converting Between Radical and Rational Exponent Notation
Plus 3 review days, not listed.
Statistics & probabilityDays 81–100
Mean, median, mode, range, IQR, box plots, standard deviation, outliers, histograms and distribution shape, then independent and dependent events, two-way tables, experimental versus theoretical probability and compound events.
- 81 · Measures of Center: Mean, Median, Mode
- 82 · Measures of Spread: Range and Interquartile Range
- 83 · Creating and Interpreting Box Plots
- 84 · Introducing Standard Deviation
- 86 · Comparing 2 Data Sets Using Statistics
- 87 · Identifying Outliers
- 88 · Constructing Frequency Tables and Histograms
- 89 · Describing the Shape of a Distribution
- 91 · Introducing Basic Probability
- 92 · Probability of Independent Events
- 93 · Probability of Dependent Events
- 94 · Using Two-Way Tables to Find Probability
- 96 · Theoretical vs. Experimental Probability
- 97 · Finding the Probability of Compound Events
- 98 · Using Probability to Make Predictions
- 99 · Solving Multi-Step Probability and Statistics Problems
Plus 4 review days, not listed.
Transformations, representations & cumulative reviewDays 101–120
Reflecting, shifting, stretching and combining function transformations, moving between tables, graphs, equations and words, finding key features and comparing functions, and two cumulative reviews of the whole year.
- 101 · Reflecting Functions Over the X-Axis
- 102 · Reflecting Functions Over the Y-Axis
- 103 · Horizontal Shifts of Functions
- 104 · Vertical Stretches and Compressions
- 106 · Combining Multiple Transformations
- 107 · Identifying Transformations From a Graph
- 108 · Applying Transformations to Real-World Models
- 109 · Comparing Transformations Across Function Families
- 111 · Translating Between Tables and Graphs
- 112 · Translating Between Equations and Graphs
- 113 · Translating Between Verbal Descriptions and Equations
- 114 · Choosing the Best Representation for a Situation
- 116 · Analyzing Key Features of a Graph From Any Representation
- 117 · Comparing Functions Given in Different Representations
- 118 · Year-Long Cumulative Review: Linear and Exponential Topics
- 119 · Year-Long Cumulative Review: Quadratics and Statistics Topics
Plus 4 review days, not listed.
Algebraic modeling, personal finance & deeper practiceDays 121–150
Algebraic models for area, perimeter and volume, optimization, scale models and unit pricing; a personal-finance unit on interest, loans, credit, budgets and debt with a capstone; then exponential equations, systems and regression revisited.
- 121 · Algebraic Models for Area
- 122 · Algebraic Models for Perimeter
- 123 · Algebraic Models for Volume
- 124 · Unit Conversion in Algebraic Contexts
- 126 · Solving Optimization Problems With Constraints
- 127 · Applying Algebra to Scale Models
- 128 · Applying Algebra to Unit Pricing
- 129 · Solving Multi-Step Real-World Algebraic Modeling Problems
- 131 · Introducing Simple and Compound Interest in Personal Finance
- 132 · Understanding Loans and Amortization Basics
- 133 · Understanding Credit and APR
- 134 · Building a Simple Budget Using Algebra
- 136 · Comparing Savings Growth Under Different Interest Rates
- 137 · Modeling Debt Payoff Strategies
- 138 · Evaluating Real Financial Scenarios
- 139 · Synthesizing a Personal Finance Capstone Project
- 141 · Creating Exponential Equations
- 142 · Solving Simple Exponential Equations via Exponent Laws
- 143 · Applying Literal Equations to Real-World Formulas
- 144 · Applying Systems of Equations to Real-World Problems
- 146 · Deepening Linear Regression: Making Predictions
- 147 · Analyzing Residual Plots for Model Fit
- 148 · Correlation Coefficient: Strength and Direction in Real Data
- 149 · Synthesizing Two-Variable Statistics: A Data Investigation
Plus 6 review days, not listed.
Cumulative review, practice & explainer projectsDays 151–170
Cumulative reviews of equations, functions, systems, quadratics, statistics and probability, a timed practice assessment, common errors, a reflection, then explainer projects and real-world projects such as an event budget, a road trip, a garden and phone plans.
- 151 · Cumulative Review: Equations and Inequalities
- 152 · Cumulative Review: Functions and Graphing
- 153 · Cumulative Review: Systems and Quadratics
- 154 · Cumulative Review: Statistics and Probability
- 156 · Practicing a Comprehensive Mixed Review Set
- 157 · Timed Practice Assessment
- 158 · Reviewing Common Error Patterns
- 159 · Reflecting on a Year of Algebra I Growth
- 161 · Explainer Project: Teaching Quadratics
- 162 · Explainer Project: Teaching Systems of Equations
- 163 · Real-World Synthesis Project: Planning an Event Budget
- 164 · Real-World Synthesis Project: Analyzing a Road Trip
- 166 · Real-World Synthesis Project: Designing a Garden
- 167 · Real-World Synthesis Project: Comparing Phone Plans
- 168 · Explainer Project: Teaching Probability
- 169 · Completing a Final Applied Project of Your Choice
Plus 4 review days, not listed.
Final review & celebrationDays 171–180
Final reviews of equations, functions, quadratics, radicals and statistics, preparing and giving a presentation, three celebration days, a look ahead to Geometry, and a final reflection.
- 171 · Final Review: Equations, Inequalities, and Functions
- 172 · Final Review: Quadratics, Radicals, and Statistics
- 173 · Preparing Your Year-End Math Presentation
- 174 · Delivering Your Year-End Math Presentation
- 175 · Celebration Day: Reflecting on a Year of Algebra I!
- 176 · Celebration Day: A Favorite Problem Challenge
- 177 · Celebration Day: Math Around You
- 178 · Looking Ahead: Geometry Next Year
- 179 · Final Reflection: My Year in Algebra I
- 180 · Congratulations! You Completed Algebra I!
By the end of the year, your child can
- Solve linear equations, inequalities and systems of equations, and write them from word problems
- Graph and compare linear, quadratic and exponential functions and use function notation
- Factor quadratics and solve them by factoring, completing the square or the quadratic formula
- Add, subtract, multiply and factor polynomials and simplify expressions with radicals and exponents
- Fit a line to data and describe its fit with residuals and correlation
- Find probabilities of independent, dependent and compound events
Other 9th Grade subjects: English 9: Literature · English 9: Composition & Grammar · Biology · World History