Algebra 1

Shift the mindset from calculating to finding rules, and build fluency with expressions.

Common CoreA-SSE.A.1

1. 1.1Generalizing Patterns (the n-th Term)Turn a pattern into an algebraic rule
2. 1.2Variables & Evaluating Expressions (Substitution)Replace variables with numbers and calculate the result
3. 1.3The Distributive Property (Area Models)Multiply a number by a sum using area models
4. 1.4Distributing NegativesMultiply grouped terms by a negative number without sign errors
5. 1.5Combining Like Terms & SimplifyingGroup and combine similar parts of an expression
6. 1.6Review & AssessmentPractice and test your skills with patterns, substitution, and distribution

Move from the balance scale to procedural fluency with multi-step and literal equations.

Common CoreA-REI.B.3A-CED.A.4

1. 2.1One- and Two-Step Equations ReviewIsolate a variable using inverse operations
2. 2.2Multi-Step Equations: Variables on Both SidesGet all your variables on one side before you solve
3. 2.3No Solution vs. Infinite SolutionsRecognize equations with no answer or infinitely many answers
4. 2.4Clearing Denominators (LCM Method)Get rid of fractions to make equations easier to solve
5. 2.5Literal Equations (Solving for a Variable)Rearrange a formula to isolate any letter
6. 2.6Review & AssessmentMulti-step and literal equations

Solve, graph, and model inequalities and absolute value relationships.

Common CoreA-REI.B.3A-CED.A.1

1. 3.1Multi-Step Inequalities (The Flip Rule)Solve inequalities and learn when to flip the sign
2. 3.2Compound Inequalities (And vs. Or)Solve and graph double inequalities using 'and' or 'or'
3. 3.3Absolute Value EquationsSolve equations with absolute value by splitting them into two cases
4. 3.4Absolute Value InequalitiesSolve absolute value inequalities using 'and' or 'or'
5. 3.5Modeling with InequalitiesWrite inequalities to solve real-world problems
6. 3.6Review & AssessmentInequalities and absolute value, mixed

Build the language, notation, and graph-reading skills needed to understand functions.

Common CoreF-IF.A.1F-IF.A.2F-IF.B.4F-IF.B.6

1. 4.1Relations, Domain & RangeThe inputs and outputs of a relation
2. 4.2Function Notation f(x) vs. yLearn how to use f(x) instead of y to show inputs and outputs
3. 4.3The Vertical Line TestDecide whether a graph is a function
4. 4.4Evaluating & Interpreting FunctionsInput numbers into a function and read function values from a graph
5. 4.5Key Features of GraphsFind intercepts, peaks, valleys, and where a graph goes up or down
6. 4.6Average Rate of ChangeHow fast a function changes over an interval
7. 4.7Review & AssessmentNotation, evaluation, and reading graphs

Interpret and graph lines through slope, intercepts, and special cases.

Common Core8.EE.B.5F-IF.B.4F-IF.C.7aF-LE.B.5

1. 5.1Slope as Rate of Change (Rise / Run)Measure steepness as rise over run in real-world situations
2. 5.2The Slope FormulaFind the steepness of a line using any two points
3. 5.3Slope-Intercept Form (y = mx + b)Graph lines and understand equations using slope and starting values
4. 5.4Graphing with Intercepts (Cover-Up Method)Find where a line crosses the axes to graph it quickly
5. 5.5Horizontal & Vertical LinesGraph flat and straight-up lines and find their slopes
6. 5.6Direct Variation (y = kx)Proportional relationships and lines that pass through the origin
7. 5.7Review & AssessmentGraphing and interpreting linear functions

Write, compare, transform, and model linear equations, and fit lines to data.

Common CoreA-CED.A.2S-ID.B.6S-ID.C.7

1. 6.1Point-Slope FormWrite a line from a point and a slope
2. 6.2Writing Equations from Two PointsFind the slope, then build the equation
3. 6.3Standard Form & Converting Between FormsAx + By = C, and how to switch forms
4. 6.4Parallel & Perpendicular LinesLines that never meet or meet at a right angle
5. 6.5Scatter Plots & Line of Best FitModel real data with a trend line
6. 6.6Review & AssessmentWriting and modeling with lines

Solve systems by graphing, substitution, elimination, modeling, and method selection.

Common CoreA-REI.C.5A-REI.C.6A-REI.D.12

1. 7.1Solving Systems by GraphingFind the solution as the intersection of two lines
2. 7.2Solving Systems by SubstitutionSwap one equation into the other
3. 7.3Solving Systems by EliminationAdd or subtract equations to cancel a variable
4. 7.4Systems Word Problems (Mixture / Motion)Model and solve real situations
5. 7.5Systems of Inequalities (intro)Shade the overlapping solution region
6. 7.6Choosing the Best MethodPick the fastest approach for a given system
7. 7.7Review & AssessmentSystems, mixed practice

Extend function graphing to absolute value, piecewise, and step functions.

Common CoreF-IF.C.7bF-BF.B.3

1. 8.1Graphing Absolute Value FunctionsThe V-shaped graph and its vertex
2. 8.2Transformations of Absolute Value FunctionsShift, stretch, and flip the V
3. 8.3Evaluating Piecewise FunctionsPick the right rule for each input
4. 8.4Graphing Piecewise FunctionsDraw a function defined in parts
5. 8.5Step Functions & Real-World ModelsFunctions that jump from one value to the next
6. 8.6Review & AssessmentAbsolute value and piecewise graphs

Extend exponent laws into radicals, rational exponents, and the real number system.

Common CoreN-RN.A.1N-RN.A.2N-RN.B.38.EE.A.18.EE.A.4

1. 9.1Product, Quotient & Power RulesCombine powers with the core exponent laws
2. 9.2Zero & Negative ExponentsSimplify expressions with zero and negative exponents
3. 9.3Rational Exponents & RootsConnect a one-half power to a square root
4. 9.4Simplifying RadicalsTidy up square roots and rationalize denominators
5. 9.5Rational vs. Irrational NumbersSums and products of each kind
6. 9.6Pythagorean Theorem & the Distance FormulaRoots in action on the coordinate plane
7. 9.7Scientific Notation ArithmeticMultiply, divide, add, and subtract in scientific notation
8. 9.8Review & AssessmentExponent and radical rules

Model, graph, and compare arithmetic, geometric, and exponential relationships.

Common CoreF-BF.A.2F-LE.A.1F-LE.A.2F-IF.A.3

1. 10.1Arithmetic SequencesAdd the same amount each step
2. 10.2Geometric SequencesMultiply by the same factor each step
3. 10.3Exponential Growth & Decay ModelsBuild and read y = a times b to the x
4. 10.4Graphing Exponential CurvesCurves that climb or fade; the asymptote
5. 10.5Exponential Growth (intro)Growth that builds on itself
6. 10.6Linear vs. Exponential GrowthAdding the same amount vs. multiplying by the same factor
7. 10.7Review & AssessmentSequences and exponential modeling

Classify, add, subtract, multiply, and divide polynomials.

Common CoreA-APR.A.1A-SSE.A.2

1. 11.1Classifying Polynomials (Degree & Terms)Name a polynomial by its size and shape
2. 11.2Adding & Subtracting PolynomialsCombine like terms across polynomials
3. 11.3Multiplying Polynomials (FOIL & Area Models)Multiply binomials and larger products
4. 11.4Special Products (Difference of Squares, Perfect Squares)Difference of squares and perfect-square shortcuts
5. 11.5Dividing Polynomials by a MonomialDivide a polynomial term by term
6. 11.6Review & AssessmentPolynomial operations, mixed

Introduce factoring as reverse distribution to build confidence.

Common CoreA-SSE.B.3A-APR.B.3

1. 12.1Factoring the GCFReverse the distributive property
2. 12.2Factoring Trinomials (x^2 + bx + c)Find two numbers that multiply and add right
3. 12.3The Diamond / Box MethodAn organizer that makes factoring reliable
4. 12.4Factoring by GroupingFactor four-term polynomials in pairs
5. 12.5Factoring Difference of Squaresa^2 - b^2 = (a + b)(a - b)
6. 12.6Review & AssessmentBasic factoring, mixed

Combine factoring methods in a full chapter dedicated to strategy and method diagnosis.

Common CoreA-SSE.B.3

1. 13.1Factoring ax^2 + bx + c (a > 1)Factor when the leading number isn't 1
2. 13.2Factoring Perfect-Square TrinomialsRecognize and factor the square pattern
3. 13.3Multi-Step Factoring (GCF First!)Combine techniques in the right order
4. 13.4Choosing a Factoring StrategyDiagnose which method a polynomial needs
5. 13.5Review & AssessmentComplete factoring, mixed

Study quadratic graphs, forms, transformations, and modeling.

Common CoreF-IF.C.7aF-BF.B.3A-SSE.B.3

1. 14.1Characteristics of Parabolas (Vertex / Symmetry)Vertex, axis of symmetry, and direction
2. 14.2Graphing Quadratics in Standard FormGraph y = ax^2 + bx + c
3. 14.3Vertex Form & TransformationsShift, stretch, and flip a parabola
4. 14.4Modeling with Quadratics (Projectile Motion)Height, area, and path problems
5. 14.5Comparing Forms (Standard / Vertex / Factored)Switch to whichever form is useful
6. 14.6Review & AssessmentQuadratic graphing and feature-reading

Solve quadratics by factoring, square roots, completing the square, and the quadratic formula.

Common CoreA-REI.B.4A-SSE.B.3A-APR.B.3

1. 15.1Solving by Factoring (Zero-Product Property)Set each factor to zero
2. 15.2Solving by Square RootsSolve x^2 = k and (x - h)^2 = k
3. 15.3Completing the SquareMake a perfect square to solve any quadratic
4. 15.4The Quadratic Formula (Part 1: The Discriminant)Predict how many solutions you'll get
5. 15.5The Quadratic Formula (Part 2: Solving)The formula that always works
6. 15.6Choosing a Solution MethodPick the best tool for the job
7. 15.7Review & AssessmentMixed quadratic solving

Close Algebra 1 with statistics, bivariate data, probability, and cumulative synthesis.

Common CoreS-ID.A.1S-ID.A.2S-ID.A.3S-ID.B.5S-ID.B.6S-ID.C.8S-ID.C.9S-CP.A.2

1. 16.1Representing Data: Dot Plots, Histograms & Box PlotsShow a data set's shape
2. 16.2Comparing Distributions: Center & SpreadMean/median, range, IQR & standard deviation
3. 16.3Two-Way Frequency TablesCompare two categories at once
4. 16.4Scatter Plots, Linear Models & ResidualsFit a line and check how well it fits
5. 16.5Correlation & CausationDoes a relationship mean one thing causes the other?
6. 16.6Probability: Independent & Dependent EventsThe chances of combined events
7. 16.7Review & Final ExamCumulative review, practice final, and final exam