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Algebra I

Master the language of algebra — linear equations, inequalities, systems, polynomials, factoring, quadratic functions, exponential growth, and mathematical modeling. Interactive Desmos explorations bring abstract concepts to life. TEKS §111.39 aligned.

14 Units

40-55 minutes per unit

What You Will Learn

Functions & Modeling

Linear, quadratic, and exponential functions. Real-world applications and mathematical modeling throughout.

Interactive Visualizations

Desmos-powered explorations — manipulate graphs, test conjectures, and build intuition before formalizing concepts.

TEKS §111.39 Aligned

Covers Texas Essential Knowledge and Skills for Algebra I.

All Units

Foundations: Variables and Expressions

Build fluency with variables, algebraic expressions, order of operations, and translating between verbal descriptions and algebraic notation.

•Write and evaluate algebraic expressions using variables
•Translate verbal descriptions into algebraic expressions and equations
•Identify the parts of an expression: terms, coefficients, constants, and degree
+1 more objectives

The Real Number System

Explore the real number system, master the properties of operations, and understand absolute value as distance from zero.

•Classify numbers within the real number system (natural, whole, integer, rational, irrational)
•Apply commutative, associative, and distributive properties to simplify expressions
•Evaluate absolute value expressions and interpret absolute value as distance
+1 more objectives

Solving Linear Equations

Master solving linear equations from one-step through multi-step, including variables on both sides and special cases of identity and no-solution equations.

•Solve one-step and two-step linear equations using inverse operations
•Solve multi-step equations involving the distributive property and combining like terms
•Solve equations with variables on both sides
+1 more objectives

Linear Inequalities

Solve and graph one-variable linear inequalities, compound inequalities, and absolute value inequalities on the number line.

•Solve one-step and multi-step linear inequalities
•Graph solution sets on a number line using open and closed circles
•Solve and graph compound inequalities (AND and OR)
+1 more objectives

Linear Functions and Graphs

Master slope, slope-intercept form, point-slope form, and standard form; graph lines; and understand parallel and perpendicular relationships.

•Calculate slope from two points and interpret it as a rate of change
•Graph linear equations in slope-intercept, point-slope, and standard form
•Write linear equations given slope and a point, or two points
+1 more objectives

Systems of Equations

Solve systems of two linear equations by graphing, substitution, and elimination; classify systems by the number of solutions.

•Solve systems of equations by graphing and identify the solution as an intersection point
•Solve systems using the substitution method
•Solve systems using the elimination (linear combination) method
+1 more objectives

Exponents and Polynomials

Master the laws of exponents, work with scientific notation, and perform polynomial operations including addition, subtraction, and multiplication.

•Apply the laws of exponents to simplify expressions
•Convert between standard notation and scientific notation
•Add, subtract, and multiply polynomials
+1 more objectives

Factor polynomials using the greatest common factor, trinomial methods, and special patterns including difference of squares, perfect square trinomials, and sum/difference of cubes.

•Factor out the greatest common factor from polynomial expressions
•Factor trinomials of the form x² + bx + c and ax² + bx + c
•Recognize and factor difference of squares and perfect square trinomials
+1 more objectives

Quadratic Functions

Graph quadratic functions in standard and vertex form, identify the vertex, axis of symmetry, direction of opening, and intercepts, and apply transformations to the parent function f(x) = x².

•Identify key features of a parabola including vertex, axis of symmetry, direction of opening, and intercepts
•Graph quadratic functions in standard form and vertex form
•Describe transformations of the parent function f(x) = x² including shifts, reflections, and stretches
+1 more objectives

Solving Quadratic Equations

Solve quadratic equations by factoring, taking square roots, completing the square, and applying the quadratic formula; use the discriminant to predict the number and type of solutions.

•Solve quadratic equations by factoring using the Zero Product Property
•Solve equations of the form ax² = c by taking square roots
•Complete the square to solve quadratic equations and convert to vertex form
+1 more objectives

Exponential Functions

Explore exponential growth and decay, graph exponential functions, apply the compound interest formula, and distinguish exponential change from linear and quadratic change.

•Identify and graph exponential functions of the form f(x) = ab^x
•Distinguish exponential growth from exponential decay using the base
•Apply the compound interest formula to solve financial problems
+1 more objectives

Sequences and Series

Identify, write explicit and recursive formulas for arithmetic and geometric sequences, connect sequences to linear and exponential functions, and apply sequence models to real-world patterns.

•Identify whether a sequence is arithmetic, geometric, or neither
•Write explicit and recursive formulas for arithmetic and geometric sequences
•Connect arithmetic sequences to linear functions and geometric sequences to exponential functions
+1 more objectives

Data Analysis and Statistics

Analyze data using measures of center and spread, create scatter plots, identify correlation, fit lines of best fit, interpret two-way frequency tables, and distinguish correlation from causation.

•Calculate and interpret measures of center (mean, median, mode) and spread (range, IQR, standard deviation)
•Create scatter plots and describe the direction, form, and strength of association
•Fit a line of best fit and use it to make predictions
+1 more objectives

Algebra I Capstone

Synthesize the entire Algebra I course by reviewing function families, selecting appropriate models for real-world situations, and solving multi-step problems that integrate linear, quadratic, and exponential reasoning.

•Identify which function type best models a given situation based on data patterns and context
•Build, interpret, and evaluate mathematical models for realistic scenarios
•Solve multi-step problems that require combining skills from across the course
+1 more objectives

Grade 9 Algebra I. Texas FHSP graduation requirement. TEKS §111.39 aligned.