In this course, students build on their basic understanding of math to explore symbolic relationships in a variety of ways. Students useintegers and fractions to represent relationships in graphs and functions. Algebra 1 uses problem situations, physical models, and appropriate technology to extend algebraic thinking and engage student reasoning. The concepts emphasized in the course include functions, solving equations, slope as rates of change, proportionality, quadratic equations, exponential growth and decay, rational expressions, and probability in data exploration.
Number Sense and Real Numbers: Students will build fluency with the real number system, including classifying real numbersand using properties of operations. Students will simplify numerical and algebraic expressions accurately using order of operations and the structure of arithmetic.
Expressions, Equations, and Problem Solving: Students will learn to translate real-world situations into algebraic expressions and equations and solve linear equations using properties of equality. Students will strengthen multi-step problem solving skills, including applications involving percent and proportional reasoning.
Linear Relationships and Functions: Students will develop a deep understanding of linear relationships by interpreting graphs, tables, and equations. Students will compute and interpret slope as a rate of change, write equations of lines from multiple representations, and analyze functions (including domain/range and function notation) in context.
Inequalities and Absolute Value: Students will solve and graph linear inequalities, compound inequalities, and absolute valueequations/inequalities. Students will interpret solution sets in real-world contexts and justify solutions using graphical and algebraic reasoning.
Systems of Equations and Inequalities: Students will learn multiple methods for solving systems of linear equations anddetermine when systems have one solution, no solution, or infinitely many solutions. Students will also model constraints usingsystems of inequalities and interpret feasible regions.
Exponents, Polynomials, and Exponential Models: Students will apply exponent rules to simplify expressions and build fluency with polynomial operations. Students will also study exponential growth/decay and use exponential models (including compound interest) to interpret real-world change over time.
Factoring and Quadratic Problem Solving: Students will factor polynomials using multiple strategies and use factoring as a tool for solving equations and interpreting behavior. Students will connect factoring to solving quadratic equations andmodeling scenarios involving maximum/minimum values.
Rational Expressions and Rational Equations: Students will simplify, combine, and solve rational expressions and rational equations while attending to restrictions and excluded values. Students will use rational relationships to model variation andinterpret how rational functions behave in equations and graphs.
Radicals, Roots, and Introductory Trigonometry: Students will simplify radicals, perform operations with radical expressions,and solve radical equations while identifying extraneous solutions. Students will apply basic right-triangle trigonometric ratios to solve for missing sides or angles in geometric and applied settings.
Quadratic Functions and Methods of Solving Quadratics: Students will solve quadratic equations using multiple approaches (square roots, completing the square, and the quadratic formula) and choose efficient methods based on the structure of the problem. Students will graph quadratic functions, interpret vertex/intercepts, and connect algebraic forms to graphical features.
Data Analysis and Mathematical Modeling: Students will represent and summarize data using graphs and numerical measures of center and spread, including standard deviation. Students will analyze relationships using tools like two-way tables and compare linear, exponential, and quadratic models to select and interpret a best-fit model for a given context.
