This course delivers a full year of Algebra I, covering six core strands: expressions, equations, systems of equations, quadratics, functions, and statistics. Sessions build from foundational algebraic manipulation through linear, quadratic, and exponential reasoning, formalizing function notation and modeling along the way — establishing the algebraic fluency required for Geometry and Algebra II.

Course Strands & Progression

1. Expressions & Structure

• Interpret expressions that represent a quantity in terms of its context
• Use the structure of an expression to identify ways to rewrite it (factoring, recognizing patterns)
• Perform arithmetic operations on polynomials, and factor polynomials using common structures
• Rewrite rational expressions and simplify using properties of exponents

2. Equations & Inequalities

• Create equations and inequalities in one variable to represent real-world relationships
• Solve linear equations and inequalities, including those with variables on both sides
• Rearrange formulas to solve for a quantity of interest (literal equations)
• Solve quadratic equations by inspection, factoring, completing the square, and the quadratic formula
• Understand solving equations as a process of reasoning, and justify each step

3. Systems of Equations

• Create systems of linear equations and inequalities to represent real-world relationships
• Solve systems of linear equations algebraically (substitution, elimination) and graphically
• Solve a simple system of a linear and a quadratic equation
• Interpret solutions to systems in context, including no-solution and infinite-solution cases

4. Functions

• Understand function notation, and interpret statements using function notation in context
• Compare properties of two functions represented in different ways (algebraically, graphically, numerically, verbally)
• Interpret key features of graphs (intercepts, intervals of increase/decrease, extrema, symmetry) in context
• Write functions that describe a relationship between two quantities, including arithmetic and geometric sequences
• Distinguish between linear and exponential models, and recognize situations modeled by each

5. Quadratic & Exponential Relationships

• Analyze quadratic functions using graphs, tables, and equations (vertex form, standard form)
• Interpret the effects of transformations on quadratic and exponential graphs
• Compare linear, quadratic, and exponential models to determine which best fits a given data set
• Solve real-world problems modeled by quadratic and exponential functions

6. Statistics & Data Interpretation

• Represent data with plots on the real number line (dot plots, histograms, box plots)
• Use statistics appropriate to the shape of a data distribution to compare center and spread of two or more data sets
• Summarize, represent, and interpret data on two categorical and quantitative variables, including two-way tables
• Fit a linear function to data and use it to solve problems, distinguishing correlation from causation