Algebra 1 Honors

In this unit, students will explore linear relationships and how they can be used to represent and analyze situations with a constant rate of change. Students will learn that the constant rate of change in a linear relationship can be visualized as the slope of its graph and interpreted within a given context. They will examine multiple algebraic representations of linear functions, recognizing that each form reveals different information about the relationship, such as the rate of change, initial value, or key points. Students will also use linear functions to model real-world scenarios and data trends that are approximately linear. In addition, students will understand that a solution to a two-variable linear equation or inequality is an ordered pair that makes the equation or inequality true.

In this unit, students will explore systems of linear equations and inequalities as a way to represent and solve situations involving more than one condition or constraint. Students will understand that a solution to a system is an ordered pair that satisfies all equations or inequalities at the same time. They will learn that solving a system means determining the value or values that make each relationship true simultaneously. Students will also use systems of linear equations and inequalities to model real-world scenarios involving multiple constraints, such as limited resources, goals, costs, or competing conditions, and interpret solutions within the context of the situation.

In this unit, students will explore quadratic functions and how they can be used to model relationships involving a linear rate of change and symmetry around a unique minimum or maximum. Students will learn that quadratic functions can be represented in multiple ways, including as a product of linear factors, and will examine how these forms reveal important features of the function. They will use quadratic functions to model contextual scenarios, analyze key characteristics of graphs, and interpret solutions in context. Students will also understand that every quadratic equation in standard form, where the leading coefficient is not zero, has at most two real solutions, and that these solutions can be determined using strategies such as factoring, graphing, and the quadratic formula.

In this unit, students will explore exponential expressions and functions, beginning with how the properties of exponents are derived from the properties of multiplication and division. Students will learn that exponential functions represent relationships with constant multiplicative growth or decay, and they will use these functions to model contextual scenarios where quantities increase or decrease by a constant factor. Students will also analyze graphs and tables to understand exponential patterns and estimate solutions to equations involving exponential expressions.