Algebra 1 Course Overview
RELATIONSHIPS BETWEEN QUANTITIES & EXPRESSIONS
By the end of 8th grade, students have had a variety of experiences working with expressions and creating equations. Students continue this work in Unit 1 by using quantities to model and analyze situations and to interpret expressions. Students solve unit conversion problems with dimensional analysis. In addition, students expand their algebraic and number sense by operating with polynomials and simplifying radicals.
REASONING WITH LINEAR EQUATIONS & INEQUALITIES
By the end of 8th grade, students have learned to solve linear equations in one variable and systems of linear equations in two variables. In Unit 2 students extend their equation-solving reasoning by justifying their steps with properties. Students develop fluency writing, interpreting, and using various forms of linear equations and inequalities to solve problems. Students solve and interpret solutions of systems of equations and inequalities. In addition, students review the concept of a function and identify linear relationships that are functions. They graph linear functions and interpret the rate of change as well as the graph's key characteristics. Finally, they create function formulas for arithmetic sequences.
MODELING & ANALYZING EXPONENTIAL FUNCTIONS
After students thoroughly learn linear functions, they explore exponential functions in Unit 3. They create function formulas for geometric sequences. Students develop fluency writing, interpreting, and using exponential functions to solve problems. They apply exponential equations to real-world situations. Students graph exponential functions and explore key characteristics of these graphs, including how transformations of the functions affect the graphs.
MODELING & ANALYZING QUADRACTIC FUNCTIONS
Students focus on another type of function in Unit 4: quadratic functions. They explore variables rate of change. In addition, they factor quadratic expressions and equations for math and real-world problems. Students rewrite polynomials in standard form to vertex form to see the vertex in an equation. They find solutions of quadratic equations by factoring or by using the quadratic formula. As a result of using the quadratic formula, they explore complex numbers as non-real solutions. Finally, they develop the concept of a discriminant of a quadratic equation.
COMPARING & CONSTRASTING FUNCTIONS
In Unit 5 students synthesize Units 2, 3, and 4. Presented with graphs, tables, and equations, students determine if they represent a linear function, a quadratic function, or an exponential function (or none of these) by checking first and second differences and evaluating the rates of change. They identify a graph as linear, exponential, quadratic, or none of these. Students also decide which function model best fits a variety of real-world situations.
Unit 6 builds upon students’ prior experiences with data, providing students with opportunities to analyze data distributions in terms of center, spread, and shape. They mathematically identify outliers. Students also analyze bivariate data in two-way tables and scatter plots. In two way tables, students calculate relative frequencies and interpret the meaning of the frequencies in context of the data collection. In scatter plots, students more formally assess how a function model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use the correlation coefficient and knowledge of the context to make judgments about the appropriateness of a linear model.