Students begin the course with one-variable statistics, building on ideas from middle school. Starting with data collection and analysis sets a tone for the course of understanding quantities in context. It also allows students to access grade-level mathematics that isn't as dependent on prior skills as some other topics. Gathering and displaying data, measuring data distribution, and interpreting statistical results encourages students to collaborate, communicate, and explore new tools and routines.

From there, students move on to expand their understanding of linear equations, inequalities, and systems of linear equations and inequalities. They use these representations to model relationships and constraints but also reason with them abstractly. Students write, rearrange, evaluate, and solve equations and inequalities, explaining and validating their reasoning with increased precision. They then take these insights to a unit on two-variable statistics, where they extend their prior knowledge of scatter plots and lines of best fit. Students use residuals and correlation coefficients to assess linear models, interpret quantitative data, and distinguish correlation and causality. They also determine associations in categorical data, by using two-way tables and relative frequencies.

Next, students study functions, continuing the work begun in grade 8. Over the next few units, they deepen their understanding of functions and deepen their ability to represent, interpret, and communicate about them—using function notation, domain and range, average rate of change, and features of graphs. They also see categories of functions, starting with linear functions (including their inverses) and piecewise-defined functions (including absolute value functions), followed by exponential and quadratic functions. For each function type, students begin their investigation with real-world and mathematical contexts, look closely at the structural attributes of the function, and analyze how these attributes are expressed in different representations.

The course ends with a close look at quadratic equations. Students extend their ability to use equations to model relationships and solve problems. They develop their capacity to write, transform, graph, and solve equations—by reasoning, rearranging equations into useful forms, and applying the quadratic formula. In solving quadratic equations students encounter rational and irrational solutions, providing an opportunity to deepen their understanding of the real number system.

Within the classroom activities, students have opportunities to engage in aspects of mathematical modeling. Additionally, modeling prompts are provided for use throughout the course. Modeling prompts offer opportunities for students to engage in the full modeling cycle. These can be implemented in a variety of ways. Please see the course guide for a more detailed explanation of modeling prompts.