In 9th grade Algebra, students will be given the opportunity for focused learning experiences in procedural skill and fluency in solving linear equations and inequalities in one variable. Additionally, students will deepen their understanding of linear equations and inequalities in two variables. Also, the course will emphasize modeling with linear equations and inequalities, culminating with solving systems of both linear equations and inequalities. From there, the course shifts to developing a deeper understanding of functions. Students will focus on linear functions by exploring situations that could be modeled by a linear function. The course concludes with a study of quadratic equations and functions, including identifying key elements of graphs, transformations with functions, and identifying domain and range. Students will develop the necessary understandings and skills that they will need in Plane Geometry and Algebra II.
The fundamental purpose of the Plane Geometry course is to formalize and extend students’ geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course and used as a tool to analyze and describe relationships between geometric figures. Students will also connect their understanding of functions to view transformations as a relationship between an input and its corresponding output. Rigid motion will then be used to define congruence. Similarity is defined through similarity transformations. From here, the criteria for triangle congruence and triangle similarity are established. This forms the basis of the proofs students will complete. Students will then use their understanding of similarity and right triangles to develop and establish trigonometric ratios for acute angles. The Pythagorean Theorem, along with trigonometric ratios, will allow students to solve right triangles that arise in a modeling context. Following a study of circles and their properties, the course finishes with geometric modeling using two-dimensional and three-dimensional figures.