Module 1: Thinking Proportionally
Students build on their experiences with ratios and proportional relationships from grade 6. They will investigate special ratios to develop and connect formulas for the circumference and area of circles. Students will identify and describe proportional and non-proportional mathematical and real-world situations to understand the characteristics of proportional relationships. They will then use formal strategies to solve proportion and percent problems.
Module 2: Constructing and Measuring
Students build on their experiences with angles and triangles and introduce the construction of familiar geometric objects. They will construct basic geometric objects with a compass and straightedge and later use these techniques to construct triangles. Students will use patty paper to investigate special types of angle relationships and then use those relationships to write and solve equations to determine unknown values in a figure. They will use their knowledge of polygons and polyhedra to create and describe cross-sections of right rectangular prisms and pyramids. Finally, students will extend their knowledge of volume and surface area to solve problems involving a variety of three-dimensional solids.
Module 3: Transforming Geometric Objects
Students build on their experience with rational numbers, proportionality, scale drawings, triangles, and angle pairs formed when two lines intersect. They will use patty paper to investigate transformations of geometric objects to develop an understanding of congruence and similarity. Students will then use this new knowledge about transformations to establish facts about triangles and relationships between special angle pairs.
Module 4: Developing Function Foundations
Students build on their experience with proportional relationships and the work they did in Transforming Geometric Objects. Students will analyze and represent linear relationships using tables, equations, graphs, and scenarios. They will develop an understanding of functions. Once they know how to describe functional relationships and construct linear models, they will apply these skills to analyze bivariate data. The concepts in this module will provide the basis for the majority of their high school algebra and statistics studies.
Module 5: Modeling Linear Equations
Students build on their experiences of solving two-step equations and graphing linear equations. They will apply number properties as strategies to write equations in equivalent forms and explore strategies for solving equations with variables on both sides of the equals sign. Students will write and solve equations to answer questions about real-world situations. They will also use systems of linear equations to solve real-world problems.
Module 6: Expanding Number Systems
Students connect numbers, equations, and geometry. Students will explore the properties that define the number systems that they are familiar with and then learn about a new system. Students will develop an understanding of the Pythagorean Theorem and its converse and then apply those theorems to solve real-world problems.
Module 5: Applying Powers
Students build on their knowledge of exponents to develop new rules for operating with integer exponents. They will learn how to write, recognize, compare, and operate with numbers expressed in scientific notation. Students will build on their prior experiences with the volume of prisms and pyramids to develop formulas for the volume of cylinders, cones, and spheres.