This course completes middle school mathematics and builds the direct foundation for high school algebra, covering six core strands: exponents and scientific notation, linear equations, functions, geometric transformations, the Pythagorean theorem, and bivariate statistics. Sessions move students from numerical reasoning into formal algebraic and functional thinking, and introduce transformational geometry and informal proof — the capstone of the K–8 progression.

Course Strands & Progression

1. Exponents, Radicals & the Number System

• Know and apply the properties of integer exponents
• Use square roots and cube roots to represent solutions to equations
• Express very large and very small numbers using scientific notation, and perform operations with numbers in scientific notation
• Understand that not all numbers are rational, and approximate irrational numbers using rational approximations

2. Linear Equations & Systems

• Solve linear equations in one variable, including equations with variables on both sides
• Understand solutions to linear equations as points on a line, and analyze slope and intercepts
• Solve systems of two linear equations by graphing, substitution, and elimination
• Solve real-world and mathematical problems leading to systems of linear equations

3. Functions

• Understand that a function assigns exactly one output to each input
• Compare properties of two functions represented in different ways (tables, graphs, equations, verbal descriptions)
• Interpret the equation y = mx + b as defining a linear function, and construct functions to model linear relationships
• Describe qualitatively the functional relationship between two quantities from a graph

4. Geometric Transformations & Congruence/Similarity

• Verify experimentally the properties of rotations, reflections, and translations
• Understand congruence and similarity using physical models, transparencies, or geometry software
• Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates
• Understand and apply facts about angles formed by parallel lines cut by a transversal, and angle sums of triangles

5. The Pythagorean Theorem

• Explain a proof of the Pythagorean theorem and its converse
• Apply the Pythagorean theorem to determine unknown side lengths in right triangles, in real-world and mathematical problems
• Apply the Pythagorean theorem to find the distance between two points in a coordinate system
• Solve real-world problems involving volume of cylinders, cones, and spheres

6. Bivariate Statistics

• Construct and interpret scatter plots for bivariate measurement data
• Describe patterns of association (clustering, outliers, positive/negative association, linear/nonlinear)
• Fit a straight line to data that suggests a linear association, and informally assess model fit
• Use the equation of a linear model to solve problems in context
• Construct and interpret two-way tables for categorical data