This course deepens seventh-grade mathematical fluency and reasoning across five core strands: ratios and proportional relationships, the rational number system, expressions and equations, geometry, and statistics and probability. Sessions extend proportional reasoning to real-world and multi-step contexts, formalize computation with all rational numbers, and introduce probability as a new lens for analyzing uncertainty — building the foundation for algebra.

Course Strands & Progression

1. Ratios & Proportional Relationships

• Compute unit rates involving ratios of fractions
• Recognize and represent proportional relationships between quantities (tables, graphs, equations)
• Identify the constant of proportionality and interpret it in context
• Solve multi-step ratio and percent problems (simple interest, tax, tips, markups, markdowns, percent increase/decrease)

2. The Number System

• Apply and extend understanding of addition and subtraction to all rational numbers, including negatives
• Apply and extend understanding of multiplication and division to all rational numbers
• Convert rational numbers to decimals using long division
• Solve real-world problems involving the four operations with rational numbers

3. Expressions & Equations

• Apply properties of operations to add, subtract, factor, and expand linear expressions
• Rewrite expressions in different but equivalent forms to reveal how quantities relate
• Solve multi-step real-world and mathematical problems using positive and negative rational numbers
• Solve word problems leading to equations of the form px + q = r and p(x + q) = r
• Solve word problems leading to inequalities, and graph the solution set

4. Geometry

• Solve problems involving scale drawings and reproduce a figure at a different scale
• Draw geometric shapes with given conditions, including from three-dimensional figures
• Solve problems involving angle relationships (supplementary, complementary, vertical, adjacent)
• Solve problems involving area, circumference, and other properties of circles
• Solve problems involving surface area and volume of three-dimensional objects (prisms, pyramids)

5. Statistics & Probability

• Understand and use random sampling to draw inferences about a population
• Draw informal comparative inferences about two populations using measures of center and variability
• Understand probability as a number between 0 and 1, and approximate probability through observed frequency
• Develop, use, and evaluate probability models, including for compound events