Intermediate Mathematics C is the third of a three-year middle school math sequence that prepares students for success in high school algebra. The course begins with properties of numbers, including exponents, as well as measurement and precision with scientific notation. After using transformations to solve linear equations with one variable, the course presents linear equations and systems with two variables. The course emphasizes modeling with linear relationships, including the use of linear functions to model relationships between bivariate statistical data. Geometry topics include distances, angles, similarity, and congruence with two-dimensional figures and volumes of three-dimensional figures. Finally, students use irrational numbers and the Pythagorean theorem to solve mathematical and real-world problems. This course aligns to national standards and is designed to focus on critical skills and knowledge needed for success in further mathematical studies, including high school algebra. After completing this course, students will be ready to take Algebra I in high school.

**Course Outline**

**SEMESTER 1**

**Unit 1: Number Properties**

In this unit, students learn about number properties including the order of operations and properties of positive and negative exponents. Then, students use scientific notation and orders of magnitude to make sense of very large or small numbers.

- Semester 1 Introduction
- Expressions
- Distributive Property
- Positive Exponents
- Negative Exponents
- Core Focus: Working with Exponents
- Scientific Notation
- Orders of Magnitude
- Core Focus: Precision
- Core Focus: Comparing Big and Small Numbers
- Unit Review
- Unit Test

**Unit 2: Equations**

In this unit, students learn how to solve equations with one variable. Students start with equations with only addition or subtraction and then only multiplication or division before moving to more complicated equations that have more than one operation.

- Addition and Subtraction Equations
- Core Focus: Addition and Subtraction Equations
- Multiplication and Division Equations, Part 1
- Multiplication and Division Equations, Part 2
- Multiple Transformations
- Variables on Both Sides of an Equation
- Strange Solutions
- Core Focus: Transforming Equations
- Core Focus: Tougher Equations
- Unit Review
- Unit Test

**Unit 3: Slope and Proportional Thinking**

In this unit, students start with the basics of graphs of equations in two variables. Then, students focus on using proportional thinking as a way to understand slope of a line. By the end of the unit, students see how to connect slope to rates, similar triangles, and proportional relationships.

- Equations in Two Variables
- Graphs
- Lines and Intercepts
- Slope
- Simple Linear Graphs
- Using Slope as a Rate
- Slope and Similar Triangles
- Comparing Proportional Relationships
- Core Focus: Graphs of Proportional Relationships
- Unit Review
- Unit Test

**Unit 4: Lines**

In this unit, students learn how to use several methods to graph linear equations in two variables. Students also learn how to figure out an equation of a line when given its graph. Finally, they see how to write an equation that models a problem situation, and then use that equation to solve the problem.

- Slope-Intercept Form
- Point-Slope Form
- Equations from Graphs
- Core Focus: Sketching Lines
- Applications: Linear Models
- Core Focus: Linear Models
- Core Focus: Interpreting Linear Models
- Unit Review
- Unit Test

**Unit 5: Systems of Equations**

In this unit, students learn how to solve systems of linear equations using graphs and substitution and by inspection. They also use systems of linear equations to solve several types of real-world problems.

- Systems of Equations
- Using Graphs to Solve Systems
- Solving Systems Using Inspection
- Substitution Method
- Core Focus: Methods of Solving Systems
- Applications: Systems of Linear Equations
- Core Focus: Applications of Linear Systems
- Core Focus: Mixture Problems
- Unit Review
- Unit Test

**Unit 6: Function Basics**

In this unit, students learn about mathematical relations and functions. Then, students see how to work with functions in graphs, equations, and other forms.

- Relations
- Functions, Part 1
- Functions, Part 2
- Function Equations, Part 1
- Function Equations, Part 2
- Interpreting Function Graphs
- Linear Function Models
- Function Representations
- Core Focus: Functions
- Core Focus: Sketching Function Graphs
- Unit Review
- Unit Test

**Unit 7: Semester Review and Test**

- Semester Review
- Semester Test

**SEMESTER 2**

**Unit 8: Linear Models**

In this unit, students use lines as simple models of real-world phenomena. Students also use lines to understand plots of two-dimensional statistical data.

- Semester 2 Introduction
- Direct Linear Variation 1
- Direct Linear Variation 2
- Core Focus: Interpreting Slope and Intercepts
- Quadratic Variation
- Patterns in Two-Way Tables
- Scatter Plots
- Clustering and Outliers
- Associations in Scatter Plots
- Lines of Best Fit
- Core Focus: Model Fit
- Unit Review
- Unit Test

**Unit 9: Basic Geometric Shapes**

In this unit, students learn how to define and use geometric figures made up of points, lines, and angles. Students also see the relationships between angles formed when lines intersect. Finally, they learn about triangles and other polygons.

- Points, Lines, and Angles
- Parallel Lines and Transversals
- Pairs of Angles
- Triangles, Part 1
- Triangles, Part 2
- Core Focus: Angles in a Triangle
- Polygons
- Core Focus: Exterior Angles
- Unit Review
- Unit Test

**Unit 10: Volume**

In this unit, students learn formulas for the volumes of cylinders, cones, and spheres. They also apply these formulas to real-world problems.

- Volumes of Cylinders
- Applications of Cylinders
- Volume of Cones
- Applications of Cones
- Volume of Spheres
- Applications of Spheres
- Core Focus: Comparing Volumes
- Unit Review
- Unit Test

**Unit 11: Congruence and Similarity**

In this unit, students learn the difference between congruence and similarity, and then explore each idea on its own. First, they see the relationship between similarity and scale. Then, students look at congruence in terms of transformations.

- Congruence and Similarity
- Similarity and Scale
- Core Focus: Similarity
- Transformations
- Verifying Properties of Transformations
- Transformations and Congruence
- Transformations and Similarity
- Transformations in the Coordinate Plane
- Core Focus: Preserving Geometric Relationships
- Unit Review
- Unit Test

**Unit 12: Irrational Numbers**

In this unit, students work with irrational numbers. First, they figure out what makes a number irrational, and then they learn to simplify and approximate irrational numbers that arise from square roots. Finally, students find irrational solutions to equations.

- Rational Numbers
- Terminating and Repeating Numbers
- Irrational Numbers
- Rational Square Roots
- Irrational Square Roots 1
- Irrational Square Roots 2
- Core Focus: Approximations of Irrationals
- Higher Roots
- Using Square Roots to Solve Equations
- Core Focus: Irrational Solutions
- Unit Review
- Unit Test

**Unit 13: The Pythagorean Theorem**

In this unit, students learn about one of the most famous and useful mathematical theorems. They learn how to use the theorem to solve problems, learn proofs of the theorem, and even use the theorem to solve problems in three dimensions.

- Pythagorean Theorem
- Proofs of the Pythagorean Theorem
- Applications of the Pythagorean Theorem
- Distances with the Pythagorean Theorem
- Core Focus: Pythagorean Theorem in 3D
- Core Focus: More Pythagorean Applications
- Unit Review
- Unit Test

**Unit 14: End-of-Year Project**

- Project Day 1
- Project Day 2
- Project Day 3
- Project Day 4
- Project Day 5

**Unit 15: Semester Review and Test**

- Semester Review
- Semester Test