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Intermediate Mathematics C (Independent Study)

Quick Overview

Intermediate Mathematics C is the third of a three-year middle school math sequence that prepares students for success in high school algebra.

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Details

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.

• 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
• 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

Course Length 12 Months
Prerequisites Intermediate Mathematics B (or equivalent)
Course Materials

Many K12 courses utilize physical materials in addition to the online content.  These materials may include the following.

K12
Standard Kits

STANDARD kits contain K12 course materials that are required for completion of the course.  These kits include K12 authored materials and/or difficult to procure materials that a student needs to complete a course. Printed reference guides are not included in Standard kits.

Consumable
Materials

CONSUMABLE kits contain only those materials from the standard kit that are intended for one time use. Families who purchase a Standard kit for Child A could later purchase a Consumable kit for Child B to complete the same course.

Materials

Offered for added convenience, ADDITIONAL kits contain easily obtained materials needed for the course which a family may already have in their home.

Learning
Coach and/or Student Reference Guides are available for purchase with some courses.  Electronic versions of these reference guides are also available within digital courses.

Course Start Date

Independent Study Courses

Courses can be started any day for independent study courses without a teacher. Full-year courses last 12 months and semester courses last 6 months.

Courses Taught by a K12 Teacher

Courses with a teacher have designated start dates throughout Fall and Spring. Full-year courses last 10 months and semester courses last 5 months. Courses are taught by teachers in K12 International Academy. For details on start dates, click here.

Teacher Assisted This course is available in two forms: taught by a teacher or designed for independent use. This teacher-supported course is taught through K12 International Academy. It is also available as independent study, where a parent will guide the course.
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To use this course, you'll need a computer with an Internet connection.  Some courses require additional free software programs, which you can download from the Internet.

Hardware and Browsers (Minimum Recommendations)

Windows OS

• CPU: 1.8 GHz or faster processor (or equivalent)

• RAM: 1GB of RAM

• Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher

• At this time our users are encouraged not to upgrade to Windows 10 or Edge (the new browser)

Mac OS

• CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor

• RAM: 1GB of RAM

• Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)

Using  Mobile Devices with the Online School

Unfortunately, many portable devices do not support the software products required to run the Online School. These devices may include (but not limited to): Chromebooks, iPads, iPhones, iPods, Kindles, eReaders, and Andriod phones.

Internet Connections

It is highly recommended that a broadband connection be used instead of dial up.