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# Intermediate Mathematics B (Independent Study)

## Quick Overview

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

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## Details

Intermediate Mathematics B is the second of a three-year middle school math sequence that prepares students for success in high school algebra. The course begins by developing an understanding of operations with rational numbers, which is applied to working with algebraic expressions and linear equations. This course also helps students develop understanding of proportional relationships and the use of these relationships to solve problems. Geometry topics focus on constructions of two-dimensional figures; properties of circles; scale factors; and problems involving area, surface area, and volume. Finally, students use the tools of probability and statistics to solve basic probability problems and to make inferences based on population samples. 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.

## Course Outline

#### SEMESTER 1

##### Unit 1: The Basics

In this unit, students focus on the building blocks of basic algebra. Building on their understanding of numbers and operations, students use the order of operations to evaluate numerical expressions. Students also interpret, write, and evaluate expressions to solve real-world problems.

• Semester 1 Introduction
• Order of Operations
• Variable Expressions
• Writing Expressions for Word Phrases
• Related Equations
• Solving Problems
• Core Focus: Word Problems
• Core Focus: Interpreting Expressions
• Unit Review
• Unit Test
##### Unit 2: Addition and Subtraction on a Number Line

Number lines are a great way to show how to add and subtract numbers. In this unit, students take a look at how addition and subtraction can also be done with negative numbers, using the number line. Problem solving with integers is also emphasized.

• Integers on a Number Line, Part 1
• Integers on a Number Line, Part 2
• Subtracting Integers
• Core Focus: Distance
• Decimals on a Number Line
• Adding Decimals, Part 1
• Adding Decimals, Part 2
• Core Focus: Opposites in the Real World
• Unit Review
• Unit Test
##### Unit 3: Addition and Subtraction Properties

This unit focusses on facts, or properties, that are true when it comes to adding integers. For example, the commutative property states that the order in which numbers are added does not change the sum. Students explore this and other properties that will help them simplify expressions and solve equations.

• Subtracting Decimals, Part 1
• Subtracting Decimals, Part 2
• Addition and Subtraction Properties
• Core Focus: Absolute Value and Distance
• Equations Involving Addition and Subtraction
• Addition and Subtraction Applications
• Core Focus: Distances Between Rationals
• Unit Review
• Unit Test
##### Unit 4: Multiplication and Division

In this unit, students extend their previous understanding of multiplication and division to signed (positive and negative) numbers as well as other rational numbers. This unit also covers rounding and estimation as well as using equations to solve problems.

• Multiplying Integers and Decimals, Part 1
• Multiplying Integers and Decimals, Part 2
• Dividing Integers and Decimals
• Multiplication and Division Properties
• Core Focus: Closure
• Rounding and Estimation
• Equations Involving Multiplication and Division
• Multiplication and Division Applications, Part 1
• Multiplication and Division Applications, Part 2
• Core Focus: Modeling with Multiplication and Division
• Core Focus: Decimal Forms of Rational Numbers
• Unit Review
• Unit Test

##### Unit 5: Fractions

This unit covers addition, subtraction, multiplication, and division with fractions. This work is also extended to mixed numbers and other forms of rational numbers. These skills are then applied to solving equations and word problems involving rational numbers.

• Equivalent Fractions
• Multiplying Fractions
• Dividing Fractions
• Core Focus: Rational Numbers
• Common Denominators
• Adding and Subtracting Fractions
• Working with Mixed Numbers
• Multiplying and Dividing with Mixed Numbers
• Equations with Fractions
• Core Focus: Fractions and Mixed Numbers
• Core Focus: Applications with Rational Numbers
• Unit Review
• Unit Test
##### Unit 6: Combined Operations

The distributive property provides a powerful tool for working with expressions and equations that have both multiplication and addition. In this unit, the distributive property is used to work with numerical expressions as well as variable expressions and equations. Also, inequalities are used to solve problems.

• The Distributive Property
• Like Terms
• Core Focus: Variable Expressions
• Expressions with Mixed Operations
• Core Focus: Algebraic Expressions
• Equations with Mixed Operations
• Core Focus: Multistep Equations
• Inequalities
• Core Focus: Applications of Inequalities
• Unit Review
• Unit Test
##### Unit 7: Semester Review and Test
• Semester Review
• Semester Test

#### SEMESTER 2

##### Unit 8: Ratio, Proportion, and Percent

In this unit, students work with ratios and proportions. After work calculating and converting ratios, students also solve proportions, and use ratios, proportions, and percents to solve real-world problems.

• Semester 2 Introduction
• Ratios, Part 1
• Ratios, Part 2
• Word Problems with Ratios
• Core Focus: Unit Rates
• Proportion, Part 1
• Proportion, Part 2
• Percents, Fractions, and Decimals
• Working with Percent
• Core Focus: Identifying Proportions
• Unit Review
• Unit Test

##### Unit 9: Proportion Applications

Proportional thinking is important in many real-world applications. In this unit, students focus on many applications of and strategies for working with proportions. Applications include markup and discount, percent problems, simple interest, and problems from science.

• Similarity and Scale
• Proportion Problems
• Direct Linear Variation
• Core Focus: Graphing Proportions
• Percent Problems
• Percent of Increase and Decrease
• Core Focus: Percent Error
• Simple Interest
• Core Focus: Multistep Ratio and Percent Problems
• Core Focus: Constant of Proportionality
• Unit Review
• Unit Test
##### Unit 10: Plane Figures

In this unit, students focus on geometry. Angles, triangles, and quadrilaterals are the focus Special attention is given to constructing triangles and to calculating areas of triangles, quadrilaterals, and other polygons.

• Parallel Lines and Transversals
• Triangles
• Constructing Triangles
• Areas of Rectangles and Triangles
• Areas of Special Quadrilaterals
• Areas of Regular Polygons
• Core Focus: How Many Triangles?
• Unit Review
• Unit Test
##### Unit 11: Circles

Circles are some of the most useful geometric shapes. In this chapter, students learn how to compute the circumference and area of a circle, and use circles to solve real-world problems.

• Circles
• Circumference
• Areas of Circles
• Core Focus: Circumference and Area
• Unit Review
• Unit Test
##### Unit 12: Solid Figures

This unit starts with finding volumes of prisms and then looking at cross-sections of solid figures. Next, students learn about surface area and then use properties of volume and surface area to solve problems.

• Volume and Capacity
• Volumes of Prisms
• Slicing Solids
• Surface Area
• Surface Areas of Prisms
• Properties of Volume and Surface Area
• Core Focus: Applications of Volume and Surface Area
• Unit Review
• Unit Test

##### Unit 13: Probability and Statistics

In this unit, students learn about simple probability and then probability of compound events. Next, the tools of statistics allow students to use samples to make predictions. Then, students use statistical graphs and measures of center and spread to compare populations.

• Probability
• Combined Probability
• Mutually Exclusive Events
• Core Focus: Compound Events
• Samples and Prediction
• Measures of Center
• Frequency Tables and Histograms
• Measures of Variability
• Comparing Populations
• Core Focus: Samples and Simulations
• 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 N/A
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.