# Problem Solving in Pre-algebra

Prerequisites: Qualifying math score and completion of Pre-algebra or equivalent

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: PS2

## Course Description

Description

CTY's Problem Solving courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards and drawing on software provided by Thinkwell, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging homework, quizzes, and chapter tests. A cumulative midterm and final exam help reinforce concepts and gain mastery. With the guidance of their instructors, students typically select enrichment or supplementary math courses of the appropriate level in between their accelerated courses to ensure a solid foundation and mastery of math concepts at each level.

Problem Solving in Pre-algebra prepares students for a more formal study of mathematics in middle school. It is appropriate for students who have a good understanding of concepts in pre-algebra, but who wish to enrich their skills through interesting word problems and applications. Students continue the study of numbers and their operations. Upon successful completion of this course, students will understand topics in:

• algebraic concepts
• geometry
• ratios
• proportions
• statistics
• probability

Students apply what they have learned to solve sets of questions at varying levels of difficulty.

This course provides an excellent foundation for students who will be advancing into Honors Algebra I.

## Materials Needed

There are no required materials for this course.

## List of Topics

### Chapter 1: Essentials of Algebra

#### Evaluating an Algebraic Expression

• Variables and Expressions

#### Simplifying Algebraic Expressions

• Equations and Their Solutions
• Simplifying Algebraic Expressions

#### Solving Simple Equations

• Solving Subtraction Equations
• Solving Multiplications Equations
• Solving Division Equations

#### Solving Literal Equations

• Translating Between Words and Math

### Chapter 2: Fundamentals of Geometry

#### Geometry Fundamentals

• Angles and Their Relationships

#### Volume and Surface Area

• Introduction to Three-Dimensional Figures
• Volume of Prisms and Cylinders
• Surface Area of Prisms and Cylinders

### Chapter 3: Radicals and Exponents

#### Introduction to Radicals and Pythagorean Theorem

• Square Roots and the Pythagorean Theorem

#### Introduction to Scientific Notation

• An Application of Exponents: Scientific Notation

### Chapter 4: Ratio and Proportion

#### Ratio

• Ratios and Rates
• Applying Rates and Ratios

• Proportions

#### Direct and Inverse Variation

• Direct Variation
• Inverse Variation

#### Similar Polygons

• Similar Figures

### Chapter 5: Statistics

#### Interpreting and Constructing Graphs

• Line Graphs
• Bar Graphs and Histograms
• Reading and Interpreting Circle Graphs

#### The Mean, Median, and Mode

• Mean, Median, Mode, and Range

#### Frequency Distribution and Histograms

• Frequency Tables
• Bar Graphs and Histograms
• Histograms

### Chapter 6: Probability

#### Simple Probability

• Introduction to Probability

#### Probability of Combined Events

• Probability of Independent and Dependent Events
• Counting Methods and Sample Spaces

## Problem Solving Help Room

Help Room

Each week, all students are invited to a Problem Solving Help Room run by a rotating staff of instructors. Students are encouraged to come with questions or just to meet other online students. Topics reviewed vary each week.

The Problem Solving Help Room meets each Tuesday from 7 – 8 p.m. ET.

Sample Video

## Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.