## COUESE OVERVIEW

Prealgebra aims to improve essential math proficiency and problem solving skills to prepare students for Algebra and high school math curriculum. Topics include:

• Basic arithmetic operations and expressions
• Fractions, decimals, and percents
• Ratios and rates
• Exponents and square roots
• Simple number theory
• Variables and linear equations
• Negative numbers
• Basic geometry

Essential Aims:

• Help students understand the concepts and knowledge necessary for more advanced mathematics
• Foster and emphasize mathematical thinking and problem solving

Contents

Section 0: Introduction

1. Intro: people intro, course run through, benchmark walkthrough (4 problems – operations/expressions, ratios/rates, number theory, equations)

Section 1: General Math Operations

1. Arithmetic operations (on whole numbers)
1. Properties: commutativity, associativity, distributivity, negation, inverse element, identity element, etc.
1. Order of operations
1. Exponents
1. Definition and properties/identities
1. Special cases: squares, cubes and square roots

Section 2: Introduction to Number Theory

1. Integers and prime numbers
1. Prime and composite numbers
1. Prime factorization
1. LCM and GCD
1. Division rules
1. LCM
1. GCD

Section 3: Non-Integer Notations

1. Fractions
1. Fraction operations
1. Reciprocals
1. Reduced form of fractions
1. Rationalization of denominators
1. Mixed numbers
1. Decimals
1. Power of 10 and scientific notation
1. Rounding
1. Conversion between fractions and decimals
1. Repeating decimals
1. Real examples: dollars and cents
1. Percents
1. Conversion between decimals and percents
1. Conversion between fractions and percents
1. Percent increase and decrease
1. Real examples: discounts, sales tax, simple interests

Section 4: Properties of Algebra

1. Variables and expressions
1. Variables
1. Expressions – arithmetic operations with variables
1. Expressions – powers of variables
1. Functions and graphing
1. Functions definition
1. Graphing functions: slope, intercept
1. Equations
1. Linear equations
1. Variables in the denominator
1. Exponents of variables
1. Inequalities
1. Rate, ratios and proportions
1. Ratio and multi-way ratio
1. Proportions
1. Rate or speed

Section 5: Number Analysis

1. Data and statistics
1. Tables, graphs and charts
1. Statistics – mean, median, mode, min, max, range
1. Counting and probabilities
1. Venn diagram
1. Probability concept

Section 6: Basic Geometry

1. Introduction to geometry
1. Angles
1. Perimeters
1. Areas