Advanced Pre-Algebra Topics


All topics listed below are presented to the students in a way that is consistent with the vision of the NCTM (National Council of Teachers of Mathematics)



Algebraic Expressions and Integers
  • Variables and Expressions
  • The Order of Operations
  • Writing and Evaluating Expressions
  • Integers and Absolute Values
  • Adding Integers
  • Subtracting Integers
  • Multiplying and Dividing Integers
  • The Coordinate Plane

Solving One-Step Equations and Inequalities
  • Properties of Numbers
  • Simplifying Variable Expressions
  • Variables and Equations
  • Solving Equations by   +, - , *, /
  • Inequalities and Their Graphs
  • Solving One-Step Inequalities by
  •  +, - , *, / 
Decimals and Equations
  • Rounding and Estimating
  • Estimating Decimal Products and Quotients
  • Mean, Median, and Mode
  • Using Formulas
  • Solving Equations by +, - , *, / 
  • Using the Metric System

Factors, Fractions, and Exponents
  • Divisibility and Factors
  • Exponents
  • Prime Factorization and Greatest Common Factors
  • Simplifying Fractions
  • Rational Numbers
  • Properties of Exponents 
  • Scientific Notation

5.  Operations with Fractions
  • Comparing and Ordering Rational Numbers
  • Fractions and Decimals
  • Adding and Subtracting Fractions
  • Multiplying and Dividing Fractions
  • Using Customary Units of Measurement
  • Solving Equations Involving Fractions

Exponents
  • product Rule, quotient Rule, Power of a Power rule
  • simplfying expressions involving exponents

Radicals
  • Product rule and Quotient Rule.
  • Using properties of radicals to simplify radical expressions.

 Ratios, Proportions ,and Percents
  • Ratios, and Units of Rate
  • Proportions
  • Similar Figures and Scale Drawings
  • Fractions, Decimals, and Percents
  • Proportions and Percents
  • Percents and Equations
  • Percent of Change
  • Markup and Discount

Solving Equations and Inequalities
  • Solving Two-Step Equations
  • Solving Multi-Step Equations
  • Multi-Step Equations with Fractions and Decimals
  • Writing Equations
  • Solving Equations with Variables on Both Sides
  • Solving Two-Step Inequalities
  • Transforming Formulas
  • Simple and Compound Interest

Linear Functions and Graphing
  • Relations and Functions
  • Equations with Two Variables
  • Slope and y-Intercept
  • Writing Rules for Linear Functions
  • Scatter Plots
  • Solving Systems of Linear Equations
  • Graphing Linear Inequalities

Special Functions
  • Recognize and graph step functions, piecewise functions, and absolute value functions

Coordinate Geometry
  • The Pythagorean Theorem
  • Distance and Midpoint Formulas

 Data Analysis and Probability
  • Frequency Tables, Line Plots, and Histograms
  • Box-and-Whisker Plots
  • Counting Outcomes and Probability
  • Independent and Dependent Events
  • Permutations and Combinations
  • Experimental Probability

Non Linear Functions and Polynomials
  • Patterns and Sequences
  • Graphing Nonlinear Functions
  • Exponential Decay and Growth
  • Polynomials
  • Adding, Subtracting, Multiplying, and Dividing Polynomials
Intro to Geometry: Points, Lines, and Planes
    • Angle Relationships and Parallel Lines
    • Classifying Polygons
    • Congruence
    • Circles
    • Translations
    • Symmetry and Reflections
    • Rotations