Integrated Algebra

Castle Learning Online's Integrated Algebra focuses on algebraic concepts integrated with number sense, operations, geometry, measurement, probability and statistics. Reference tables included.

Units: (click to view Sections)

1. Number Theory
   
   Sections:
   

   1. Properties of Real Numbers
   2. Integers and Rational Numbers
   3. Finite Number Systems
2. Radicals
   
   Sections:
   

   1. Perfect Squares
   2. Simplify Radicals (no variables)
   3. Arithmetic Operations with Radicals
3. Variables and Expressions
   
   Sections:
   

   1. Translate a Verbal Phrase into an Expression
   2. Write a Verbal Phrase that Matches a Mathematical Expression
   3. Evaluate Expressions with Fractions, Absolute Value and Exponents
4. Probability and Percentages
   
   Sections:
   

   1. The Counting Principle and the Number of Possible Events
   2. Permutations, Combinations and Factorials
   3. Sample Spaces and Venn Diagrams
   4. Calculate the Probability of Independent and Dependent Events
   5. Percentages and Ratios
5. Linear Equations and Inequalities
   
   Sections:
   

   1. Expressions and Equations
   2. Translate Sentences into Inequalities
   3. Writing Equations and Inequalities from a Given Situation
   4. Multiply and Divide Monomials with a Common Base
   5. Add, Subtract and Multiply Monomials and Polynomials
   6. Division of Monomials and Polynomials
   7. Solve Linear Equations and Inequalities
   8. Solve Algebraic Proportions
   9. Solve Literal Equations
   10. Word Problems
   11. Systems of Linear Equations
6. Quadratics
   
   Sections:
   

   1. Factor (GCF, DOTS, TRI) and Factor Completely
   2. Solve Quadratic Equations
   3. Determine Vertex and Axis of Symmetry given Graph
   4. Find Roots Graphically
   5. Word Problems
   6. System of Equations (one linear, one quadratic using factoring)
   7. Solve System of Equations Graphically
7. Exponents
   
   Sections:
   

   1. Laws of Exponents
   2. Scientific Notation
   3. Growth and Decay
8. Rational Expressions
   
   Sections:
   

   1. Undefined Fractions
   2. Simplify Rational Expressions
   3. Add and Subtract Rational Expressions
   4. Multiply and Divide Rational Expressions
9. Patterns, Relations and Functions
   
   Sections:
   

   1. Interval and Set Builder Notation
   2. Intersection of Sets
   3. Determine from Ordered Pairs when a Relation is a Function
   4. Identifying Linear, Quadratic, Absolute Value and Exponential Graphs
10. Coordinate Geometry
    
    Sections:
    

    1. Determine Slope of a Line from Two Points
    2. Equation of a Line
    3. Equation of a Line Parallel to x- or y-axis
    4. Parallel Lines
    5. Determine Whether a Point is on a Line
    6. Graph Linear Inequalities
    7. Graph and Solve Systems of Linear Inequalities
11. Trigonometry and Geometry
    
    Sections:
    

    1. Right Triangle Relationships (SOHCAHTOA)
    2. Pythagorean Theorem
    3. Area and Perimeter including Circles
    4. Volume and Surface Area
12. Rates and Conversions
    
    Sections:
    

    1. Calculate Rates Using Appropriate Units
    2. Solve Problems Using Conversion of Units
13. Statistics
    
    Sections:
    

    1. Bar Graphs and Charts
    2. Measures of Central Tendency
    3. Percentiles and Quartiles
    4. Box-and-Whisker Plots
    5. Stem-and-Leaf Plots
    6. Frequency Tables and Mulit-step Questions
    7. Scatter Plots and Lines of Best Fit

Themes:

1. Number Systems
2. Number Theory
3. Operations
4. Estimation
5. Variables and Expressions
6. Equations and Inequalities
7. Patterns, Relations and Functions
8. Geometry (angles, lines)
9. Trigonometry
10. Area, Volume, Perimeter (including polygons and circles)
11. Coordinate Geometry
12. Percentages and Ratios
13. Organization and Display of Data
14. Analysis of Data
15. Predictions from Data
16. Probability
17. Properties of Real Numbers

Attributes:

1. Diagram
2. Table
3. Graph
4. Word Problem
5. Construction
6. Short Answer Fill-in