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MODULE A: Teaching Disc #1 Unit I: The Structure of Mathematics Part A – Mathematics as a Language Mathematical Parts of Speech Mathematical Expressions Translations of Mathematical Symbols Part B – Further Investigation of Number Symbols The Development of Our Number System Fraction Forms and Decimal Forms Changing Fraction Forms to Decimal Forms Changing Decimal Forms to Fraction Forms Percent Primes, Composites, and Factoring Least Common Multiple Greatest Common Factor
(Unit I Continued) Part C – Further Investigation of Operation Symbols Order of Operations Properties of Operations Properties of Operations with Special Numbers Operations with Fractions - Multiplication Operations with Fractions - Addition and Subtraction Operations with Fractions - Division Operations with Decimals Operations with Signed Numbers – Vectors and Absolute Value Operations with Signed Numbers – Addition Operations with Signed Numbers – Subtraction Operations with Signed Numbers – Multiplication and Division
(Unit I Continued) Part D – Further Investigation of Relation Symbols Order of Numbers and the Number Line Properties of Equality Properties of Inequality Part E – Mathematical Models The Mathematics of Sets The Mathematics of Functions
MODULE B: Teaching Disc #4 Unit II: First Degree Relations with One Placeholder Part A – Basic Equations and Inequalities Solution Statements and Solution Sets First Type – Making Zeros Second Type – Making Ones Combinations Part B – Complications on Equations and Inequalities Grouping Symbols Like Terms on the Same Side Placeholders on Both Sides Combinations Part C – Special Cases of Equations and Inequalities No Solution Infinite Number of Solutions Part D – Systems of Equations and Inequalities Compound Sentences with “and” Compound Sentences with “or” Absolute Value Equal to a Positive Number (or) Absolute Value Less Than a Positive Number (and) Absolute Value Greater Than a Non-Negative Number (or)
(Unit II Continued) Part E – Problem Solving Using One Placeholder General Strategy and Set Up “Number” Problems “Consecutive Integer” Problems “Age” Problems “Geometric Figure” Problems “Motion” Problems “Percent” Problems
Unit III: First Degree Relations with Two Placeholders Part A – Solution Set for One Open Sentence Solution Sets for Equations Solution Sets for Inequalities Graphing Terminology Graphing Techniques for y = mx Graphing Techniques for y = mx + b Graphing Techniques – Intercepts Part B – Special Cases of Solution Sets y = a, y < a, y > a x = a, x < a, x > a Absolute Value
MODULE C: Teaching Disc #7 (Unit III Continued) Part C – Finding Relations For Given Solution Sets Given the Slope and y-Intercept Given the Slope and One Solution Given Two Solutions Special Cases – Given Parallel or Perpendicular Lines Part D – Solution Sets for Systems of Two Open Sentences Graphic Solution for Equations Graphic Solution for Inequalities Algebraic Solution for Equations – Elimination by Addition Algebraic Solution for Equations – Elimination by Substitution
(Unit III Continued) Part E – Special Cases of Solution Sets for Systems No Solution – Inconsistent Infinite Number of Solutions – Dependent Part F – Problem Solving Using Two Placeholders General Strategy and Set Up “Number” Problems “Age” Problems “Geometric Figure” Problems “Motion” Problems “Percent” Problems “Value” or “Mixture” Problems
Unit IV: First Degree Relations with Three or More Placeholders Part A – Solutions Sets One Open Sentence Two Open Sentences Systems of Three or More Open Sentences (Algebraic Solutions) Part B – Special Cases No Solution – Inconsistent Infinite Number of Solutions – Dependent Part C – Problem Solving Using Three or More Placeholders “Number” Problems “Age” Problems “Geometric Figure” Problems “Value” or “Mixture” Problems
MODULE D: Teaching Disc #10 Unit V: Second Degree Relations and Higher - Polynomials Part A – Exponent Notation Definitions and Terminology Operations with Powers Extensions of Operations with Powers Special Cases of Powers Scientific Notation Part B – Polynomials Algebraic Expressions Definition and Terminology Operations – Addition and Subtraction Operations – Multiplication Operations – Division
(Unit V Continued) Part C – Solving Equations and Inequalities by Factoring Principle of Zero-Products Special Products – Common Factor Special Products – Difference of Squares Special Products – Perfect Square Trinomial Special Products – General Trinomial Special Products – Four-Term Polynomial Special Products – Sum or Difference of Cubes General Factoring Strategy Synthetic Division Literal Equations
(Unit V Continued) Part D – Problem Solving with Higher-Order Relations “Number” Problems “Consecutive Integer” Problems “Geometric Figure” Problems “Formula” Problems
MODULE E: Teaching Disc #13 (Unit VI): Second Degree Relations and Higher Algebraic Fractions Part A – Operations Simplifying Multiplication Division Addition and Subtraction Complex Forms Part B – Solving Open Sentences Equations – Arithmetic Case Equations – Algebraic Case Inequalities – Algebraic Case Literal Equations Part C – Problem Solving with Algebraic Fractions “Fraction” Problems “Work” Problems “Motion” Problems “Direct Variation” Problems “Inverse Variation” Problems “Mixed Variation” Problems
Unit VII: Relations of Rational Number Degree Part A – Rational Numbers as Exponents Fractions as Exponents Odd and Even “kth” Roots Part B – Operations with Radical Expressions Multiplication Simplifying with Perfect Powers Division and Simplifying Addition and Subtraction Radical Expressions in Polynomials Rationalizing Denominators Part C – Solving Radical Equations Equations with One Radical Expression Equations with Two Radicals or More Part D – Problem-Solving with Relations Containing Radicals The “Distance” Relation “Formula” Problems Part E – The Complex Numbers as a Mathematical System Imaginary and Complex Numbers Addition and Subtraction Multiplication Division
Unit VIII: Quadratic Equations Part A – Solving Quadratic Equations of the Form ax² + bx + c = 0 Suppose a = 0, b = 0, or c = 0 Suppose a, b, c ≠ 0 The Quadratic Formula Checking Solutions Quadratic Inequalities Part B – Equations That Are Quadratic in Form Higher Integer Order Lower Rational Order, Greater Than Zero Integer Order, Less Than Zero Part C – Problem Solving With Quadratic Relations “Geometric Figure” Problems “Pythagorean Theorem” Problems “Work” Problems “Motion” Problems
Teaching Disc #16 Unit IX: The Conic Sections Part A – Parabolas – The Quadratic Function Origins The Graph of y = ax² The Graph of y = (x - h)² The Graph of y = x² + k The Graph of y = a(x – h)² + k Intercepts Part B – Circles Standard Form Not Standard Form Part C – Ellipses Standard Form Not Standard Form Part D - Hyperbolas Standard Form Not Standard Form Part E – Solving Systems of Relations One First-Degree and One Second-Degree Two Second-Degree Part F – Problem Solving with Non-Linear Systems “Number” Problems “Geometric Figures” Problems
Unit X: Literal Degree Relations Part A – Exponential Functions Graphs of Solution Sets for f(x) = a x Graphs of Solution Sets for f(y) = a y Part B – Logarithmic Functions Logarithmic Functions as Inverses of Exponential Functions Graphs of Solution Sets for f(x) = log a(x) Part C – Operations with Logarithms Properties of Logarithms Finding Logarithms Computation Part D – Solving Open Sentences Exponential Equations Logarithmic Equations
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