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ESSENTIALS OF MATHEMATICS ACADEMIC LIBRARY

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Essentials of Math Online

​Essentials: Mathematics is a semester-length review of the fundamentals taught in Pre-Algebra, Algebra I and Geometry courses and is useful at the high school level for basic skill remediation. The course highlights basic mathematical skills through multiple review, practice and sample exam questions.

Upon completion the student will be able to understand and know how to compute and define rational numbers, perform basic operations such as addition, subtraction, multiplication, and division with fractions, decimals, and percents, apply basic fundamental rules of exponents as well as scientific notation,, and more in algebraic and geometric processes..

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Essentials of Math Online

UNIT 1 – NUMBER SENSE
  1.  Course Overview
  2.  Reviewing Rational Numbers
    1. Adding decimals example 1  
    2. Adding decimals example 2  
    3. Adding decimals example 3  
    4. Subtracting decimals   
    5. Subtracting decimals up to hundredths  
    6. Adding fractions with like denominators 
    7. ​Adding fractions with common denominators  
    8. Subtracting fractions   
    9. Subtracting fractions with common denominators  
    10. Multiplying fractions and mixed numbers
    11. ​Dividing Mixed Numbers ​ 
    12. Exponent rules part 1  
    13. Exponent rules part 2  
  3.  Absolute Value and Integers
    1. Absolute value and number lines  
    2. Absolute value 1  
    3. Absolute value of integers  
    4. Adding numbers with different signs  
    5. Adding negative numbers  
    6. Learn how to add and subtract negative numbers  
    7. Multiplying positive and negative numbers  
    8. Multiplying numbers with different signs
    9. ​Why a negative times a negative is a positive 
    10. Dividing positive and negative numbers  
  4.  Quiz 1: Reviewing Rational Numbers
  5.  Converting Fractions to Decimals and Percents
    1. Fraction to decimal  
    2. Fraction to decimal with rounding  
    3. Fraction to decimal example  
    4. Representing a number as a decimal, percent, and fraction 
    5. Converting decimals to percents (ex 1)  
    6. Converting decimals to percents (ex 2)  
    7. Converting percents to decimals (ex 1)  
    8. Converting percents to decimals (ex 2)  
  6. Working with Percents (1) Increase and Decrease
    1. Percent Increase
    2. Find Percent Increase or Decrease 
    3. Percent Increase Decrease and Discount
    4. ​Percent Increase and Decrease
  7. Working with Percents (2) Applications of Percents
    1. Discounts and Sale Prices
    2. Discount, Markup, and Sales Tax
    3. Math Lessons : How to Calculate Markup Percentages
    4. Simple Interest Formula
    5. Understanding Simple Interest and Compound Interest
  8.  Quiz 2: Fractions, Decimals, and Percents
  9.  Fractions and Factoring
    1. Prime factorization  
    2. Prime factorization exercise  
    3. Greatest common factor 
    4. ​Least common multiple (LCM)  
    5. Least common multiple exercise  
    6. Least common multiple exercise 2  
  10. Using Exponent Rules
    1. Exponent rules part 1 
    2. Exponent rules part 2  
  11. Exponents in Scientific Notation
    1. Introduction to scientific notation  
    2. Scientific notation 
    3. Negative exponents  
  12. Negative Whole-Number Exponents
    1. Negative exponents  
  13. Powers and Roots
    1. Understanding square roots  
  14.  Quiz 3: Fractions and Factoring, Exponents, Powers and Roots
  15.  Test
UNIT 2 – STATISTICS, DATA, ANALYSIS, AND PROBABILITY
  1. Measures of Central Tendency
    1. Statistics intro: Mean, median and mode 
    2. ​​Finding mean, median and mode  
  2.   Evaluating Statistical Claims
    1. Learning About Line Graphs
    2. Line graphs
    3. Video for Lesson 23: Reading Simple Bar Graphs 
    4. Art of Problem Solving: Bar Charts and Pie Charts
  3.   Displaying and Comparing Data Sets
    1. Scatter Plots
    2. Scatter Plots : Introduction to Positive and Negative Correlation
    3. Scatter Plot – Correlation
  4.  Quiz 1: Working with Data
  5.   Outcomes
    1. Probability explained  
    2. Compound probability of independent events 
    3. Coin flipping probability 
    4. Finding probability example  
  6.   Representing Probabilities
    1. Applying Ratios to Probability
  7.   Independent and Dependent Variables
    1. Test taking probability and independent events 
    2. Die rolling probability with independent events  
  8.  Quiz 2: Probability
  9.  Test
UNIT 3 – ALGEBRA AND FUNCTIONS
  1. Order of Operations
    1. Introduction to order of operations  
    2. Order of operations example  
    3. Order of operations, but more complicated  
    4. Order of operations with exponents examples 
    5. Order of operations with exponents  
  2. Working with Exponents and Roots
    1. Exponent rules part 1  
    2. Exponent rules part 2  
    3. Exponent properties involving quotients 
  3. The Distributive Property
    1. The distributive property  
    2. The distributive property 2  
    3. Introduction to the Distributive Property ​
  4.   Add and Subtract Polynomials
    1. Addition and subtraction of polynomials  
    2. Terms coefficients and exponents in a polynomial  
    3. Adding and subtracting polynomials  
    4. Adding and Subtracting Polynomials
    5. Polynomials: Adding, Subtracting, Multiplying and Simplifying – Example 1
  5. ​Multiply and Divide Polynomials
    1. FOIL for multiplying binomials  
    2. Multiplying binomials example 1  
    3. Multiplying polynomials example 
    4. Polynomials: Adding, Subtracting, Multiplying and Simplifying – Example 1
    5. Polynomial division  
    6. Dividing polynomials 1  
  6.  Quiz 1: Simplifying Expressions
  7.   Inverse Operations
    1. Solving One Step Equations By Addition and Subtraction
    2. Solving One Step Equations By Multiplication and Division
  8. Solving Two-Step Equations and Inequalities
    1. Solving two-step equations (Use your previous assignments on Order of Operations and the Distributive Property in this assignment as needed. Those videos are listed below and use them as needed as you work on this assignment and communicate with your teacher)
    2. Introduction to order of operations  
    3. Order of operations example 
    4. Order of operations, but more complicated  
    5. Order of operations with exponents examples  
    6. Order of operations with exponents 
    7. The distributive property
    8. The distributive property 2  
    9. Distributive property example 1  
  9. Writing Mathematical Statements
    1. Beginning Algebra & Word Problem Steps
    2. How to write algebraic expressions
    3. Writing Equations from Word Problems
  10.  Quiz 2: Solving Equations and Inequalities
  11.  Test
UNIT 4 – MEASUREMENT AND GEOMETRY
  1. Measurement Systems
    1. U S customary units for distance  
    2. U S customary units for weight  
    3. U S customary units for fluid volume  
    4. Distance in the metric system  
    5. Metric units for fluid volume  
    6. Metric units for weight  
  2. Scale Drawings and Models
    1. Interpreting a scale drawing  
    2. Solve a scale drawing word problem  
    3. How to make a scale drawing  
    4. Ratios and Proportions Scale Drawing
    5. Scale Drawings Using Proportions
  3.  ​ Measures of Rates and Products
    1. Finding unit rates  
    2. Finding unit prices  
  4.   Perimeter and Area: 2D Figures
    1. Perimeter and area basics  
    2. Triangle area proofs  
    3. Area of a parallelogram  
    4. Area of a trapezoid  
    5. Area of a circle  
  5. Surface Area and Volume: 3D Figures
    1. Names of Three-Dimensional Figures
    2. Surface Area of a Rectangular Prism
    3. Surface Area Of A Cylinder
    4. Surface Area of a Triangular Prism PT2
  6.  Quiz 1: Measurement and Geometry
  7.  Converting Between Units of Measure
    1. Converting Between Customary Units
    2. Converting Between Metric Units
  8.   Complex 2D Objects
    1. Finding Perimeter 
    2. Finding The Perimeter Of A Semi-Circle Attached To A Square
    3. Area and Perimeter of Irregular Shapes
  9. Complex 3D Objects
    1. Surface Area of a Rectangular Prism
    2. Surface Area Of A Cylinder
    3. Surface Area of a Cube
  10. ​Geometric Shapes: Scale Factors
    1. 5B Dimensional Change 9 5 Part 1
    2. 5B Dimensional Change 9 5 Part 2
  11.  Quiz 2: Complex Objects
  12.  Pythagorean Theorem
    1. The Pythagorean theorem intro  
    2. Pythagorean theorem  
  13.  Coordinate Graphs
    1. The coordinate plane  
    2. Plot ordered pairs  
  14. Transformations and Congruent Figures
    1. Congruent Figures
    2. Congruent Figures Part 1 – Identify Corresponding Part and Congruent Triangles 4.1 
    3. Transformations – Translating A Triangle On The Coordinate Plane
    4. Transformations – Reflection
  15.  Quiz 3: Coordinate Geometry
  16.  Test
UNIT 5 – MATHEMATICAL REASONING
  1. Analyzing Problems
  2. Making Conjectures
    1. How to Math: 1.1 Patterns and Inductive Reasoning
    2. Counterexample
  3. Estimation (1)
    1. Rounding whole numbers 2 
    2. Rounding whole numbers 3   
  4. Estimation (2)
    1. Interpolation and Extrapolation: Estimating Values from a Graph
    2. 5.7 interpolation and extrapolation
  5. Inductive and Deductive Reasoning
    1. Difference between inductive and deductive reasoning  
    2. Inductive Reasoning
    3. Deductive Reasoning
  6. Solving Problems (In this lesson use material learned from previous lessons in this unit, instructional presentations on the topics in this unit, previous learning along with communication with your teacher)
  7.  Quiz 1: Mathematical Reasoning
  8.  Test
UNIT 6 – ALGEBRA I
  1. Graphs and Charts
    1. Prealgebra 9.2c – Line Graphs 
    2. Line graphs
    3. Drawing Line Graphs by Hand
  2.   Represent Data
    1. Direct Variation
  3. Graphing Linear Functions
    1. The coordinate plane  
    2. Graphing using x- and y-intercepts  
    3. x- and y-intercepts  
    4. Multiple examples of constructing linear equations in slope-intercept form  
  4. Parallel Lines
    1. Slopes of Parallel Lines Quick Review
    2. Algebra I Help: Slopes of Parallel and Perpendicular Lines
  5. Solutions of Linear Equations
    1. Beginning Algebra & Graphing Linear Equations
    2. Graphing by Finding Intercepts
    3. Graphing linear equations with tables
  6.   Graphing Higher Power Functions
    1. Solving Quadratic Equations using the Quadratic Formula – Example 1
    2. Solving Quadratic Equations using the Quadratic Formula – Example 2, Complex Solutions
    3. Solving Quadratic Equations using the Quadratic Formula – Example 3
    4. Graphing Quadratic Functions – Example 1
    5. Solving Quadratic Equations by Graphing
    6. Graphing Cubic Functions
  7. Quiz 1: Graphing
  8. Solving Absolute Value Inequalities
    1. Absolute value inequalities  
    2. Absolute value inequalities example 1 
    3. Absolute value inequalities example 2  
    4. Absolute value inequalities example 3 
  9. Solving Linear Equations
    1. Variables on both sides  
    2. Example 1: Variables on both sides  
    3. Example 2: Variables on both sides  
  10. Solving Linear Inequalities
    1. Solving Inequalities
    2. How to Solve Linear Inequalities
  11.  Quiz 2: Equations
  12. Multi-Step Word Problems (Rate)
    1. Beginning Algebra & Rate Time Distance Problems 
  13. Multi-Step Word Problems (Work)
    1. How to Solve Algebra Word Problems: Work
  14. ​Multi-Step Word Problems (Percent Mixture)
    1. Mixture Word Problems
    2. Interest Word Problems
  15.  System of Equations
    1. Solving linear systems by substitution  
  16. System of Linear Inequalities
    1. Visualizing the solution set for a system of inequalities  
    2. Graphing systems of inequalities  
  17.  Quiz 3: Equations
  18.  Test
UNIT 7 – FINAL EXAM