Eighth Grade Mathematics

Unit 1: Number Connections

  • Problem Solving
    • Four-step method
      • Read, plan, solve, look back
    • Strategies
      • Draw a picture/diagram
      • Work backwards
      • Solve a simpler problem, then adjust
      • Guess and check (1 high, 1 low, 1 right)
  • Integers and Absolute Value
    • Integers: whole numbers and their opposites
    • Absolute Value: the distance a number is from zero on the number line (always positive)
  • Operations with Integers
    • Addition: – 2 + 3, –8 + –6
    • Subtraction: –3 – 5, –7 – (–4)
    • Multiplication: (–2)(7), (–8)( –11)
    • Division: (–56) (8), (42) (–6), (–36) (–6)
  • Powers
    • Base, Exponent, Power, Repeated Multiplication, Standard Form
  • Order of Operations
    • Please Excuse My Dear Aunt Sally
    • PEMDAS
  • Evaluating Expressions
  • Multiplying and Dividing with Exponents
  • Properties of Numbers
    • Distributive Property
    • Associative Property
    • Commutative Property
  • Percents
  • Converting between Fractions, Decimals & Percents
  • Problems involving Sales and Discounts (%)
  • Problems involving Tips and Commission (%)
  • Simple Interest
    • I=P*R*T
  • Percent of Change
    • Percent of Increase (Mark-up)
    • Percent of Decrease (Discount)
  • Proportions
  • Unit Rates

Unit 2: Algebra Expressions, Equations & Inequalities

  • Algebra Vocabulary
    • Variable, coefficient, constant, term, monomial, binomial, trinomial, polynomial
  • Combining Like Terms
  • Translating Algebraic and Verbal Expressions
    • English to Math
    • Math to English
  • Problem Solving Five-Step Process
    • Let statement, Equation, Solve, Answer, Check
  • Solving Two-Step Equations
    • Add or subtract, then multiply or divide
  • Solving Equations with Like Terms
    • Combine like terms, then add or subtract, then multiply or divide
  • Solving Equations with a Variable of Both Sides
    • Eliminate the lesser term (by subtracting), then add or subtract, then multiply or divide
  • Solving Equations using the Distributive Property
    • Distribute, then combine like terms, then add or subtract, then multiply or divide
    • Be careful with negatives!
  • Solving and Graphing Inequalities
    • Switch the sign if you multiply or divide by a negative number
    • Graph solution on number line

Unit 3: Algebra:Operations with Polynomials

  • Adding and Subtracting Polynomials
    • Line up like terms
    • Do not add the exponents
  • Multiplying Monomials
    • When multiplying with powers, add the exponents
  • Standard Form
    • When there is only one variable
    • Combine all like terms
    • Write in order from highest exponent to lowest exponent
  • Multiplying Polynomials
    • Using Algebra Tiles
    • Table/Box Method
    • Distributive Property
  • Area and Perimeter
    • Label answer with “units” for perimeter
    • Label answer with “square units” for area
  • Dividing Monomials by Monomials
    • When dividing with powers, subtract the exponents
  • Dividing Polynomials by Monomials
    • Break up into several fractions
    • Separate with “+” or “–” where appropriate
    • When dividing with powers, subtract the exponents

Unit 4: Algebra: Factoring

  • Prime, Composite or Neither
  • Prime Factorization
  • Greatest Common Factor (GCF)
  • Factoring using GCF
    • GCF(leftovers)
  • Factoring “Easy” Trinomials
    • Product of 2 binomials
    • (x +/- #)(x +/- #)
  • Linear vs. Quadratic Equations
    • Linear:
      • Highest exponent of the variable is 1
      • Graph is a line
    • Quadratic:
      • Highest exponent of the variable is 2 (squared)
      • Graph is a parabola (U-shape, smile or frown)

Unit 5: Geometry:Angles & The Pythagorean Theorem

  • Angle Types
    • Acute, obtuse, right, straight
  • Parallel Lines Cut by a Transversal
  • Angle Pairs
    • Adjacent, vertical, complementary, supplementary, corresponding, alternate interior, alternate exterior
  • Finding Missing Angle Measures
    • Using algebra
  • Pythagorean Theorem
    • For right triangles only
    • a2 + b2 = c2