Study Guides | overview | Eighth Grade Topics

Study Guide: Eighth Grade Topics

1: Foundations of Algebra

Vocabulary
Absolute Value Additive Inverse Algebraic expression
Base (of an exponent) Coefficient (of a variable) Constant term
Exponent Integers Irrational numbers
Like terms Multiplicative inverse Natural numbers
Opposite numbers Order of Operations Perfect square
Power Principle square root Real numbers
Reciprocal Repeating decimal Square root
Term Terminating decimal Variable
Whole numbers

Understanding and Skills
  1. Memorize multiplication up to 12 × 12
  2. Memorize perfect squares up to 144
  3. Working with Commutative, Associative, Distributive and Identity Properties
  4. Identifying types of numbers, including Natural, Whole, Integer, Rational, Irrational
  5. Converting between fractions, decimals and percents.
  6. Simplifying expressions
  7. Adding and subtracting real numbers
  8. Multiplying and dividing real numbers
  9. Simplifying powers, exponents, and roots
  10. Simplifying rational and irrational numbers

2: Equations

Vocabulary
Cross products Cross multiplication Identity
Percent Proportion Rate
Ratio Scale Solution (of an equation)
Solution set (of and equation) Unit rate Formulas
Literal equations Number line Positive and negative numbers

Understanding and Skills

  1. Solving one-step, two-step, and multi-step equations
  2. Solving equations with variables on both sides
  3. Solving proportions
  4. Solving literal equations for a variable
  5. Solving absolute value equations
  6. Using formulas to find the radius, diameter and circumference of a circle
  7. Using the simple interest formula to find the principal, final amount, and interest rate

3: Inequalities

Vocabulary
Inequality Compound inequality Equivalent inequality
Solution (of an inequality) Intersection (of inequalities) Union (of inequalities)

Understanding and Skills

  1. Graphing and writing inequalities
  2. Solving inequalities by adding or subtracting
  3. Solving inequalities by multiplying or dividing
  4. Solving two-step and multi-step inequalities
  5. Solving inequalities with variables on both sides.
  6. Solving compound inequalities
  7. Solving absolute value inequalities

4: Functions

Vocabulary
Arithmetic sequence Correlation Dependent variable
Domain Function Independent variable
Negative correlation No correlation Positive correlation
Range Relation Scatter plot
Term Trend line Tables
Mapping diagrams Coordinate grid x- and y-values

Understanding and Skills

  1. Graphing relationships
  2. Writing and graphing functions
  3. Using scatter plots and trend lines
  4. Arithmetic sequences

5: Linear Functions

Vocabulary
Constant of variation Direct variation Linear equation
Linear function Parallel lines Perpendicular lines
Rate of change Rise Run
Rise over run x-intercept y-intercept
Quadrants (on a coordinate grid) Points (on a line) Origin (on a coordinate grid

Understanding and Skills

  1. Working with linear equations and functions
  2. Using x- and y-intercepts
  3. Finding the slope of a linear equation
  4. Finding the constant of variation
  5. Identifying direct variation
  6. Using the Slope-Intercept form of a linear equation
  7. Using the Point-Slope form of a linear equation
  8. Using slope to find parallel and perpendicular lines

6: Systems of Equations and Inequalities

Vocabulary
Consistent system Dependent system Inconsistent system
Independent system Linear inequality System of linear equations
System of linear inequalities Special systems of linear equations

Understanding and Skills

  1. Solving systems of linear equations by graphing
  2. Solving systems of linear equations by substitution
  3. Solving systems of linear equations by elimination
  4. Solving special systems of linear equations
  5. Solving linear inequalities
  6. Solving systems of linear inequalities

7: Exponents and Polynomials

Vocabulary
Roots Decimal System Negative exponents
Powers 0f 10 Scientific Notation

Understanding and Skills

  1. Simplifying integer exponents
  2. Working with Powers of 10
  3. Using Scientific Notation for very large numbers
  4. Using Scientific Notation for very small numbers
  5. Using the multiplication properties of exponents
  6. Using the division properties of exponents
  7. Simplifying fractional exponents

8: Algebra and Geometry

Vocabulary
Triangle Right triangle Acute triangle
Obtuse triangle Circumference Diameter
Radius Origin (of a circle) Angles and degrees
Complimentary angles Pythagorean Theorem Surface area
Volume Face Edge
1D, 2D and 3D Square Rectangle
Pyramid Cone Cylinder
Similarity Points Lines
Quadrilaterals Transformations Transition
Reflection Rotation Dilation

Understanding and Skills

  1. Understanding points, lines, planes and angles
  2. Identifying the shape of objects
  3. Reducing complex objects into simpler shapes
  4. Finding the radius, diameter, and circumference of circles
  5. Finding the perimeter and area of triangles and quadrilaterals
  6. Finding the surface area and volume of 3D objects
  7. Adding the z-access to the coordinate plane
  8. Mapping objects on 2D and 3D coordinate planes
Source: https://class.ronliskey.com/study/mathematics-8/topics_g8/