Grade 8
Subject Mathematics
Topic Overview
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 |
|---|
- Memorize multiplication up to 12 × 12
- Memorize perfect squares up to 144
- Working with Commutative, Associative, Distributive and Identity Properties
- Identifying types of numbers, including Natural, Whole, Integer, Rational, Irrational
- Converting between fractions, decimals and percents.
- Simplifying expressions
- Adding and subtracting real numbers
- Multiplying and dividing real numbers
- Simplifying powers, exponents, and roots
- 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
- Solving one-step, two-step, and multi-step equations
- Solving equations with variables on both sides
- Solving proportions
- Solving literal equations for a variable
- Solving absolute value equations
- Using formulas to find the radius, diameter and circumference of a circle
- 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
- Graphing and writing inequalities
- Solving inequalities by adding or subtracting
- Solving inequalities by multiplying or dividing
- Solving two-step and multi-step inequalities
- Solving inequalities with variables on both sides.
- Solving compound inequalities
- 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
- Graphing relationships
- Writing and graphing functions
- Using scatter plots and trend lines
- 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
- Working with linear equations and functions
- Using x- and y-intercepts
- Finding the slope of a linear equation
- Finding the constant of variation
- Identifying direct variation
- Using the Slope-Intercept form of a linear equation
- Using the Point-Slope form of a linear equation
- 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
- Solving systems of linear equations by graphing
- Solving systems of linear equations by substitution
- Solving systems of linear equations by elimination
- Solving special systems of linear equations
- Solving linear inequalities
- Solving systems of linear inequalities
7: Exponents and Polynomials
| Vocabulary | ||
|---|---|---|
| Roots | Decimal System | Negative exponents |
| Powers 0f 10 | Scientific Notation |
Understanding and Skills
- Simplifying integer exponents
- Working with Powers of 10
- Using Scientific Notation for very large numbers
- Using Scientific Notation for very small numbers
- Using the multiplication properties of exponents
- Using the division properties of exponents
- 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
- Understanding points, lines, planes and angles
- Identifying the shape of objects
- Reducing complex objects into simpler shapes
- Finding the radius, diameter, and circumference of circles
- Finding the perimeter and area of triangles and quadrilaterals
- Finding the surface area and volume of 3D objects
- Adding the z-access to the coordinate plane
- Mapping objects on 2D and 3D coordinate planes
Source: https://class.ronliskey.com/study/mathematics-8/topics_g8/