Numbers

Numbers are used to quantify and measure things. They can be classified into various types such as whole numbers, integers, rational numbers, and irrational numbers.

Whole Numbers

Whole numbers are the numbers 0, 1, 2, 3, 4, ... and so on. They do not include negative numbers or fractions.

Integers

Integers are the set of whole numbers and their negative counterparts, along with zero. They are represented as ..., -3, -2, -1, 0, 1, 2, 3, ...

Rational Numbers

Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. This includes fractions and terminating or repeating decimals.

Irrational Numbers

Irrational numbers cannot be expressed as a simple fraction and their decimal representation goes on forever without repeating. Examples include the square root of 2 and pi.

Real Numbers

Real numbers include all rational and irrational numbers. They can be represented on the number line.

Complex Numbers

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e., the square root of -1).

Study Guide

What are whole numbers and give examples?
Explain the concept of integers with examples.
Differentiate between rational and irrational numbers.
Draw and label a number line with different types of numbers.
Simplify the expression (3 + 4i) - (2 - 5i).

◂Math Worksheets and Study Guides Eighth Grade. Functions

The resources above cover the following skills:

Grade 8 Curriculum Focal Points (NCTM)

Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations

Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.

Connections to the Grade 8 Focal Points (NCTM)

Algebra: Students encounter some nonlinear functions (such as the inverse proportions that they studied in grade 7 as well as basic quadratic and exponential functions) whose rates of change contrast with the constant rate of change of linear functions. They view arithmetic sequences, including those arising from patterns or problems, as linear functions whose inputs are counting numbers. They apply ideas about linear functions to solve problems involving rates such as motion at a constant speed.

Numbers

Whole Numbers

Integers

Rational Numbers

Irrational Numbers

Real Numbers

Complex Numbers

Study Guide

[Numbers] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Eighth Grade. Functions

The resources above cover the following skills: