Math Vocabulary for 8th Grade

107 terms

JamWise Education Team·Updated March 2026

In 8th grade, students in the middle school (6-8) band encounter 107 essential math vocabulary terms. These words form the foundation for classroom discussions, reading comprehension, written assignments, and standardized assessments. Mastering this vocabulary gives students the language they need to express their understanding with clarity and confidence.

Below you will find every math term for 8th grade, organized by topic where applicable. Each term links to a detailed definition page with grade-level explanations, related vocabulary, and connections to JamWise learning resources.

7th Grade (87)

expressions

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Coefficient

A constant that a variable or expression is multiplied by. In 8x, the coefficient is 8. If no number is written, the coefficient is 1.

Constant

A fixed value that does not change. In the expression 5x + 3, the number 3 is a constant.

Elimination

A method for solving a system of equations by adding or subtracting the equations to eliminate one variable.

Equation

A mathematical statement that two expressions are equal, connected by an equals sign. For example, 2x - 5 = 11.

Exponent

The number written as a superscript that tells how many times the base is multiplied by itself. In 3⁴, the exponent 4 means 3 × 3 × 3 × 3.

Expression

A combination of numbers, variables, and operations. Unlike an equation, an expression does not have an equals sign.

Laws of exponents

Rules for working with exponents: when multiplying same bases, add exponents (aᵐ × aⁿ = aᵐ⁺ⁿ); when dividing, subtract exponents; when raising a power to a power, multiply exponents.

Like terms

Terms that have the same variable raised to the same power. 3x and 7x are like terms; 3x and 3x² are not.

Linear equation

An equation whose graph is a straight line. It can be written in the form y = mx + b, where m and b are constants.

Negative exponent

An exponent that means you take the reciprocal. For example, 2⁻³ = 1/2³ = 1/8. Moving from the numerator to the denominator changes the sign.

Point-slope form

A way to write a linear equation when you know the slope and one point. Written as y - y₁ = m(x - x₁).

Power

An expression written as a base raised to an exponent, like 2⁵. The base is 2 and the exponent is 5, meaning 2 × 2 × 2 × 2 × 2.

Scientific notation

A way to write very large or very small numbers as a number between 1 and 10 multiplied by a power of 10. For example, 93,000,000 = 9.3 × 10⁷.

Slope

A number that measures how steep a line is. Slope equals the rise (vertical change) divided by the run (horizontal change) between any two points on the line.

Slope-intercept form

The form y = mx + b for a linear equation, where m is the slope and b is the y-intercept.

Solution of a system

An ordered pair that satisfies every equation in the system. Graphically, it is the point where the lines intersect.

Standard form of a linear equation

A linear equation written as Ax + By = C, where A, B, and C are constants and A and B are not both zero.

Substitution

A method for solving a system of equations by replacing a variable in one equation with an expression from the other equation.

System of equations

Two or more equations that are solved together. The solution is the point (or points) that makes all equations true at the same time.

Y-intercept

The point where a line crosses the y-axis. In the equation y = mx + b, the y-intercept is the value b, which is the point (0, b).

Zero exponent

Any nonzero number raised to the power of 0 equals 1. For example, 5⁰ = 1 and 100⁰ = 1.

functions

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Decreasing function

A function whose output gets smaller as the input gets larger. Its graph goes down from left to right.

Domain

The set of all possible input values for a function. For example, if f(x) = √x, the domain is all non-negative numbers.

Function

A rule that assigns exactly one output to each input. If you put in an input value, you always get the same output. Written as f(x).

Function notation

A way to write functions using the format f(x), where f names the function and x is the input. f(3) means the output when the input is 3.

Graph of a function

The set of all points (x, f(x)) plotted on a coordinate plane. Each input x maps to one output f(x).

Increasing function

A function whose output gets larger as the input gets larger. Its graph goes up from left to right.

Initial value

The output of a function when the input is zero. In y = mx + b, the initial value is b. On a graph, it is the y-intercept.

Input

The value you put into a function. Also called the independent variable or x-value. In f(3), the input is 3.

Linear function

A function whose graph is a straight line. It can be written as f(x) = mx + b, where m is the slope and b is the y-intercept.

Nonlinear function

A function whose graph is not a straight line. The rate of change is not constant. Quadratic and exponential functions are nonlinear.

Ordered pair

A pair of numbers (x, y) that gives the position of a point on a coordinate plane. The first number is the x-coordinate and the second is the y-coordinate.

Output

The value a function produces for a given input. Also called the dependent variable or y-value. If f(x) = 2x + 1, the output for input 3 is 7.

Qualitative graph

A graph that shows the general shape of a relationship without exact numbers. It describes patterns like increasing, decreasing, or staying constant.

Range

The set of all possible output values of a function. It depends on the domain and the function rule.

Rate of change

How quickly one quantity changes compared to another. For a linear function, the rate of change is constant and equals the slope.

Table of values

A table showing input-output pairs for a function. Each row has an x-value and its corresponding y-value.

Vertical line test

A test to determine if a graph represents a function. If any vertical line touches the graph at more than one point, it is not a function.

X-intercept

The point where a graph crosses the x-axis. At this point, the y-value is zero.

geometry

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Alternate interior angles

Angles on opposite sides of a transversal and between the two lines it crosses. When the lines are parallel, these angles are equal.

Angle-angle similarity

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. This is called the AA criterion.

Cone

A three-dimensional figure with one circular base that tapers to a single point called the apex.

Congruence transformation

A combination of translations, rotations, and reflections that moves a figure to a new position without changing its size or shape.

Congruent

Figures that are the same shape and same size. One can be moved onto the other using translations, rotations, and reflections.

Converse of the Pythagorean theorem

If the sum of the squares of two sides of a triangle equals the square of the third side (a² + b² = c²), then the triangle is a right triangle.

Coordinate proof

A way to prove geometric relationships by placing figures on a coordinate plane and using algebra (distance formula, slope, midpoint).

Corresponding angles

Angles in matching positions when a transversal crosses two lines. When the lines are parallel, corresponding angles are equal.

Cylinder

A three-dimensional figure with two identical circular bases connected by a curved surface. A soup can is shaped like a cylinder.

Dilation

A transformation that makes a figure larger or smaller by a scale factor from a center point. It changes size but not shape.

Exterior angle of a triangle

An angle formed by one side of a triangle and the extension of an adjacent side. It equals the sum of the two non-adjacent interior angles.

Hypotenuse

The longest side of a right triangle, located opposite the right angle.

Interior angles of a triangle

The three angles inside a triangle. They always add up to 180 degrees.

Legs of a right triangle

The two sides of a right triangle that form the right angle. They are shorter than the hypotenuse.

Parallel lines

Two lines in a plane that never intersect. They are always the same distance apart.

Perpendicular lines

Two lines that intersect to form a 90-degree angle.

Pythagorean theorem

In a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c².

Reflection

A transformation that flips a figure across a line, creating a mirror image. The line of reflection acts like a mirror.

Rigid motion

A transformation that preserves the size and shape of a figure. Translations, rotations, and reflections are rigid motions. Dilations are not.

Rotation

A transformation that turns a figure around a fixed point called the center of rotation. Every point moves along a circular path.

Similar

Figures that have the same shape but possibly different sizes. Corresponding angles are equal and corresponding sides are proportional.

Similarity transformation

A sequence of rigid motions followed by a dilation. It can change a figure's size but keeps the same shape.

Sphere

A perfectly round three-dimensional figure where every point on the surface is the same distance from the center. A basketball is a sphere.

Supplementary angles

Two angles whose measures add up to 180 degrees. Together they form a straight line.

Translation

A transformation that slides every point of a figure the same distance in the same direction. The figure does not rotate or flip.

Transversal

A line that crosses two or more other lines at different points. When a transversal crosses parallel lines, it creates special angle pairs.

Volume of a cone

The space inside a cone, calculated with V = (1/3)πr²h. A cone's volume is one-third the volume of a cylinder with the same base and height.

Volume of a cylinder

The space inside a cylinder, calculated with V = πr²h, where r is the radius and h is the height.

Volume of a sphere

The space inside a sphere, calculated with V = (4/3)πr³, where r is the radius.

number-system

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Cube root

A number that, when used as a factor three times, gives the original number. The cube root of 27 is 3, because 3 × 3 × 3 = 27. Written as ∛27.

Integer

A whole number or its negative. The integers are ..., -3, -2, -1, 0, 1, 2, 3, ... They do not include fractions or decimals.

Irrational number

A number that cannot be written as a fraction of two integers. Its decimal form goes on forever without repeating. Pi and the square root of 2 are irrational.

Perfect square

A whole number that is the square of another whole number. 1, 4, 9, 16, 25, and 36 are perfect squares.

Rational number

A number that can be written as a fraction p/q where p and q are integers and q is not zero. Includes integers, fractions, and terminating or repeating decimals.

Real number

Any number on the number line, including both rational and irrational numbers. Every point on the number line corresponds to a real number.

Repeating decimal

A decimal in which a digit or group of digits repeats forever. Written with a bar over the repeating part. For example, 1/3 = 0.333... = 0.3̄.

Square root

A number that, when multiplied by itself, gives the original number. The square root of 25 is 5, because 5 × 5 = 25. Written as √25.

Terminating decimal

A decimal that ends after a finite number of digits. For example, 1/4 = 0.25 and 3/8 = 0.375 are terminating decimals.

Truncate

To shorten a decimal by cutting off digits after a certain place without rounding. Truncating 3.14159 to two decimal places gives 3.14.

statistics

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Cluster

A group of data points on a scatter plot that are close together, suggesting a concentration of data in that area.

Line of best fit

A straight line drawn through a scatter plot that comes closest to the data points. It shows the general trend of the data.

Linear association

A relationship between two variables where the data points cluster around a straight line on a scatter plot.

Negative association

A pattern in a scatter plot where one variable tends to increase while the other decreases.

No association

When the data points in a scatter plot show no clear pattern or trend between the two variables.

Nonlinear association

A relationship between two variables where the data points cluster around a curve rather than a straight line on a scatter plot.

Outlier

A data point that is much smaller or larger than most of the other data values. It stands far away from the main pattern.

Positive association

A pattern in a scatter plot where both variables tend to increase together. As one goes up, the other goes up too.

Relative frequency

A frequency divided by the total number of data points, often expressed as a percentage. It shows the proportion of the data in each category.

Scatter plot

A graph that shows pairs of data as dots on a coordinate plane to reveal relationships or patterns between two variables.

Two-way frequency table

A table that shows the frequency of data for two different categories at once. Rows represent one category and columns represent another.