Middle School Math Vocabulary: Units 1–7

Vocabulary practice cards categorized by units across numbers and operations, algebraic thinking, proportional reasoning, percents, statistics, probability, and geometry.

Integers

The set of whole numbers, their opposites, and zero, written as $\{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\}$.

Negative numbers

Numbers with a value less than zero ($< 0$), located to the left of zero on a standard horizontal number line.

Absolute value

The distance a number is from zero on a number line, written with vertical bars $|x|$, which is always non-negative ($|x| \ge 0$).

Opposite Numbers

Two numbers that are the same distance from zero on a number line but in opposite directions (such as $a$ and $-a$), whose sum is $0$.

Zero pairs

A pair of numbers, one positive number and one negative number of equal value (such as $+1$ and $-1$) that add together to equal $0$.

Evaluate

To solve for the numerical answer of a mathematical expression by performing the indicated operations.

Expression

A mathematical phrase that can contain numbers, variables, and operations, but does not contain an equality sign ($=$) or inequality symbol.

Rational Number

Any number that can be expressed as the quotient or fraction of two integers in the form $\frac{a}{b}$, where $b \ne 0$.

Reciprocal

The multiplicative inverse of a number; for any non-zero fraction $\frac{a}{b}$, its reciprocal is $\frac{b}{a}$, such that $\frac{a}{b} \times \frac{b}{a} = 1$.

Repeating decimal

A decimal representation of a number whose digits repeat in a pattern without terminating,with a bar over the repeating digits

Terminating Decimals

A decimal that ends or terminates

Complex Fractions

A fraction in which the numerator, denominator, or both contain fractions, such as $\frac{\frac{a}{b}}{\frac{c}{d}}$,

Equation

A mathematical statement showing that two expressions are equal, joined by an equal sign ($=$).

Equivalent Expression

Two or more expressions that have the same answer or value

Inequality

A mathematical sentence that compares two expressions using inequality symbols such as $<$, $>$, $\le$, or $\ge$.

Like Terms

Terms in an algebraic expression that have the same variable and raised to the same powers, differing only by their numerical coefficients.

Factor

Numbers in a multiplication problem

Inverse Operations

Pairs of operations that undo each other, such as addition and subtraction, or multiplication and division.

Center of Circle

The inside point in a plane that is equidistant from all points along the outside of the circle.

Diameter

A straight line segment passing through the center of a circle connecting two points on its outside, having a length of $d = 2r$ .

Radius

A line segment from the center of a circle to any point on its outside, equal to half of the diameter ($r = \frac{d}{2}$).

Circumference

The distance around the outside of a circle, given by the formulas $C = 2\pi r$ or $C = \pi d$.

Pi

The ratio of the circumference of a circle divided by its diameter, denoted by $\pi$ and approximately equal to $3.14159$ or $\frac{22}{7}$.

Constant of Proportionality (COP)

The constant ratio between two proportional quantities, denoted by $k = \frac{y}{x}$ in the linear equation $y = kx$.

Proportional Relationships

A relationship between two variable quantities in which their ratio remains constant, represented graphically by a straight line passing through the origin ($0, 0$).

Commission

A fee or percentage of sales paid to an agent or employee for executing a commercial transaction.

Mark Up

The amount added to the wholesale or cost price of an item to establish its retail selling price.

Mark Down

The reduction in the original selling price of an item to arrive at a discounted sale price.

Percent Increase

The ratio of the amount of increase to the original amount, expressed as a percent using $\frac{\text{New Amount} - \text{Original Amount}}{\text{Original Amount}} \times 100\%$.

Percent Decrease

The ratio of the amount of decrease to the original amount, expressed as a percent using $\frac{\text{Original Amount} - \text{New Amount}}{\text{Original Amount}} \times 100\%$.

Discount

The money taken off from the original list (tag) price of a product or service.

Population

In statistics (Unit 5), the entire group of individuals, objects, or measurements about which information is desired.

Sample

A subset of individuals selected from a larger population used to represent the whole in a statistical study.

Random Sample

A sampling method in which every member of the target population has an equal likelihood of being chosen.

Simple Interest

Interest calculated solely on the principal sum, given by the formula $I = Prt$, where $P$ is the principal, $r$ is the annual rate, and $t$ is time in years.

Event

An outcome or collection of outcomes from an experiment in probability.

Compound Event

An event in probability formed by combining two or more simple events.

Probability

A measure of the likelihood that a particular event will occur, represented by a value ranging from $0$ (impossible) to $1$ (certain).

Experimental Probability

The ratio of the number of times an event occurs to the total number of trials conducted in an actual statistical experiment.

Experiment

In Unit 7, a planned procedure or test carried out under controlled conditions to observe potential probability outcomes.

Outcome

A single possible result of a probability experiment or trial.

Theoretical Probability

The ratio of the number of favorable outcomes to the total number of possible outcomes when all outcomes are equally likely: $P(\text{event}) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}$.

Tree Diagram

A branching diagram used in probability to systematically organize and list all possible outcomes of a sequence of events.

Adjacent Angles

Two angles that share a common vertex and a common side but do not overlap in their interiors.

Complimentary Angles

Two angles whose degree measures add up to a sum of $90^\circ$,

Corresponding Angles

Angles that lie in the same relative position at each intersection where a transversal intersects two or more lines. (THey equal the same number of degrees)

Transversal

A line that intersects two or more lines in the same plane at distinct points.

Straight Angle

An angle that forms a straight line and measures exactly $180^\circ$.

Interior(corresponding) Angles

Angles positioned in the inner area between two lines cut by a transversal,

Exterior Angles(corresponding)

Angles positioned outside the space between two lines cut by a transversal.

Vertical Angles

The opposite, non-adjacent angles formed by the intersection of two straight lines, which are always congruent in measure.

Supplementary Angles

Two angles whose angle measures add up to a sum of $180^\circ$.