Glossary of Mathematical Terms - Seventh Grade Mathematics

This alphabetical glossary provides precise mathematical definitions, formulas, and illustrative contextual examples for the foundational vocabulary of seventh grade mathematics.

Alphabetical Lexicon of Core Terms

Absolute Value

The non-negative distance of a number from zero on a horizontal or vertical number line, represented by vertical bars surrounding the number. For example, the absolute value of negative seven is written as vertical bar negative seven vertical bar, which evaluates to positive seven.

Additive Inverse

The opposite of a given number that, when added to the original number, yields a sum of exactly zero. For any real number a, its additive inverse is negative a, satisfying the identity a plus negative a equals zero.

Adjacent Angles

Two angles in a plane that share a common vertex and a common ray (side), but do not share any interior points (do not overlap).

Apex

The highest vertex of a pyramid, opposite the base, where all triangular lateral faces converge at a single geometric point.

Biased Sample

A statistical sample that does not accurately represent the true distribution or demographics of the target population, systematically favoring specific outcomes due to flawed selection procedures.

Circumference

The complete linear boundary distance enclosing a two-dimensional circle, given by the formulas C equals pi times diameter (pi * d) or C equals two times pi times radius (2 * pi * r).

Coefficient

The numerical factor multiplying a variable in an algebraic term. In the term negative eight x, the coefficient is negative eight. If a variable appears alone, its coefficient is an understood positive one.

Commutative Property

An algebraic axiom stating that the order in which two real numbers are added or multiplied does not alter their sum or product: a plus b equals b plus a, and a times b equals b times a.

Complementary Angles

Two angles whose angle measures sum to exactly ninety degrees. When adjacent, complementary angles form a right angle.

Complex Fraction

A fraction whose numerator, denominator, or both contain one or more fractions, evaluated by multiplying the numerator by the reciprocal of the denominator.

Composite Figure

A two-dimensional geometric shape composed of two or more fundamental polygons (rectangles, triangles, trapezoids) and circular regions.

Constant of Proportionality

The invariant ratio k between the dependent variable y and the independent variable x in any proportional relationship, defined by the formula k equals y divided by x.

Dependent Events

Two or more events in which the outcome of the first event changes the sample space and alters the probability of subsequent events, typically occurring in sampling without replacement.

Distributive Property

An algebraic property stating that multiplying a sum by a factor yields the identical result as multiplying each addend individually by that factor: a times the quantity b plus c equals a times b plus a times c.

Euler's Formula

A topological theorem for convex three-dimensional polyhedra stating that the number of faces (F) minus the number of edges (E) plus the number of vertices (V) always equals two: F minus E plus V equals two.

Experimental Probability

The likelihood of an event determined empirically by calculating the relative frequency of the event across repeated real-world experimental trials: frequency divided by total trials.

Greatest Common Factor (GCF)

The largest positive integer that divides evenly into two or more integers without leaving a remainder, used to factor linear expressions.

Independent Events

Two or more events in which the occurrence of one event has no physical or mathematical effect on the probability of subsequent events: P(A and B) equals P(A) times P(B).

Inequality

A mathematical statement establishing that two expressions are not equal, joined by inequality symbols such as strictly less than, strictly greater than, less than or equal to, or greater than or equal to.

Integers

The infinite set of numbers comprising all positive counting numbers, their negative opposites, and zero: ..., -3, -2, -1, 0, 1, 2, 3, ...

Interquartile Range (IQR)

A robust measure of statistical dispersion representing the spread of the middle fifty percent of a dataset, calculated as the difference between the third quartile and the first quartile: IQR equals Q3 minus Q1.

Mean

The arithmetic average and physical balance point of a numerical dataset, calculated by dividing the sum of all values by the total count of values.

Mean Absolute Deviation (MAD)

The average distance separating each individual data point in a distribution from the distribution's arithmetic mean, serving as a measure of consistency and variability.

Median

The physical middle value in a dataset when all observations are arranged in numerical sequence from least to greatest. If the count is even, the median is the mean of the two central numbers.

Mode

The value or values that appear with the greatest frequency in a dataset. A dataset may be unimodal, bimodal, multimodal, or have no mode.

Outlier

A data value that lies substantially apart from the overall pattern of a distribution, capable of distorting the arithmetic mean and range.

Percent

A proportional ratio comparing a quantity to a baseline of one hundred, denoted by the percent symbol (%).

Percent Change

The relative magnitude of increase or decrease in a quantity expressed as a percentage of the original starting baseline: absolute change divided by original value times one hundred percent.

Percent Error

A standardized measure of accuracy comparing an estimated or experimental measurement to the true accepted standard value: absolute error divided by actual value times one hundred percent.

Pi (pi)

The universal irrational mathematical constant representing the invariant ratio of a circle's circumference to its diameter: pi equals C divided by d, approximately equal to 3.14159 or 22/7.

Polyhedron

A closed three-dimensional geometric solid whose boundary consists entirely of flat planar polygonal surfaces meeting along straight edges at corner vertices.

Population

The entire overarching collection of individuals, objects, or measurements about which statistical inferences are to be drawn.

Principal

The initial sum of money borrowed in a loan or invested into an interest-bearing account upon which simple interest is calculated.

Prism

A three-dimensional polyhedron possessing two congruent, parallel polygonal bases connected by rectangular or parallelogram lateral faces.

Proportion

An algebraic equation stating that two ratios or rates are mathematically equal: a divided by b equals c divided by d.

Pyramid

A three-dimensional polyhedron consisting of a single polygonal base connected to triangular lateral faces that converge upward at a single apex point.

Radius

A straight line segment extending from the center of a circle or sphere to any point on its outer boundary, equal to half of the diameter.

Random Sample

A statistical sampling method where every member of the target population possesses an equal, non-zero probability of selection, eliminating human selection bias.

Range

The simplest measure of statistical variability, calculated as the difference between the maximum value and the minimum value in a dataset.

Rational Numbers

The infinite set of numbers that can be written in the formal algebraic form p divided by q, where p and q are both integers and q is not equal to zero.

Scale Factor

The dimensionless ratio comparing any linear measurement in a scale drawing or model to the corresponding actual measurement in the physical world, expressed in identical units.

Simple Interest

Interest calculated exclusively on the original principal sum over time: Interest equals Principal times annual Rate times Time in years (I = Prt).

Slant Height

The altitude of a triangular lateral face of a regular pyramid measured along its sloped exterior surface, used to calculate lateral surface area.

Supplementary Angles

Two angles whose angle measures sum to exactly one hundred eighty degrees, forming a straight line when placed adjacently.

Surface Area

The total sum of the two-dimensional planar areas of all exterior faces bounding a three-dimensional solid, measured in square units.

Theoretical Probability

The mathematical likelihood of an event calculated from structural symmetry under the assumption of equally likely outcomes: favorable outcomes divided by total sample space outcomes.

Unit Rate

A rate in which the denominator quantity is scaled to precisely one unit, such as miles per hour or cost per pound.

Vertical Angles

The pair of opposite, non-adjacent angles formed by two intersecting straight lines, proven to be congruent in measure.

Volume

The total three-dimensional capacity or space enclosed within the boundary surfaces of a solid, measured in cubic units.

Exercises

Work through each problem carefully in your notebook before reading the provided solutions.

Exercise 1. Using the definitions from the glossary, describe the fundamental geometric difference between a prism and a pyramid.

Exercise 2. Differentiate between an independent compound event and a dependent compound event using an example involving drawing colored marbles from a bag.

Exercise 3. Explain why the mean is considered a measure of central tendency while the Mean Absolute Deviation (MAD) is considered a measure of variability.

Exercise 4. A student confuses the term rational number with whole number. Based on the glossary definitions, clarify why negative three-fourths is a rational number but not a whole number.

Solutions

Solution to Exercise 1. A prism has two congruent, parallel polygonal bases connected by rectangular lateral faces, maintaining a uniform cross-section throughout its length without tapering. In contrast, a pyramid has exactly one polygonal base, and its lateral faces are triangles that slope inward and converge at a single top vertex called the apex.

Solution to Exercise 2. An independent compound event occurs when the outcome of the first action has no influence on the probability of the second action, which happens when a drawn marble is recorded and replaced back into the bag before the second draw. A dependent compound event occurs when the first action alters the available outcomes for the second action, which happens when a marble is drawn and kept out of the bag (without replacement), reducing both the matching color count and the total marble count for the second draw.

Solution to Exercise 3. The mean is a measure of central tendency because it identifies the single representative balance point or center around which all data points distribute. In contrast, the Mean Absolute Deviation (MAD) does not describe where the center is located; instead, it measures how dispersed and spread out the data points are around that center by computing the average physical distance separating each observation from the mean.

Solution to Exercise 4. A whole number belongs to the set of non-negative counting integers including zero: zero, one, two, three, and so on; it cannot be negative and cannot have a fractional part. A rational number is defined much more broadly as any number that can be expressed as a ratio of two integers p divided by q, where q is non-zero. Negative three-fourths is the ratio of the integer negative three to the integer positive four, satisfying the definition of a rational number, even though it is not a whole number.