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7th Grade Mathematics - Important Vocabulary Words

The mathematical vocabulary terms below can be found in the Mathworks Math Explorations textbooks.


Absolute Value

  1. The absolute value of a number is its distance from zero.
  2. For any x, |x| is defined as follows: | x |= x, if x > 0, and | x |= −x, if x < 0

Acute Angle
An angle whose measure is greater than 0 degrees and less than 90 degrees.

acute angle
Example of an acute angle

Acute Triangle
A triangle in which all three angles are acute angles.

Addition Property of Equality
If a= b, then a + c= b + c.

Additive Inverse
For any number x, there exists a number −x, such that x + −x= 0.

Adjacent Angle
Two angles that share a common vertex and a common side.

Altitude of a Triangle
A segment drawn from a vertex of the triangle perpendicular to the opposite side of the triangle, called the base, (or perpendicular to an extension of the base).

triangle altitude
AD is an altitude of the triangle

An angle is formed when two rays share a common vertex.

The surface area of a two-dimensional figure.

Area Model
A mathematical model based on the area of a rectangle, used to represent multiplication or to represent  fractional parts of a whole.

Arithmetic Sequence
A sequence a1, a2, a3, a4,... is an arithmetic sequence if there is a number c such that for each n, an + 1= an + c, that is an + 1 – an = c.

Associative Property of Addition
For any numbers x, y , and z: (x + y) + z= x + (y + z).

A distinguishing characteristic of an object such as angles or sides of a triangle.

See: Mean.

A number line in a plane. Plural form is axes. Also see: Coordinate Plane.

Bar Graph
A graph in which rectangular bars, either vertical or horizontal, are used to display data.

bar graph
Example of a bar graph


  1. If any number x is raised to the nth power, written as x^n, x is called the base of the expression;
  2. Any side of a triangle;
  3. Either of the parallel sides of a trapezoid;
  4. Either of the parallel sides of a parallelogram.

Box and Whisker Plot
For data ordered smallest to largest the median, lower quartile and upper quartile are found and displayed in a box along a number line. Whiskers are added to the right and left and extended to the least and greatest values of the data.

box plot
Example of a box and whisker plot

Cartesian Coordinate System
See: Coordinate Plane.

Center of a Circle
A point in the interior of the circle that is equidistant from all points of the circle.

circle center
A circle and its center

A segment whose endpoints are points on a circle.

circle chord
PQ is a chord of the circle

The set of points in a plane equidistant from a point in the plane.

Circle Graph
See: Pie graph.

The distance around a circle. Its length is the product of the diameter of the circle and pi.

In the product of a constant and a variable the constant is the numerical coefficient of the variable and is frequently referred to simply as the coefficient.

Combining Like Terms
nk + nm= n(k + m). Also commonly called factoring.

Common Denominator
A common multiple of the denominators of two or more fractions. Also see: Least Common Denominator

Common Factor
A factor that two or more integers have in common. Also see: Greatest Common Factor.

Common Multiple
See: Least Common Multiple.

Commutative Property of Addition
For any numbers x and y: x + y = y + x.

Commutative Property of Multiplication
For any numbers a and b: ab= ba.

The complement of a set is a set of all the elements of the universal set that are not in the given set.

Complementary Angles
Two angles are complementary if the sum of their measures totals 90º.

Complementary angles, a and b

Composite Number
A prime number is an integer p greater than 1 with exactly two positive factors: 1 and p. A composite number is an integer greater than 1 that has more than two positive factors. The number 1 is neither a prime nor a composite number.

Compound Interest
Interest added to the principal of an account, so that the added interest also earns interest going forward.

Compound Event
See: Event.

A three-dimensional figure with a circular base joined to a point called the apex.

Example of a cone

Used to refer to angles or sides having the same measure and to polygons that have the same shape and size.

An assumption that is thought to be true based on observations.

A fixed value.

Constant of Proportionality
If a function has a rule in the form y= Kx, then for any input x0, the quotient of y/x will always have the value K. The number K is called constant of proportionality.

Constant Rate Of Change
y= mx + b, here m is the constant rate of change.

Constant Rate Of Proportionality
Another term for scale factor.

A number assigned to each point on the number line which shows its position or location on the line. In a coordinate plane that ordered pair, (x,y), assigned to each point of the plane showing its position in relation to the x-axis and y-axis.

Coordinate Plane
A plane that consists of a horizontal and vertical number line, intersecting at right angles at their origins. The number lines, called axes, divide the plane into four quadrants. The quadrants are numbered I, II, III, and IV beginning in the upper right quadrant and moving counterclockwise.

coordinate plane
Coordinate Plane

Corresponding Angles

  1. If two lines are cut by a transversal the angles on the same side of the transversal and on the same side of the two lines are corresponding angles. If the lines are parallel the pairs of angles will have equal measure.
  2. If two polygons are similar the angles that are in the same relative position in the figures are corresponding angles and have equal measures.

Corresponding Sides
If two polygons are similar the sides of the polygons in the same relative positions are corresponding sides and the ratio of the lengths of each pair is the same.

A circular movement opposite to the direction of the movement of the hands of a clock.

Counterclockwise direction

Counting Numbers
The counting numbers are the numbers in the following never-ending sequence: 1, 2, 3, 4, 5, 6, 7... We can also write this as +1, +2, +3, +4, +5, +6, +7,... These numbers are also called the positive integers or natural  numbers.

A percentage discount or a fixed amount of money taken off the sale price of an item.


  1. A three-dimensional shape having six congruent square faces.
  2. The third power of a number.


A three-dimensional figure with parallel circular bases of equal size joined by a lateral surface whose net is a rectangle.


A collection of information, frequently in the form of numbers. Each individual piece of information is called a data point.

Data Analysis
The process of making sense of collected data.

Data Point
See: Data.


  1. The circumference of a circle is divided into 360 equal parts or arcs. Radii drawn to both ends of the arc form an angle of 1 degree.
  2. The degree of a term is the sum of the exponents of the variables. The degree of a polynomial is the highest degree of any of its terms.

The denominator of a fraction indicates into how many equal parts the whole is divided. The denominator appears beneath the fraction bar.

Dependent Variable
The output values for a function.

A segment with endpoints on the circle that passes through its center.

Distributive Property
n(k + m)= nk + nm.

For any two numbers x and y, the distance between x and y is the absolute value of their difference; that is,  Distance= |x – y|.

The quantity that is to be divided.

Suppose that n and d are integers, and that d is not 0. The number n is divisible by d if there is an integer q such that n= dq. Equivalently, d is a factor of n or n is a multiple of d.

Division Algorithm
Given two positive integers a and b, we can always find unique integers q and r such that a= bq + r and 0  r < b. We call a the dividend, b the divisor, q the quotient, and r the remainder.

The quantity by which the dividend is divided.

The set of input values in a function.

A segment that joins consecutive vertices of a polygon or a polyhedron.

Members of a set.

Empirical Probability
Probability determined by real data collected from real experiments.

Empty set
Also called a Null Set. A set that has no elements.

A math sentence using the equal sign to state that two expressions represent the same number.

Equilateral Triangle
An equilateral triangle is a triangle with three congruent sides. An equilateral triangle also has three congruent angles, which we can also call equiangular triangle.


  1. A term used to describe equations or inequalities that have the same solution.
  2. A term used to describe fractions or ratios that are equal.
  3. A term used to describe fractions, decimals, and percents that are equal.

An event is any subset of the sample space. A simple event is a subset of the sample space containing only one possible outcome of an experiment. A compound event is a subset of the sample space containing two or more outcomes.

A repeatable action with a set of outcomes.

Experimental Probability
See: Empirical Probability.

Mathematical phrases used to describe quantities.

Suppose that n is a whole number. Then, for any number x, the nth power of x, or x to the nth power, is the product of n factors of the number x. This number is usually written x^n. The number x is usually called the base of the expression x^n, and n is called the exponent.

Exponential Notation
A notation that expresses a number in terms of a base and an exponent.

Each of the surface polygons that form a polyhedron.

An integer that divides evenly into a dividend. Use interchangeably with divisor except in the Division Algorithm.

The factorial of a non-negative number n is written n! and is the product of all positive integers less than or equal to n. By definition 0!= 1!= 1.

Numbers of the form m/n, where n is not zero.

The number of times a data point appears in a data set.

A function is a rule which assigns to each member of a set of inputs, called the domain, a member of a set of outputs, called the range.

Graph of a Function
The pictorial representation of a function.

Greater than, Less Than
Suppose that x and y are integers. We say that x is less than y, x < y, if x is to the left of y on the number line. We say that x is greater than y, x > y, if x is to the right of y on the number line.

Greatest Common Factor, GCF
Suppose m and n are positive integers. An integer d is a common factor of m and n if d is a factor of both m and n. The greatest common factor, or GCF, of m and n is the greatest positive integer that is a factor of both m and n. We write the GCF of m and n as GCF (m,n).

The length of the perpendicular between the bases of a parallelogram or trapezoid; also the altitude of a triangle.

Horizontal Axis
See: Coordinate Plane.

The side opposite the right angle in a right triangle.

Hypotenuse of a right triangle

Improper Fraction
A fraction in which the numerator is greater than or equal to the denominator.

Independent Events
If the outcome of the first event does not affect the outcome of the second event.

Independent Variable
The input values for a function.

A statement that one expression is less than or greater than another.

Input Values
The values of the domain of a function.

The collection of integers is composed of the counting numbers, their negatives, and zero; ... −4, −3, −2, −1, 0, 1, 2, 3, 4...

Intersection of Sets
A set whose elements are all the elements that the given sets have in common, written A B.

Irregular Polygon
A polygon that is not a regular polygon.

Isosceles Triangle
A triangle with at least two sides of equal length is called an isosceles triangle.

Isosceles Triangle

Lateral Area
The surface area of any three-dimensional figure excluding the area of any surface designated as a base of the figure.

Lattice Point
A point of the coordinate plane, (x,y), in which both x and y are integers.

Law Of Large Numbers
As the number of trials in an experiment are increased, the average of the experimental probability approaches the theoretical probability.

Least Common Denominator
The least common denominator of the fractions p/n and k/m is LCM(n, m).

Least Common Multiple, LCM
The integers a and b are positive. An integer m is a common multiple of a and b if m is a multiple of both a and b. The least common multiple, or LCM, of a and b is the smallest integer that is a common multiple of a and b. We write the LCM of a and b as LCM (a,b).


  1. The two sides of a right triangle that form the right angle.
  2. The equal sides of an isosceles triangle or the non-parallel sides of a trapezoid.
Legs of a right triangle

Less Than
See: Greater Than.

Line Graph
A graph used to display data that occurs in a sequence. Consecutive points are connected by segments.

line graph
Example of a line graph

Line Plot
A graph that shows frequency of data along a number line.

Line Plot
Example of a line plot

Line of Symmetry
Half of the figure is the mirror image of the other half.

line of symmetry
Example of a line of symmetry

Line of Reflection
The line across which a figure is reflected.

Examples of lines of reflections

Linear Model for Multiplication
Skip counting on a number line.

The absolute value of a number; its distance from zero.

The average of a set of data; sum of the data divided by the number of items. Also called the arithmetic mean or average.

Measures of Central Tendency
Generally measured by the mean, median, or mode of the data set

The middle value of a set of data arranged in increasing or decreasing order. If the set has an even number of items the median is the average of the middle two items.

Missing Factor Model
A model for division in which the quotient of an indicated division is viewed as a missing factor of a related multiplication.

Mixed Numbers
The sum of an integer and a proper fraction.

The value of the element that appears most frequently in a data set.

Multiplicative Inverse
The number x is called the multiplicative inverse or reciprocal of the positive integer n if x · n= 1.

The number of times a factor appears in a factorization.

Natural Numbers
See: Counting Numbers.

Net Yardage
Total number of yards gained or lost at the end of a series of plays in a sports game.

Negative Integers
Integers less than zero.

One way to see the surface area of a three dimensional figure by cutting along its edges to produce a  two-dimensional figure.

Example of a net of a square pyramid

A technical system of symbols used to convey mathematical information.

Number Line Model
A pictorial representation of numbers on a straight line.

Null Set
See: Empty Set.

The expression written above the fraction bar in a common fraction to indicate the number of parts counted.

Obtuse Angle
An angle whose measure is greater than 90 degrees and less than 180 degrees.

Example of an obtuse angle

Obtuse Triangle
A triangle that has one obtuse angle.

Opposite Angle
The angle that is opposite to a given side of a plane figure.

Order Of Operations
The order of mathematical operations, with computations inside parentheses to be done first, and addition and subtraction from left to right done last.

Ordered Pair
A pair of numbers that represent the coordinates of a point in the coordinate plane with the first number  measured along the horizontal scale and the second along the vertical scale.

The point with coordinate 0 on a number line; the point with coordinates (0,0) in the coordinate plane.


The set of possible results of an experiment.

A term referring to a value that is drastically different from most of the other data values.

Output Values
The set of results obtained by applying a function rule to a set of input values.

Parallel Lines
Two lines in a plane that never intersect.

Example of two parallel lines

A parallelogram is a four-sided figure with opposite sides parallel.


A way of expressing a number as parts out of 100; the numerator of a ratio with a denominator of 100.

Perfect Cube
An integer n that can be written in the form n= k³, where k is an integer.

Perfect Square
An integer n that can be written in the form n= k², where k is an integer.

The perimeter of a polygon is the sum of the lengths of its sides.

Two lines or segments are perpendicular if they intersect to form a right angle.

Perpendicular Lines

The ratio of the circumference to the diameter of any circle, represented either by the symbol π, or the  approximation 22/7 or 3.1415926...

Pie Graph
A graph using sectors of a circle that are proportional to the percent of the data represented.

pie graph
Example of a pie graph

A polygon is a simple, closed, plane figure formed by three or more line segments.

Examples of polygons

A three-dimensional figure with four or more faces, all of which are polygons.

Examples of polyhedrons

Positive Integers
See: Counting Numbers.

See: Exponent.

Prime Number
See: Composite Number.

Prime Factorization
The process of finding the prime factors of an integer. The term is also used to refer to the result of the process.

A type of polyhedron that has two bases that are both congruent and parallel, and lateral faces which are parallelograms.

Examples of prisms

In an experiment in which each outcome is equally likely, the probability P(A) of an event A is m/n where m is the number of outcomes in the subset A and n is the total number of outcomes in the sample space S.

A reasoning to help establish a fact.

Proper Fraction
A fraction whose value is greater than 0 and less than 1.

An equation of ratios in the form a/b = c/d, where b and d are not equal to zero.

An instrument used to measure angles in degrees.

Example of a protractor

A type of polyhedron that has one face, called a base, and triangular lateral faces that meet at a point called the apex.

Square Pyramid

Pythagorean Theorem
The formula that states that if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a² + b² = c².

See: Coordinate Plane.

A plane figure with four straight edges and four angles.

The result obtained by doing division. See the Division Algorithm for a different use of quotient.

Radical Notation
A math symbol to denote the root of an expression, such as square roots.

The distance from the center of a circle a point of the circle. Plural form is radii.

The difference between the largest and smallest values of a data set. See Function for another meaning of  range.

A rate is a division comparison between two quantities with different units. Also see Unit Rate.

A division comparison of two quantities with or without the same units. If the units are different they must be expressed to make the ratio meaningful.

Rational Number
A number that can be written as a/b where a is an integer and b is a natural number.

Part of a line that has a starting point and continues forever in only one direction.

Money that the customer receives, typically from the manufacturer, after making a purchase.

See: Multiplicative Inverse.

Rectangular Prism
A solid 3D object that has six faces, each face being a rectangle.

rectangular prism
Example of a rectangular prism

The transformation that moves points or shapes by “flipping” them across a line or axis; a mirror image of the original set of points. If B is the reflection of A in line L, then L is the perpendicular bisector of segment AB.

Regular Polygon
A polygon with equal length sides and equal angle measures.

Relatively Prime
Two integers m and n are relatively prime if the GCF of m and n is 1.

See: Division Algorithm.

Repeating Decimal
A decimal in which a cycle of one or more digits is repeated infinitely.

Right Angle
An angle formed by the intersection of perpendicular lines; an angle with a measure of 90º.

Right Triangle
A triangle that has a right angle.

The nodes in a tree diagram to represent events.

A reduction in the sale price of an item.

Sample Space
The set of all possible outcomes of an experiment.

A method of division in which partial quotients are computed, stacked, and then combined.

Scale Factor
If polygons A and B are similar and s is a positive number so that for each side of A with length k there is a  corresponding side of B with length sk, then s is the scale factor of A to B.

Scalene Triangle
A triangle with all three sides of different lengths is called a scalene triangle.

scalene triangle
Examples of scalene triangles


  1. A process by which a shape is reduced or expanded proportionally.
  2. Choosing the unit of measure to be used on a number line.

Scientific Notation
A mathematical shorthand to represent large numbers.

A region of a circle bounded by two radii and an arc of the circle which joins their endpoints.

circle sector
Example of a sector of a circle

A list of terms ordered by the natural numbers. The outputs of a function whose domain is the natural numbers or whole numbers.

A collection of objects or elements.

Set Model
A representation of groups of objects.

Similar Polygons
Two polygons whose corresponding angles have equal measures and whose corresponding side lengths form equal ratios.

Simple Event
See: Event.

Simple Interest
Interest (money) that one earns by investing money in an account.

Simplest Form of a Fraction
A form in which the greatest common factor of the numerator and denominator is 1.

The process of finding equivalent fractions to obtain the simplest form.

An uneven representation of a set of data.

Slant Height
An altitude of a face of a pyramid or a cone.

The value of the variable that makes the equation true.

Square Root
For non-negative numbers x and y, y= x , read “y is equal to the square root of x,” means y² = x.

Standard Notation
Mathematical notation that is commonly used.

Stem and Leaf Plot
A method of showing the frequency of a certain data by sorting and ordering the values.

stem and leaf
Example of a stem and leaf plot

Straight Angle
An angle with a measure of 180 degrees formed by opposite rays.

Set B is a subset of set A if every element of set B is also an element of set A.

Subtraction Property of Equality
If a= b, then a – c= b – c.

Supplementary Angles
Two angles are supplementary if the sum of their measures totals 180º.

Two supplementary angles, x and y

Surface Area
The total area of all the faces of a polyhedron. The total of the lateral area and base area of a cone. The total of the lateral area and the two bases of a cylinder.


  1. Each member of a sequence.
  2. Each expression in a polynomial separated by addition and subtraction signs.

Terminating Decimal
If a and b are natural numbers with b0 and a ÷ b yields a finite quotient, the decimal formed is a terminating decimal.

Tiling of a plane with some shape.

Example of a tessellation

Theoretical Probability
Probability based on mathematical law rather than a collection of data.

A transformation that moves a figure along a line in a plane but does not alter its size or shape.

Any line that intersects two or more lines at different points.

A four sided plane figure with exactly one set of parallel sides.

Example of a trapezoid

Tree Diagram

  1. A process used to find the prime factors on an integer.
  2. A method to organize the sample space of compound events.

A plane figure with three straight edges and three angles.

Triangle Sum Theorem
The sum of the measures of the interior angles of any triangle is 180 degrees.

A property stating that exactly one of these statements is true for each real number: it is positive, negative, or zero.

Unit Fractions
Fractions of the form 1/n

Union of Two Sets
A set that contains all of the elements that appear in either of the given sets, written A B.

Unit Rate
A ratio of two unlike quantities that has a denominator of 1 unit.

Universal Set
A set containing all of the elements under consideration.

A letter or symbol that represents an unknown quantity.

Venn Diagram
A diagram involving two or more overlapping circles that aids in organizing data.

venn diagram
Example of a Venn diagram


  1. The common endpoint of two rays forming an angle.
  2. A point of a polygon or polyhedron where edges meet.

Vertical Angles
If two straight lines intersect at a point, then each line is divided into two rays. The angles formed by using opposite rays from each line are called vertical angles.

Vertical Angle Theorem
If two lines intersect at a point P, then the vertical angles formed will always have the same measure.

Vertical Axis
See: Coordinate Plane.

A measure of space; the number of unit cubes needed to fill a three-dimensional shape.

Whole Numbers
The whole numbers are the numbers in the following never-ending sequence: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ....

The horizontal axis of a coordinate plane.

The first number provided in an ordered pair (a, b).

The second number provided in an ordered pair (a, b).

The vertical axis of a coordinate plane.

Zero Pair
For any natural number n, n + (−n) is called a zero pair because their sum is zero.