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This 2006 mathematics glossary is intended to be used with other similar resources to inform classroom teaching and learning. Please consult multiple resources since there are often differences when defining mathematics terms.
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Absolute Value

The numerical value of a number without regard to its sign; the distance from 0 to a point on the number line (| | means absolute value).
Examples: | 3 | = 3 and | -3| = 3; | 9 | = 9 and | -9 | = 9; | 0 | = 0.

Acute Angle

An angle which measures less than 90 degrees and greater than 0 degrees.

Acute Triangle

A triangle with three acute angles.


Any number that is added; addend + addend = sum.
Example: in 3 + 4 = 7, 3 and 4 are addends.


An operation joining two or more sets where the result is the whole.

Adjacent Angles

Angles in the same plane that have a common side and a common vertex, but whose interiors do not intersect.


A step-by-step method for computing.


To breakdown a whole into component parts so that it may be more easily understood.


Two rays that share an endpoint; classified according to the number of degrees of its measure.


To obtain a number close to an exact amount.


The area of a flat or plane figure is the number of unit squares that can be contained within it. The unit square is usually some standard unit, like a square meter, a square foot, or a square inch.


A reason or reasons offered for or against something; suggests the use of logic and facts to support or refute a statement or idea.

Arithmetic Progression Or Sequence

A list of numbers, called terms, in which the difference between any two adjacent terms is the same. The first number in the list is called the initial value.
Example: The list 1, 3, 5, 7,... is an arithmetic sequence because the difference between any two adjacent numbers is 2. That difference is called the common difference.

Associative Property Of Addition

The sum stays the same when the grouping of addends is changed.
   (a + b) + c = a + (b + c)
   (30 + 4) + 20 = 30 + (4 + 20)

Associative Property Of Multiplication

The product stays the same when the grouping of factors is changed.
   (a · b) · c = a · (b · c)
   (2 · 3) · 4 = 2 · (3 · 4)


A characteristic or distinctive feature.


A measure of central tendency; generally, average will imply arithmetic average, which could be the mean, median, or mode.


Perpendicular lines used as reference lines in a coordinate system or graph; traditionally, the horizontal axis represents the independent variable and the vertical axis the dependent variable.


A self-evident and generally accepted statement.
Example: Two points determine exactly one line.


See x-axis and y-axis. The plural of "axis" is "axes".

Bar Graph

A graph that uses the length of solid bars to represent numbers and compare data.

Bivariate Data

Data involving two variables, such as height and weight, or amount of smoking and a measure of health; often graphed in a scatter plot.

Box-And-Whisker Plot

A graph which displays the following five points from a data set- the minimum value, the lower quartile (25th percentile), the median, the upper quartile (75th percentile), and the maximum value.


Volume and capacity are both terms for the measures of the "size" of three-dimensional regions. Standard units of volume are expressed in terms of length units, such as, cubic centimeters. Capacity units are generally applied to liquids or the containers that hold liquids. Standard capacity units include quarts and gallons, liters and milliliters.

Cardinal Number

Number that designates how many objects, or the number of units in the set; answers the question, "How many...?".
Example: There are 28 students in the room. The cardinality or cardinal number is 28.

Central Tendency

A single number that describes all the numbers in a set. Three common measures of central tendency are mean, median, and mode.
Example: For the set of numbers 95, 86, and 83, the mean is 88.

Certain Event

An event that will definitely happen. A certain event has a probability of 1.


A distinguishing element.


A method of displaying information in the form of a graph or table.


A set of points in a plane that are all the same distance from a given point.
Example: Circle P is drawn below.

Circle Graph

Sometimes called a pie chart, a way of representing data that shows the fractional part or percent of an overall set as a corresponding part of a circle.


The boundary, or perimeter, of a circle; also, the length of the perimeter of a circle.

Closure Property

A set of numbers is said to be closed under an operation, if the result of performing the operation on any two numbers in the set produces a number in the set.


In terms of statistics, a relatively large number of data closely grouped around a particular value.


A number multiplied by a variable.
Example: The number 6 in the term 6x2 is a coefficient.

Collinear Points

Points on the same line.


A collection of objects in no particular order.
Example: The collection 1, 2, 3 is the same combination as 3, 1, 2.

Common Denominator

A number divisible by all of the denominators of two or more fractions.
Example: 12 is the common denominator of , , .

Common Multiple

A number that is a multiple of each of two or more numbers; used to find a common denominator when operating with fractions having unlike denominators.
Example: 12 is a common multiple of 2, 3, and 4. See multiple.

Commutative Property Of Addition

The order in which two numbers are added does not affect the results. (The commutative property does not apply to subtraction.)
   a + b = b + a
   4 + 50 = 50 + 4

Commutative Property Of Multiplication

It makes no difference in which order two numbers are multiplied. (The commutative property does not apply to division.)
    a · b = b · a
    3 · 5 = 5 · 3


Look for similarities and differences.

Compatible Numbers

Numbers in a problem that are adjusted to make mental math easier.
Example: 16 + 11 + 24 + 35 is adjusted so that 11 + 24 = 35 and 35 + 35 = 70 and 70 + 16 = 86. So, 86 is the final answer.

Complementary Angles

Two angles whose measures sum to 90 degrees.

Complementary Events

Two events whose probabilities of occurring sum to one. In other words, these events are mutually exclusive and the only two things that can occur.
Example: Getting a head and getting a tail are complementary events, when flipping a coin.


To make by combining parts.

Composing Numbers

Building larger units from smaller units.
Example: Ten units build one ten in base ten.

Composite Number

An integer greater than one which has whole number factors other than itself and 1.
Example: 10 is a composite number because it has the factors 1, 2, 5, and 10.

Compound Events

An event that consists of two or more simple events.
Example: Consider the event of rolling a cube and flipping a coin and getting a "6" and "tails".


To make a judgment or decision after investigating or reasoning; to infer.


A statement that follows logically from other facts.

Conditional Probability

The probability that an event will occur given that another event has already occurred.


A three-dimensional figure with one circular or elliptical base and a curved surface that joins the base to the vertex.

Congruent Figures

Figures that have the same shape and size.


Inference or judgment based on inconclusive or incomplete evidence; an educated guess.

Consecutive Vertices

Two vertices of a polygon that are endpoints of one side of the polygon.


To emphasize differences.


Ordered pairs of numbers that identify points on a coordinate plane.
Example: The point (3,4) has an x-coordinate of 3 and a y-coordinate of 4.

Coplanar Points

Points that are on the same plane.


A rectangular prism having six congruent square faces.

Cube Root

One of three (and only three) equal factors of a given number.
Example: 3 is the cube root of 27 because 3 · 3 · 3 = 27.


A solid figure with two circular or elliptical bases that are congruent and parallel to each other.


Collected pieces of information.

Decimal Number

A number expressed in base 10, such as 39.456.

Decomposing Numbers

Breaking larger units into smaller units in a base.
Example: One ten breaks into ten units in base ten.

Deductive Reasoning

Using logic, definitions, and other statements known to be true in order to prove another statement is true.


The number below the fraction bar; indicates the number of equivalent pieces or sets into which something is divided.

Dependent Event

An event whose probability is affected by the outcome of another event.

Derived Unit Of Measure

A measurement determined by finding the ratio of other measurements.
Example: Density is determined by dividing the mass of quantity by its volume; speed by dividing distance covered by time elapsed.


A segment joining two non-consecutive vertices of a polygon.


A drawing that represents a mathematical situation.


A line segment (or the length of a segment) passing through the center of the circle with endpoints on the circle.


The number found when subtracting one number from another; the result of a subtraction operation; the amount by which a quantity is more or less than another number.


Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.


The length, width, or height of an object.

Direct Measurement

A measurement determined by use of a tool (not a calculation). See measurement.

Direct Proportion

Indicates that two quantities or variables are related in a linear manner (y = mx). If one quantity doubles in size, so does the other; if one of the variables diminishes to 1/10 of its former value, so does the other.


Composed of distinct parts or discontinuous elements; a set of numbers or points that has no limit points.
Examples: Discrete — taking coins out of your pocket one at a time. Non-discrete (or continuous) — pouring water from one container to another container.

Distributive Property

The product of a number and a sum is equal to the sum of the products of the number with each of the addends in the sum. That is, for all real numbers a, b, and c in a given set, a(b + c) = ab + ac.

Distributive Property Of Multiplication Over Addition

A property of real numbers that states a · (b + c) = (a · b) + (a · c) where a, b, and c stand for any real numbers.
Example: 3 · (40 + 5) = (3 · 40) + (3 · 5)


A number which is to be divided by another number. Dividend ÷ divisor = quotient.
Examples: In 15 ÷ 3 = 5, 15 is the dividend.


One integer is divisible by another non-zero integer if the quotient is an integer with remainder of zero.
Example: 12 is divisible by 3 because 12 ÷ 3 is an integer, namely 4.


An operation on two numbers to determine the number of sets or the size of the sets. Problems where the number of sets is unknown may be called measurement or repeated subtraction problems. Problems where the size of sets is unknown may be called fair sharing or partition problems.


The number by which the dividend is to be divided.
Examples: In 15 ÷ 3 = 5, 3 is the divisor.


Set of all values of the independent variable of a given function, usually the x-values on a coordinate plane.


The line segment formed by the intersection of two faces of a three-dimensional figure; a cube has 12 edges

Empirical Frequency

The number of times in an experiment that a particular event occurs.

Empirical Results

The results of an experiment or simulation.


Two or more sets of values are equal.

Equally Likely

Two outcomes are equally likely if they have the same probability of occurring.


A mathematical sentence built from expressions using one or more equal signs.
      4 + 8 = 6 + 6
      4 + 8 = 24 ÷ 2
      4 + x = 12


Having congruent sides.

Equivalent Fractions

Fractions that name the same number.
Example: and and are equivalent fractions.


To find an approximate value or measurement of something without exact calculation.


The process of finding an approximate value or measurement of something without exact calculation.
Measurement estimation — an approximate measurement found without taking an exact measurement.
Quantity estimation — an approximate number of items in a collection.
Computational estimation — a number that is an approximation of a computation that we cannot (or do not wish to) determine exactly.

Even Number

Any of the integers that are exactly divisible by two.
Example: 0, 4, and 678 are even numbers.


Any subset of the sample space.
Example: In rolling a number cube, the event of rolling a "3" is a singleton event because it contains only one outcome. The event of rolling an "even number" contains three outcomes.

Expanded Form

A number written in component parts showing the cumulative place values of each digit in the number.
Example: 546 = 500 + 40 + 6.

Experimental Probability

The ratio of the number of times an event occurs to the number of trials.


A numeral written above and to the right of another numeral to indicate how many times the original number is used as a factor.
Example: The exponent "3" in 43 means 4 is a factor 3 times; 43 = 4 · 4 · 4.

Exponential (Relationship)

Any data set or information that can be reasonably modeled by an equation of the form y = ax.


A combination of variables, numbers, and symbols that represent a mathematical relationship.


To estimate or approximate a value beyond a given set of data.


A flat surface of a solid (3-D) figure.


One of two or more numbers that are multiplied together to obtain a product.
Example: In 4 · 3 = 12, 4 and 3 are factors.


The product of all whole numbers from x down through 1, symbolized by x!.
Example: 4! = (4) (3) (2) (1) = 24


A set of points and/or lines in 2 or 3 dimensions.


See reflection.


Understanding of mathematical procedures and the skill to use them with efficiency, accuracy, and flexibility.


A general mathematical statement, equation, or rule.


A number that can be represented as a ratio of two real numbers.

Fraction Families

Sets of fractions having denominators that are multiples of a single number.
Examples: Halves, fourths, eighths, and sixteenths are a family. Thirds, sixths, and ninths are a family.

Function (f(x))

A relation in which every value of x is associated with a unique value of y: the value of y depends on the value of x.
Example: If y = x + 5, then f(x) = x + 5.

Function Machine

Applies a function rule to a set of numbers which determines a corresponding set of numbers.
Examples: 9 ® Input ® Rule · 7 ® Output ® 63
If you apply the function rule "multiply by 7" to the values 5, 7, and 9, the corresponding values would be:
5 ® 35
7 ® 49
9 ® 63

Fundamental Counting Principle

If one event has m possible outcomes and a second independent event has n possible outcomes, then there are m · n total possible outcomes for the two events together.


A conclusion reached through inductive reasoning.

Geometric Sequence

A list of numbers, called terms, in which each successive term is determined by multiplying the previous term by a common factor.
Example: 1, 2, 4, 8, 16... is a geometric sequence with a first term of 1 and a common factor of 2.


A "picture" showing how certain facts are related to each other or how they compare to one another.

Greatest Common Factor (Divisor)

The largest factor of two or more numbers; often abbreviated as GCF. The GCF is also called the greatest common divisor.
Examples: To find the GCF of 24 and 36:
1) Factors of 24 = {1, 2, 3, 4, 6, 8, 12, 24}.
2) Factors of 36 = {1, 2, 3, 4, 6, 9, 12, 18, 36}.
3) Common factors of 24 and 36 are {1, 2, 3, 4, 6, 12}, the largest being 12.
4) 12 is the GCF of 24 and 36.


A pattern of regularly spaced horizontal and vertical lines on a plane that can be used to locate points.


To organize objects, numbers, symbols according to common characteristic(s) or to achieve a specific amount or measurement.


A six-sided polygon.


A graph that shows the frequency distribution for a set of data. The graph is noted for the labels of the bars being given in intervals and for no spaces between successive bars.


Extending side to side, parallel to the horizon.


The longest side of a right triangle (opposite the right angle).

Identity Property Of Addition

Adding zero to a number gives a sum identical to the given number.

Identity Property Of Multiplication

Multiplying a number by one gives a product identical to the given number.

Impossible Event

An event that cannot happen, or an event with a probability of 0.

Improper Fraction

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

Independent Events

Two events whose outcomes have no effect on one another.
Example: The second flip of a coin is independent of the first flip of a coin.

Indirect Measurement

A measurement determined without the direct application of measurement tools.
   1. Determine the likelihood a desk will pass through a doorway.
   2. Which is longer, the distance around your wrist or an eraser?
   3. Find a measure by the use of the Pythagorean Theorem, by similarity, or through ratios or scale factors.

Inductive Reasoning

A method of reasoning in which a general statement or conjecture is made based on particular facts and/or observations.
Example: Deriving a general rule to describe a set of numbers from an observed pattern.


Two or more sets of values that are not equal.


To draw a conclusion from facts or evidence.


A conjecture based on inductive reasoning.


The counting numbers (1, 2, 3,...), their opposites (-1, -2, -3,...), and zero.


Refers to being an integer.


To estimate or approximate a value between two given values.


To explain the meaning of information, facts, and/or observation.


To meet or cross.

Intersecting Lines

Lines that meet at a point.


Spacing of (or space between) two numbers on a number line.

Inverse Property Of Multiplication

Each non-zero real number x has a multiplicative inverse, denoted by , such that their product is 1.
Example: The number 3 has a multiplicative inverse of .

Inverse Proportion

Two quantities are inversely proportional when increase in one corresponds to decrease in the other. If one quantity doubles in size the other is halved. If one quantity is multiplied by ten the other is divided by ten.
Example: If the time spent traveling a certain distance is doubled, the speed of travel halved.


To research using careful observation and examination of the facts; to inquire.

Irrational Number

A number that cannot be written as a ratio of two integers. The decimal extensions of irrational numbers never terminate and never repeat.

Irregular Polygon

A polygon whose interior angles are not equal and/or its sides are not equal in length.

Isosceles Triangle

A triangle with two congruent sides; an alternate definition is a triangle with at least two congruent sides (there is no common agreement on a definition of an isosceles triangle).


To prove or show to be true or valid using logic and/or evidence.

Least Common Multiple

The smallest positive multiple of two or more integers.
Example: 12 is the LCM of 3, 2, and 4, because it is the smallest number that is a multiple of all three numbers.

Less Likely

An event or outcome that has a probability of occurring less than the probability of another event or outcome.


Probably will happen.


See undefined term.

Line Graph

A graph that uses lines (segments) to show that something is increasing, decreasing, or staying the same over time.

Line Of Best Fit

A line drawn on a scatter plot to estimate the linear relation between two sets of data.

Line Of Symmetry

A line on which a figure can be folded into two parts that are congruent mirror images of each other.

Line Plot

A line plot, sometimes called a dot plot, starts with a line that represents one variable. The values of the variable are labels on the line. Each observation is marked as a point above the line.

Line Segment

A part of a line defined by two endpoints and all the points of the line between them.

Linear Equation

An equation whose graph on a coordinate grid is a line. The equation can be written in the form y = mx + b.

Linear Inequality

An inequality whose graph on a coordinate grid is bounded by a line. The inequality can be written in the form y (£ , <, >, or ³) mx + b.

Linear Model

An equation that may be expressed as y = mx + b to exactly or nearly represent a data set.

Linear Or Linear Relation

Any data set or information that could be reasonably modeled with a line.


The position on a number line, coordinate plane, or 3-dimensional space where an object is or can be found.

Lower Quartile

The median of the lower half of an ordered set of data.


The amount of matter in an object.


A measure of central tendency found by summing the members of a set of data and dividing the sum by the number of members of the set (also called the arithmetic mean).
Example: If A = 20 children, B = 29 children, and C = 26 children, the mean number of children is found by summing the three numbers 20 + 29 + 26 to = 75 and then dividing the sum, 75, by the number 3. So, 25 is the mean of 20, 29, 26.


The numerical amount associated with dimensions, quantity, length, or capacity.
Example: The length of a line segment and the volume of a cube are measurements.

Measures Of Central Tendency

Numbers that give some indication of the distribution of data. Three common measures of central tendency are mean, median, and mode.


The number in the middle of a set of data arranged in order from least to greatest or from greatest to least; or the average of the two middle terms if there is an even number of terms.
   1) For the data: 6, 14, 23, 46, 69, 72, 94 ® the median is 46 (the middle number).
   2) For the data: 6, 14, 23, 61, 72, 94 ® the median is 42 (the average of the two middle numbers in the list).


A systematic way of accomplishing a task.


In subtraction, the minuend is the number you subtract from.
       90,000 (minuend)
       -3,456 (subtrahend)
       86,544 (difference)

Mixed Number

A number expressed as the sum of an integer and a proper fraction; having a whole part and a fractional part.
Example: 6


The item that occurs most frequently in a set of data. There may be one, more than one, or no mode.
Example: The mode in {1, 3, 4, 5, 7, 7, 9} is 7.

More Likely

An event or outcome that has a probability of occurring greater than the probability of another event or outcome.


A multiple of a number is the product of that number and an integer.
    Multiples of 2 = {2, 4, 6, 8, 10, 12,...}.
    Multiples of 3 = {3, 6, 9, 12,...}.
    Multiples of 4 = {4, 8, 12,...}.

Multiple Transformations

A combination of transformations applied sequentially to a figure.
Example: Reflection of one figure over one line followed by reflection over a second line or, translation of one figure on a graph followed by a reflection over an axis.


In multiplication, the multiplicand is the factor being multiplied.
      83.9 (multiplicand)
    x 3.06 (multiplier)
  256.734 (product)


An operation on two numbers that tells how many in all. The first number is the number of sets and the second number tells how many in each set. Problem formats can be expressed as repeated addition, fair shares, an array approach, or a Cartesian product approach.


In multiplication, the multiplier is the factor being multiplied by.
      83.9 (multiplicand)
    x 3.06 (multiplier)
  256.734 (product)

Mutually Exclusive

Two events are mutually exclusive if it is not possible for both of them to occur at the same time.
Example: If a die is rolled, the event "getting a 1" and the event "getting a 2" are mutually exclusive since it is not possible for the die to be both a one and a two on the same roll.

Natural Number

A number from the set of numbers {1, 2, 3, 4,...}. The natural numbers are also called the counting numbers or positive integers.


A representation of a three-dimensional figure that is "unfolded".


A set of points in space that cannot be contained in the same plane.


A data set or function that, when plotted, does not have the characteristics of a line.

Non-Repeating Decimal

A decimal number in which there are no digits that endlessly repeat a pattern.

Non-Standard Units Of Measure

Measurement units that are not commonly accepted as standard but are applied uniformly when measuring.
Example: Paperclips, pencils, cubes


A symbol that represents an amount or measurement.

Number Line

A line that shows numbers ordered by magnitude; an arrowhead at each end indicates that the line continues endlessly in both directions; equal intervals are marked and labeled.

Number Pattern

A repeated sequence of numbers or a sequence of numbers created by following a particular rule.

Number Periods

A group of three places used for the digits in large numbers (e.g., ones, thousands, millions, billions).


A symbol (not a variable) used to represent a number.


The number above the line in a fraction; indicates the number of parts being considered.

Obtuse Angle

An angle with measure greater than 90 degrees and less than 180 degrees.

Obtuse Triangle

A triangle with one obtuse angle.


An eight-sided polygon.

Odd Number

Integers that are not divisible by two.
Examples: 53 and 701 are odd numbers.


A ratio of probabilities in favor of, or against the occurrence of an event. The odds in favor = P(an event can occur): P(an event cannot occur). The odds against = P(an event cannot occur): P(an event can occur).


A shape (geometric figure) having only length; no width or height (a line or line segment).

Open-Ended Problem

A problem with different possible solution paths and which may have different solutions depending on the route taken.


A mathematical process that combines numbers; basic operations of arithmetic include addition, subtraction, multiplication, and division.


To organize according to size, amount, or value.

Order Of Operations

In simplifying an expression involving a number of indicated operations, perform the operations in the following order:
1. Complete all operations that are grouped with grouping symbols.
2. Calculate powers and roots and in the order they occur from left to right.
3. Calculate all multiplications and divisions — left to right.
4. Calculate all additions and subtractions — left to right.
  7 + 3 · 8 = 31 [multiply 3 · 8 before adding 7]
  (7 + 3) · 8 = 80 [add 7 and 3 before multiplying by 8]
  7 + 32 · 8 = 79 [square 3, multiply by 8, and then add 7]

Ordered Pair

Two numbers (elements), for which order is important. When used to locate points on a coordinate graph the first element indicates distance along the x-axis (horizontal) and the second indicates distance along the y-axis (vertical). See illustration for coordinates.

Ordinal Number

A number that designates the position of an object in order; first, second, and third are examples of ordinal numbers.
Examples: Eraser is the second element in the set {pencil, eraser, desk, chalkboard, book, file, paper}; Z is the twenty-sixth element in the set {a, b, c, d,...z}.


Zero on a number line or the point (0,0) on a coordinate plane.


One of the possible results in a probability situation or activity.


A number in a set of data that is much larger or smaller than most of the other numbers in the set.

Parallel Lines

Lines that lie in the same plane and never intersect.


A quadrilateral with opposite sides parallel.


The arrangement of numbers, pictures, etc., in an organized and predictable way.
Examples: 3, 6, 9, 12,... or , , , , , .


A five-sided polygon.


A ratio of a number to 100. Percent means per hundred and is represented by the symbol %.
Example: "35 to 100" means 35%.


The distance around the outside of a shape or figure.

Perimeter Of Polygon

The sum of the lengths of the sides of the polygon.

Perpendicular Lines

Lines that lie on the same plane that intersect to form right angles.

Pi (p )

The ratio of the circumference to the diameter of the same circle. The value of pi is approximately 3.14159 and is represented by the symbol p .


Graph that uses pictures or symbols to represent similar data.

Place Value

The value of a digit as determined by its place in a number.
Example: In the number 135, the 3 means 3 · 10 or 30. In the number 356, the 3 means 3 hundreds or 300.


See undefined term.


See undefined term. Although this is an undefined term it is helpful to visualize a point as the intersection of two lines.


A closed plane figure having three or more straight sides.


A solid (3-D) figure, the faces of which are polygons.


A group of people, objects, or events that fit a particular description.

Possible Outcomes

All of the outcomes that can occur.
Example: If there are three colors on a spinner, each color is a possible outcome.


A number (exponent) representing repeated multiplication.
Example: In 34 , 4 is a power of 3 that represents repeated multiplication so that 34 = 3 · 3 · 3 · 3 = 81.


An indication of how finely a measurement is made; related to the unit of measurement and the calibration of the tool.


To tell about or make known in advance, especially on the basis of special knowledge or inference.


A prediction is a description of what will happen before it happens. It is a foretelling that is based on a scientific law or mathematical model.

Prime Number

A whole number greater than 1 having exactly two whole number factors, itself and 1.
Example: 7 is prime since its only whole number factors are 1 and 7. 1 is not a prime number.


A 3-dimensional figure that has 2 congruent and parallel faces (bases) that are polygons and the remaining (lateral) faces are parallelograms.


The numerical measure of the chance that a particular event will occur, depending on the possible events. The probability of an event, P(E), is always between 0 and 1, with 0 meaning that there is no chance of occurrence and 1 meaning a certainty of occurrence.


The result of a multiplication expression; factor · factor = product.
Example: 3 · 4 = 12, 12 is the product.


A logical argument that a specified statement is true based on assumed statements and previously determined true statements.

Proper Fraction

A fraction, the absolute value of whose numerator is an integer less than its integer denominator.
Examples: is a proper fraction; is not. is a proper fraction; is not.


An equation showing that two ratios are equivalent.
Example: =


Constituting a proportion; having the same, or a constant, ratio; as proportional quantities.


A solid (3-D) figure whose base is a polygon and whose other faces are triangles that meet at a common point (vertex).

Pythagorean Theorem

In any right triangle having a hypotenuse of length c and two legs of lengths a and b, a2 + b2 = c2 .


The four sections of a coordinate grid that are separated by the axes. By convention, they are numbered counterclockwise from upper right, I, II, III, IV.

Quadratic Equation

An equation of the form ax2 + bx + c = 0, where a ¹ 0.


A four-sided polygon.


A set of questions for a survey.


The result of dividing one number by another number. Dividend ÷ divisor = quotient.
Examples: In 15 ÷ 3 = 5, 5 is the quotient.


The segment, or length of the segment, from the center of a circle to a point on the circle.

Random Sample

A sample in which every person, object, or event in the population has the same chance of being selected for the sample.

Range (Functional)

The set of all values of the dependent variable of a given function, usually the y-value on a coordinate plane.

Range (Statistical)

The absolute value of the difference between the largest and smallest values in a set of data.
Example: The range of {2, 4, 6, 7, 9, 13} is |2-13| or 13-2 or 11.


A ratio comparing two different quantities.
Examples: Miles per hour, gallons per mile, and heartbeats per minute are rates.


A comparison of two numbers using a variety of written forms.
Examples: The ratio of two and five may be written "2 to 5" or 2:5 or .

Rational Number

Any number that can be expressed as a ratio of two integers, with the denominator non-zero.
Examples: 34 can be written , 4.32 can be written as , 3 can be written as .


A part of a line that has one end point and extends indefinitely in one direction.

Real Number

The combined set of the rational and irrational numbers.

Real Number System



Within likely bounds; sensible.


Two numbers that have a product of 1.
Example: and are reciprocals because · = 1.


A quadrilateral with four right angles. A square is a rectangle.

Rectangular Prism

A prism with 2 rectangular bases.

Reflection Or Reflection On A Line

A transformation of a figure by flipping the figure over a line, creating a mirror image.


Use place value to think of a number in a different way to make addition and subtraction easier.
Example: 425 can be thought of as 300 + 120 + 5 in order to make subtracting 172 easier.

Regular Polygon

A polygon with all sides having the same length and all angles having the same measure.
Example: ABCDEF is a regular polygon called a hexagon.

Relative Value

A comparison based on size, amount or value.


The undivided part that is left after division; it is less than the divisor.

Repeating Decimal

A decimal number whose expression contains a repeating pattern of decimals from some point in the expression forward.
Example: 3.121212... is a repeating decimal with the pattern of the digits "12". This decimal can be written as 3.12.


To present clearly; describe; show.


To change or modify based on reflection and evaluation.


A quadrilateral with all four sides equal in length.

Right Angle

An angle whose measure is 90 degrees. See angle and triangle.

Right Circular Cylinder

A cylinder whose bases are circles and the centers of whose sections form a line cylinder perpendicular to the bases.

Right Cylinder

A cylinder with centers of whose sections form a line perpendicular to the bases.

Right Prism

A prism with rectangular lateral faces (sides).

Right Triangle

A triangle having one right angle. See angle and triangle.


A transformation of a figure (or points) in a plane resulting from turning a figure around a center point O either clockwise counterclockwise.


A procedure; a prescribed method; a way of describing the relationship between two sets of numbers.
Example: In the following data, the rule is to add 3.


A portion of a population or set used in statistics.
Example: All boys under the age of ten constitute a sample of the population of all male children.

Sample Space

A set of all possible outcomes to a specified experiment.


Sequenced collinear marks, usually at regular intervals or else representing equal steps, that are used as a reference in making measurements.

Scale Factor

A ratio that compares two sets of measurements such as the size of a model to the actual size of the object being modeled.

Scalene Polygon

A polygon with no two sides equal.

Scatter Plot

A graph of points (x,y), one for each item being measured, on a coordinate plane. The two coordinates of a point represent their observed, paired values.
Example: The ordered pairs may relate temperature to time of day (time, temp).

Scientific Notation

A number expressed in the form of a · 10n where 1 £ a < 10 and n is an integer.
Examples: 342.15 is written in scientific notation as 3.4215 · 102.


A set of numbers arranged in a special order or pattern.


The indicated sum or difference of a sequence of numbers.
Example: The series 1 + 3 + 5 +...+ 19 is the series of the first ten odd whole numbers.


A group of objects.


A line segment connected to other segments to form the boundary of a polygon.

Similar Figures

Having the same shape but not necessarily the same size (congruent corresponding angles and proportional corresponding sides).


Characteristic of similar figures.

Simulation (Probability)

An experiment to model a real-world situation.
Example: Toss a coin to model true-false; heads=true, tails=false.

Single Variable Equation

An equation with one variable (must have an "=" sign).
Example: 3x + 2 = 8

Single Variable Expression

An expression with one variable (must not have "=" or inequality sign).
Example: 3x + 2

Single Variable Inequalities

An inequality with one variable (must use <, £, >, ³ or ¹).
Example: 3x + 2 > 8

Skip Count

Counting by groups as in skip count by 2s, 3s, 4s,..., 12s. Can be thought of as a precursor to multiplication.


See translation.


The ratio of the change in y-units (vertical) to the change in x-units (horizontal) between two points on a line.
Example: The slope of a line through (3,4) and (9,5) is or .


A geometric figure with three dimensions.

Solution Of An Equation

A number that, when substituted for the variable in an equation, results in a true statement.


To find the solution to an equation or problem.


Of, pertaining to, involving, or having the nature of space or three-dimensions.


A closed surface consisting of all points in space that are the same distance from a given point (the center).
Example: A basketball.


A rectangle with congruent sides. See rectangle.

Square Number

An integer that is a square of another integer.
Example: 49 is a square number because 49 is the square of 7. (49 = 7 · 7)

Square Root

One of two equal non-negative factors of a given real number.
Example: 7 is the square root of 49 because 7 · 7 = 49.

Square Unit

A unit, such as a square meter (m2) or a square foot (ft2), used to measure area.

Standard Form Of A Number

A number written with one digit for each place value.
Example: The standard form for five hundred forty-six is 546. The standard form for three thousand six is 3,006.

Standard Units Of Measure

Units of measure commonly used, generally classified in the U.S. customary system or metric system.
Examples: feet, meters, acres, gallons, liters

Stem-And-Leaf Plot

A method of organizing a list of numbers into stems and leaves where leaves represent units and stems represent the other digits. Stems are listed in increasing or decreasing order. Leaves are associated with their stem but need not be sequential.


A systematic plan used in problem solving; such as looking for a pattern, drawing a diagram, working backward, etc.


An operation that is a removal of sets from an initial set; or finds the difference between two amounts when comparing two quantities.


In subtraction, the subtrahend is the number being subtracted.
   90,000 (minuend)
   -3,456 (subtrahend)
   86,544 (difference)

Successive Events

Events that follow one another in a compound probability setting.


The result of addition. Addend + Addend = Sum
Example: The sum of 32 and 46 is 78.


A series of statements containing evidence, facts, and/or procedures that support a result.


To uphold or argue as valid or correct.

Surface Area

The sum of the areas of all of the faces (or surfaces) of a 3-D object. Also the area of a net of a 3-D object. Calculations of surface area are in square units (in.2, m2, or cm2).


To get an overview by gathering data.


A letter or sign used to represent a number, function, variable, operation, quantity, or relationship.
Examples: a, =, +,...


Having a line, plane, or point of symmetry such that for each point on the figure, there is a corresponding point that is the reflection of that point. See line of symmetry.

Symmetry (Line)

The geometric property of being balanced about a line.
Example: A figure is symmetric with respect to a line, called the axis of symmetry, if it can be folded on the line and the two halves of the figure are congruent and match.

Symmetry (Rotation)

A figure is symmetric about a point if there is a rotation of the figure of less than 360 degrees about the point that allows the figure to correspond with itself.

System Of Equations

Two or more equations in terms of the same variables. The solution of a system is a set of values for the unknowns (variables) that satisfy all the equations simultaneously.
Example: Given the system of two equations x + y = 3 and 2x - y = 0; (x,y) = (1,2) is the solution for the system because (1,2) is a solution for both x + y = 3 and 2x - y = 0.


A table of two sets of values; an input-output table.


A method of displaying data in rows and columns.

Terminating Decimal

A terminating decimal is a fraction whose decimal representation contains a finite number of digits.
Example: = .25


To form or arrange congruent figures (sometimes polygons) in a pattern on a plane with no gaps and no overlaps.

Theoretical Probability

Measure of the likelihood that an event will occur; the ratio of favorable outcomes to the number of possible outcomes.
Example: Knowing that there are six possible outcomes for rolling a fair number cube one can assign the probability of to each of the possible outcomes.

Three-Dimensional Figure (3-D Figure)

A closed shape in space having length, width, and height.

Transformation (Geometric)

A change in position/location of a figure. Types of transformations include translation (slide), reflection (flip), rotation (turn), (or combinations of these).


A transformation of a figure by sliding without turning or flipping in any direction.


A quadrilateral that has exactly two parallel sides; an alternate definition is a quadrilateral with at least two parallel sides. (There is no common agreement on a definition of a trapezoid.)


The general direction or tendency of a set of data.


A three-sided polygon.


See rotation.

Two-Dimensional Figure (2-D Figure)

A shape (geometric figure) having length and width. (A flat figure.)

Undefined Term

A term whose meaning is not defined in terms of other mathematical words, but instead is accepted with an intuitive understanding of what the term represents. The words "point," "line," and "plane" are undefined terms from geometry.


Means there is one and only one object or result.
Example: The product of two integers is unique.

Univariate Data

Data involving one variable.
Example: A list of test scores.


In algebra, the quantity represented by a variable.

Valid Statement

A statement taken as being true in a reasoning situation.


To determine, substantiate, verify, or confirm whether a given statement or argument passes specific standards.

Variability Of Data

Range, average deviation, standard deviation, and spread are all ways to describe the variability of data.


A symbol used to represent a quantity that changes or can have different values.
Example: In 5n, the n is a variable.

Variation (Direct)

A relationship between two variables than can be expressed in the form y = kx where k ¹ 0; y = kx can be read as "y varies directly with respect to x".

Variation (Inverse)

A relationship between two variables that can be expressed in the y = where k ¹ 0. y = can be read as "y varies inversely with respect to x".

Venn Diagram

A diagram that shows relationships among sets of objects.


To establish as true by presentation of evidence.


A point at which two line segments, lines, or rays meet to form an angle, where edges of a polygon or polyhedron intersect, or the point opposite the base in a pyramid or cone.


Extending straight up and down; perpendicular to the horizon.
   1) A power pole is vertical to the ground.
   2) Lines drawn on paper from top to bottom that are parallel to the sides of the paper represent vertical lines.


Plural of vertex.


A measure in cubic units of the space contained in the interior of a solid figure.
Example: The number of cubic units contained in the interior of a rectangular solid.


A measure of the heaviness of, or the force of gravity on, an object.

Whole Number

A number from the set of numbers {0, 1, 2, 3, 4...}.

Word Form

The expression of numbers and/or symbols in words.
Example: 546 is "five hundred forty-six". The "<" symbol means "is less than". The ">" symbol means "is greater than". The "=" symbol means "equals" or "is equal to".


One of two intersecting straight (number) lines that determine a coordinate system in a plane; typically the horizontal axis.


One of two intersecting straight (number) lines that determine a coordinate system in a plane; typically the vertical axis.

Zero Property Of Addition

Adding zero to a number gives a sum identical to the original number. Zero is the identity element of addition. See identity property of addition.
Examples: 4 + 0 = 4 and 56.89 + 0 = 56.89

Zero Property Of Multiplication

The product of any number and zero is zero.
Examples: 4 · 0 = 0 and 0 · 456.7 = 0