absolute value	a number's distance from zero on a number line. The absolute value of -4 is 4; the absolute value of 4 is 4.
algorithms	a mechanical procedure for performing a given calculation or solving a problem through step-by-step procedures such as those used in long division
arithmetic sequence	a set of elements ordered in some specific way (e.g., {2, 5, 8, 11, 14, ...}) in which there is a common difference between successive terms. As in the example above, where 3 is the common difference. Each successive term of the arithmetic sequence is found by adding the common difference to the preceding term.
asymptote	a straight line to which a curve gets closer and closer but never meets, as the distance from the origin increases
axiomatic system	system that includes self-evident truths: truths without proof and from which further statements, or theorems, can be derived
bilateral symmetry	symmetry about a fixed line in a plane (line of symmetry). Each point P of the symmetrical configuration has an image point P' such that the line of symmetry is the perpendicular bisector of PP'. Points on the line transform into themselves. In three dimensions bilateral symmetry can exist about a fixed plane.
binomial	in algebra, an expression consisting of two terms connected by a plus or minus sign, such as 4a + 6
bivariate	involving two variables
box and whisker plots	a graphic method for showing a summary of data using median, quartiles and extremes of data. A box plot shows where the data are spread out and where they are concentrated.
combination	a set of items selected from a given set of items without regard to order
complex numbers	numbers which have the form a + bi where a and b are real numbers and i is an imaginary number
congruent	two shapes are said to be congruent if they have the same size and shape
conjecture	a hypothesis drawn from observed patterns in several examples
coordinate system	any set of two or more magnitudes used to locate points, lines or curves. Commonly placed by using a horizontal axis (x-axis) and vertical axis (y-axis).

cosine	the trigonometric function which is defined as the ratio of the leg adjacent to an angle to the hypotenuse of its right triangle
dimensional analysis	a tool for obtaining information about physical systems too complicated for full mathematical solutions to be feasible. It enables one to predict the behavior of large systems from a study of small scale models. A convenient means of checking mathematical equations.
directed graphs	usually equivalent to an arrow diagram, a set of points or nodes connected by lines or arcs, each of which is associated with a given direction
expanded form	the form a quantity takes when written as a sum of terms, or as a continued product, or in general in any type of extended form. The writing of an expression in full (e.g., (x + a )^3= x^3 + 3x^2a + 3xa^2 + a^3).
explicit function	an explicit function of x is a function whose values are given by an explicit expression (algebraic or otherwise) in x. For example, the equation y=2x-3 gives values of y as an explicit function of x (solving for x in terms of y would express the value of x as an explicit function of y).
exponent	tells how many times a number or variable is used as a factor. For example, 6 with an exponent of 3, written 6^3, indicates that 6 is a factor 3 times (6x6x6).
exponential function	a function commonly used to study growth and decay. It has a form y = a^x, for a>0, usually a [not equal to] 1.
extrapolate	when estimating from a graph, the estimation of a value beyond the given points

factors	any of two or more quantities which are multiplied together
finite sequence	a sequence with a finite number of terms. The number of terms in a finite sequence can be counted, and in every finite sequence there is a last term.
fluency	the state of being able to smoothly and easily perform a given function or task
function	a dependent relationship between two sets of numbers in which a value in the first set has only one defined element in the second set
geometric sequences	a sequence in which there is a common ratio between successive terms. Each successive term of a geometric sequence is found by multiplying the preceding term by the common ratio. (e.g., in the sequence {1, 3, 9, 27, 81, ...} the common ratio is 3).
histogram	a vertical block graph with no spaces between the block, having discrete units or class boundaries with contiguous end points along the horizontal axis and frequency density as units on the vertical axis. The area of the blocks or rectangles is proportional to the frequencies within a class or across several classes. The total area is proportional to the sum of the frequencies.
inequalities	statements indicating that two quantities are not equal, utilizing symbols > (greater than) or < (less than) and _
integers	a set of numbers consisting of the positive and negative whole numbers and zero, and their opposites {...-2, -1, 0, 1, 2...}

interpolate	in a table of numerical values, any procedure for estimating intermediate values that are not listed. When estimating from a graph, the estimation of a value between given points.
irrational numbers	a set of numbers which cannot be represented as an exact ratio of two integers. For example, the square root of 2, [pi].
linear function	a function that has a constant rate of change and can be modeled by a straight line
logarithm	an alternative notation for expressing an exponent; the inverse of exponentiation
manipulatives	a wide variety of physical materials and supplies that students use to foster the learning of abstract ideas in math
mean	in statistics, the average obtained by dividing the sum of two or more quantities by the number of these quantities
median	in statistics, the quantity designating the middle value in a set of numbers
mode	in statistics, the value that occurs most frequently in a given series of numbers
monomial	in algebra, an expression consisting of a single term
multiple	a number into which another number may be divided with no remainder
non-standard unit	measurement expressed in terms of objects such as paper clips, sticks of gum, shoes, etc.
norm	(1) mean; average. (2) customary degree or condition. (3) established pattern or form.
parallel	refers to lines that extend in the same direction, are equidistant, and never meet or intersect
permutation	any possible arrangement, or ordering, of the distinct items in a set
piecewise defined function	using different rules for different parts of the domain
polar equations	any relation between the polar coordinates (r,Ø) of a set of points. (e.g., r= 2cosØ is the polar equation of a circle referred to a point on its circumference and its diameter as an initial line).
polynomial	in algebra, an expression consisting of two or more terms, such as x^2 - 2xy + y^2
primes	counting numbers that can only be evenly divided by two numbers which are the number itself and 1. For example, the numbers 2, 3, 5, 7.
quadratic function	a function that has an equation of the form y= Ax^2 + Bx + C where "A" does not equal 0.
random variable	a quantity that can take any one of a number of unpredicted values
range	in statistics, the difference between the greatest and smallest values in a set of data
ratio	a comparison expressed as indicated division. For example, there is a ratio of three boys to two girls in our class (3/2, 3:2).
rational numbers	numbers that can be expressed as an exact ratio of two integers
real numbers	all rational and irrational numbers
recursive function	in discrete mathematics, a series of numbers in which values are derived by applying a formula to the previous value
reflect	in geometry, a transformation, also called a flip, which produces a mirror image of a geometric figure
root extraction	finding a number that can be used as a factor a given number of times to produce the original number. (e.g., the fifth root of 32= 2 because 2x2x2x2x2= 32).
rose	the graph in a polar coordinates of r= a sin nØ, or r= a cos nØ, where n is a positive integer. It consists of rose petal-shaped loops with the origin a point common to all of them. When n is odd there are n loops; when n is even there are 2n loops.
rotation	in geometry, a transformation which turns a figure about a point
scalar matrix	a diagonal matrix whose elements are equal. Multiplication by such a matrix is equivalent to multiplication by a scalar (a real number, a quantity with magnitude but no direction). The unit matrix is a special case.
scatter plot	a graph of the points representing a collection of data
scientific notation	a shorthand way of writing very large or very small numbers. A number expressed in scientific notation is expressed as a decimal number between 1 and 10 multiplied by a power of 10. (e.g., 7000 = 7 x 10^3 or .0000019 = 1.9 x 10^-6)
significant digit	any digit that is obtained by actual measurement and thus is not simply a placeholder used to position the decimal point
similarity	in geometry, objects or figures that are the same shape but not necessarily the same size
simultaneous linear equations	pair of equations of the first degree upon which two different conditions are put on the same two variables at the same time (e.g., find two numbers whose sum is 7 and whose difference is 1. x + y= 7 and x - y= 1 The solution to the set is the single pair x=4, y=3).
sine	a trigonometric function which is defined as the ratio of the leg opposite the angle of the hypotenuse of its right triangle
square root	two equal factors of a number. For example, 4 is the square root of 16.
standard deviation	a statistic which measures the dispersion of a sample
symmetry	a correspondence in size, form and arrangement of parts on opposite sides of a plane, line or point. For example, a figure that has line symmetry has two halves which coincide if folded along its line of symmetry.
tangram	a puzzle made by cutting a square into triangles, a square and a rhomboid which can be recombined in many different figures
translate	a rigid motion that preserves exactly the size, shape, and orientation of a figure
transversal	in geometry, a line intersecting two or more lines

trigonometric ratios	the ratios of the lengths of pairs of sides in a right triangle, i.e., sine, cosine and tangent
unit fraction	a fraction whose numerator is 1 (e.g.,,,).
unit vector	a vector with a magnitude of 1 unit.
validity	an argument which is correctly inferred or deduced from a premise
variability	numbers which describe how spread out a set of data is (for example, range and quartile)
variable	place holders in algebraic expressions. 3x+y=23, x and y are variables.
vector	quantity that has magnitude (length) and direction. It may be represented as a directed line segment.
Venn diagram	geometric figures used to picture sets and set relations. Generally a rectangle is used to represent the universal set, and circles are used to represent subsets of the universal set. Venn diagrams are useful for illustrating set operations.
zeros of a function	the values of the domain of a function which are mapped on to zero or, less formally, the points at which the value of a function is zero

Arizona State Department of Education. Mathematics Performance Objectives Mathematics Glossary. Arizona: state Board of Education. Adopted August 26, 1996.

Glenn, John, and Littler Graham, editors. A Dictionary of Mathematics. Totwa, New Jersey: Barnes and Noble Books. 1984.

James/James. Mathematics Dictionary 4th Edition. San Francisco: Van Nostrand Reinhold Company. 1976.

Karush, William, and Torcov, Oscar, ed. The Crescent Dictionary of Mathematics. Palo Alto, California: Dale Seymour Publications. 1962.

McGraw-Hill Encyclopedia of Science and Technology. Volume 5, 8th Edition. San Francisco: McGraw-Hill. 1997.

West, Beverly Henderson, et al. The Prentice-Hall Encyclopedia of Mathematics. Englewood Cliffs, New Jersey: Prentice-Hall Incorporated. 1982.

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