| Arizona Standards Mathematics Standards
(Adopted 8/26/96)
Mathematics Glossary
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.
algebraic methods The use of symbols to represent
quantities and signs to represent their relationships.
algebraic sentence A general term for equations and
inequalities.
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.
angle measure The measure of the space between two
lines that meet in a point. Angles are measured in degrees or radians.
axiomatic systems Systems that include self-evident
truths; truths without proof and from which further statements, or theorems, can be
derived.
binomial In algebra, an expression consisting of two
terms connected by a plus or minus sign, such as 4a + 6.
box-and-whisker plot 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.
census The count of a population.
combinations Subsets of a larger number of items
(e.g., the number of different teams of three that can be chosen from a group of 21).
computational techniques Operations or
tools–number lines, calculators.
complex numbers Numbers that have the form a + bi
where a and b are real numbers and i is an imaginary number.
congruence The state of having the same size and
shape.
conjecture An inference drawn from observed patterns
in several examples.
contextual situation Relating mathematical problems to
real, modeled or illustrated circumstance.
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).
correlation coefficient A statistical measure that
relates how well a set of data points can be modeled by a line.
cosine The trigonometric function that is defined as
the ratio of the leg adjacent to an angle to the hypotenuse of its right triangle.
counterexample An example of a conditional statement
in which the hypothesis is true and the conclusion is false.
curve fitting Plotting data and observing the pattern
to predict trends.
deductive reasoning A series of logical steps in which
a conclusion is drawn directly from a set of statements that are known or assumed to be
true.
dilation A transformation that either enlarges or
reduces a geometric figure proportionately.
direct proof A conclusion proved through deductive
reasoning.
discrete math The study of mathematical properties of
sets and systems that have only a specific number of elements. For example, the results of
tossing dice form a discrete set of events, since a die has to land on one of its six
faces.
empirical Relating to the collection of actual data.
equation A mathematical statement in which one
expression is equal to another.
Euclidean transformations In geometry, the process of
changing one configuration into another, including slides, rotations and reflections.
exponent Tells how many times a number or variable is
used as a factor. For example, 6 with an exponent of 3 (63) indicates that 6 is
a factor 3 times (6 x 6 x 6).
exponential function A function commonly used to study
growth and decay. It has a form y = ax.
expression A mathematical phrase with no equal sign,
such as 3x, 6, 2n + 3m.
factors Any of two or more quantities that are
multiplied together.
finite graph A structure consisting of vertices and
edges, where the edges indicate a mapping among the vertices (e.g., the vertices may
represent players in a tournament, and the edges indicate who plays whom).
flip A transformation, also called a reflection, that
produces a mirror image of a geometric figure.
fractal An algebraically generated complex geometric
shape having the property of being endlessly self-similar under magnification. Some
computer screen savers utilize fractals.
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.
identify To state, match, select, write.
imaginary numbers The square root of a negative number
usually expressed using i.
indirect proof A deductive proof using contradiction
or elimination to rule out all except the desired conclusion.
inductive reasoning A form of reasoning from
individual cases to general ones or from observed instances to unobserved ones.
inequalities Statements indicating that two quantities
are not equal, utilizing symbols > (greater than) or < (less than) and
¹ .
integers A set of numbers consisting of the whole
numbers and their opposites {. . . –2, -1, 0, 1, 2 . . .}.
inverse A related but opposite process or number such
as multiplication being the inverse of division and 2/1 being the inverse of 1/2.
irrational numbers A set of numbers that cannot be
represented as an exact ratio of two integers. For example, the square root of 2.
iterative processes In discrete math, a method of
calculating an amount by using an initial value and applying a function repeatedly.
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.
logic A system of reasoning used to validate
arguments.
magnitude Size or quantity.
manipulatives A wide variety of physical materials and
supplies that students use to foster the learning of abstract ideas in mathematics.
matrices A rectangular array of numbers or letters
arranged in rows and columns.
mean In statistics, the average obtained by dividing
the sum of two or more quantities by the number of these quantities.
measures of central tendency Numbers that communicate
the "center" or "middle" of a set of data. The mean, median and mode
are statistical measures of central tendency.
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.
model (noun) A display of concrete materials, objects
or drawings.
model (verb) Use of concrete materials, symbolic.
monomial In algebra, an expression consisting of a
single term such as 5y.
multiple A number into which another number may be
divided with no remainder.
nonstandard measurement Measurement expressed in terms
of objects such as paper clips, sticks of gun, shoes, etc.
normal curve In statistics, the distribution of data
along a bell-shaped curve that reaches its maximum height at the mean.
open sentence A statement that contains at least one
unknown. For example, 6 + x = 14.
parallelism The state of being parallel, not
intersecting.
parameter A quantity whose value varies with the
circumstances of its application, such as the radius of a group of circles.
permutations Ordered arrangements of a given number of
items in a set.
polynomial In algebra, an expression consisting of two
or more terms such as x2 – 2xy + y2.
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.
proportion An equality between ratios. For example,
2/6 = 3/9.
quadratic function A function that has an equation of
the form y = Ax2 + Bx + C where A does not equal 0.
radian The size of the central angle of a circle when
the arc length equals the radius.
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.
rectangular array An organized arrangement of square
units (tiles).
recurrence relations In discrete mathematics, a value
in a series is derived by applying a formula to the previous value.
recursive sequence In discrete mathematics, a series
of numbers in which values are derived by applying a formula to the previous value.
reflection In geometry, a transformation, also called
a flip, that produces a mirror image of a geometric figure.
rotation In geometry, a transformation that turns a
figure about a point.
sample A part of the total population. Used in
statistics to make predictions about the characteristics of the entire group.
scatter plots 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.
similarity In geometry, objects or figures that are
the same shape but not necessarily the same size.
sine A trigonometric function that is defined as the
ratio of the leg opposite the angle to the hypotenuse of its right triangle.
skip counting Counting by equal intervals.
slides In geometry, a transformation where a figure
moves in a given direction.
square root Two equal factors of a number. For
example, 4 is the square root of 16.
standard deviation A statistic that measures the
dispersion of a sample.
stem-and-leaf plot A table utilizing digit(s) of a
number as stems and the other digit(s) as leaves. For example, 5 | 7, 8 shows 57 and 58.
survey Interview, questionnaire and/or polling.
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 that coincide if folded along its line of symmetry.
synthetic representation The geometric form as opposed
to the algebraic representation of a figure.
tangent A trigonometric function of an angle which is
defined as the ratio of the lengths of the leg opposite to the leg adjacent to an angle in
its right triangle. Also a line having one point in common with a curve.
tessellations A mosaic formed by repetitions of a
single shape.
theoretical (mathematical) Relating to the probability
of a given event, using mathematical relationships (e.g., the chance of a red side coming
up on the flip of a two-colored counter is one in two or 1/2).
transformation A geometric process for changing one
figure into another.
trigonometric ratios The ratios of the lengths of
pairs of sides in a right triangle, i.e., sine, cosine and tangent.
trigonometry The branch of mathematics involving
triangles that combines arithmetic, algebra and geometry. Trigonometry is used in
surveying, navigation and physics.
validity An argument that is correctly inferred or
deduced from a premise.
variability Numbers that describe how spread out a set
of data is (e.g., range and quartile).
variable A place holder in algebraic expressions. In 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 (?).
whole numbers The counting numbers and zero {0, 1, 2,
3 . . .}.
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