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The terms defined in this glossary pertain to the Sunshine State Standards in mathematics for grades 3 through 10 and the content assessed on FCAT in mathematics.
Note: The following notations are used to identify the level at which students are likely to encounter the mathematical terms.
|
E
- Elementary
|
M
- Middle School
|
H
- High School
|
| Absolute value | a number’s
distance from zero (0) on a number line. For example: |3| = |-3| |
H
|
| Acute angle | an angle that measures less than 90 and greater than 0. |
E
|
| Additive
identity |
the number zero (0); that is, adding 0 does not change a number’s value (e.g., 5 + 0 = 5). |
H
|
| Additive
inverse property |
a number
and its additive inverse have a sum of zero (0) (e.g., in the equation 3 + -3 = 0, 3 and –3 are additive inverse of each other). |
H
|
| Algebraic
equation |
a mathematical sentence in which two expressions are connected by an equality symbol. |
H
|
| Algebraic
expression |
an expression containing numbers and variables (e.g., 7x), and operations that involve numbers and variables (e.g., 2x + y or 3a – 4). Algebraic expressions do not contain equality or inequality symbols. |
H
|
| Algebraic
order of operations |
the order
of performing computations is parentheses first, then exponents,
followed by multiplication and/or division, then
addition and/or subtraction. For example: 5 + (12 – 2) ÷2 – 3 x 2 5 + 10 ÷ 2 – 3 x 2 5 + 5 – 6 10 – 6 4 |
H
|
| Algebraic
rule |
a mathematical expression that contains variables and describes a pattern or relationship. |
E
|
| Altitude |
the perpendicular distance from a vertex in a polygon to its opposite side. |
H
|
| Angle |
the shape made by two rays extending from a common end point, the vertex. Measures of angles are described using the degree system. |
E
|
| Area
|
the inside region of a two-dimensional figure measured in square units (e.g., a rectangle with sides of 4 units by 6 units contains 24 square units or has an area of 24 square units). |
E
|
| Associative
property |
the way
in which three or more numbers are grouped for addition or multiplication
does not change their sum or product [e.g., (5 + 6) + 9 = 5 + (6 + 9) or (2 x 3) x 8 = 2 x (3 x 8)]. |
M
|
| Axes
(of a graph) |
the horizontal and vertical number lines used in a rectangular graph or coordinate grid system. |
E
|
| Bar graph
|
a graph that uses bars to display data. |
E
|
| Base |
the line or plane upon which a figure is thought to rest. |
E
|
| Break |
a zigzag on the line of the x- or y-axis in a line or bar graph indicating that the data being displayed do not include all of the values that exist on the number line used. Also called a Squiggle. |
M
|
| Capacity |
the amount of space that can be filled. Both capacity and volume are used to measure three-dimensional spaces; however, capacity usually refers to fluids, whereas volume usually refers to solids. |
E
|
| Central
angle |
an angle that has its vertex at the center of a circle. |
M
|
| Chart |
a data display. |
M
|
| Circle
graph |
a data display. |
M
|
| Circumference |
the perimeter of a circle is called its circumference. |
M
|
| Closed
figure |
a two-dimensional
figure whose beginning and ending points meet, such that the plane in which the figure lies is divided into tow parts–the part inside the figure and the part outside the figure (e.g., circles, squares, rectangles). |
E
|
| Commutative
property |
the order
in which two numbers are added or multiplied does not change their
sum or product (e.g., 2 + 3 = 3 + 2 or 4 x 7 = 7 x 4). |
M
|
| Complementary
angles |
two angles, the sum of which is exactly 90. |
M
|
| Composite
number |
a whole number that has more than two factors. |
E
|
| Concrete representations of numbers | having a definite form or relating to an actual object. |
M
|
| Congruent |
a term describing figures or objects that are the same shape and size. |
E
|
| Coordinate
grid or system |
a network of evenly spaced, parallel, horizontal and vertical lines especially designed for locating points, displaying data, or drawing maps. |
E
|
| Coordinates |
numbers that correspond to points on a coordinate graph in the form (x, y), or a number that corresponds to a point on a number line. |
M
|
| Counting
principle |
if a first event has n outcomes and a second event has m outcomes, then the first event followed by the second event has n x m outcomes. |
M
|
| Customary
units |
the units of measure developed and used in the United States. Customary units for length are inches, feet, yards, and miles. Customary units for weight are ounces, pounds, and tons. Customary units for volume are cubic inches, cubic feet, and cubic yards. Customaryunits for capacity are fluid ounces, cups, pints, quarts, and gallons. |
E
|
| Cylinder
|
a three-dimensional figure with two parallel bases that are congruent circles. |
M
|
| Data
displays/ graphs |
different
ways of displaying data in tables, charts, or graphs, including pictographs, circle graphs, single-, double-, or triple-bar and line graphs, histograms, stem-and-leaf plots, box-and-whiskers plots, and scatter plots. |
M
|
| Decimal
number |
any number
written with a decimal point in the number. A decimal number falls between two whole numbers (e.g., 1.5 falls between 1 and 2). Decimal numbers smaller than 1 are sometimes called decimal fractions (e.g., five-tenths is written 0.5). |
E
|
| Diameter
|
a line segment from any point on the circle passing through the center to another point on the circle. |
M
|
| Direct
measure |
obtaining the measure of an object by using measuring devices, either standard devices of the customary or metric systems, or nonstandard devices such as a paper clip or pencil. |
E
|
| Distributive
property |
for any real numbers a, b, and x, x(a + b) = ax + bx. |
M
|
| Divisible
|
a term describing a number capable of being divided into equal parts without a remainder. |
E
|
| Effects
of operations |
the results of applying an operation to given numbers (e.g., adding two whole numbers results in a number greater than or equal to the original numbers. |
E
|
| Empirical
probability |
the likelihood of an event happening that is based on experience and observation rather than on theory. |
E
|
| Enlargement
|
an increase in size in all dimensions by a uniform amount. |
M
|
| Equation
|
a mathematical sentence (e.g., 2x = 10) that equates one expression (2x) to another expression (10). |
E
|
| Equivalent
expressions |
expressions that have the same value but are presented in a different format using the properties of numbers. [e.g., ax + bx = (a + b)x]. |
M
|
| Equivalent
forms of a number |
the same number expressed in different forms (e.g., 3/4, 0.75, 75%). |
E
|
| Explain
in words |
directions requesting a written description of the procedures for finding the solution to the problem presented. |
E
|
| Exponent
(exponential form) |
the number of times the base occurs as a factor. For example, 23 is the exponential form of 2 x 2 x 2. The numeral 2 is called the base, and the numeral 3 is called the exponent. |
M
|
| Expression
|
a collection of numbers, symbols, and/or operation signs that stands for a number. |
E
|
| Extrapolate
|
to estimate or infer a value or quantity beyond the known range. |
M
|
| Face
|
one of the plane surfaces bounding a three-dimensional figure (a side). |
E
|
| Factor
|
a number
or expression that divides exactly another number (e.g., 1, 2, 4, 5, 10, and 20 are factors of 10). |
E
|
| Finite
graph |
a graph
having definable limits. |
H
|
| Flip
|
a transformation
that produces the mirror image of a geometric figure. Also called
a Reflection. |
E
|
| Fraction
|
any part
of a whole is called a fraction (e.g., one-half written in fractional
form is 1/2). |
E
|
| Function
|
a relation in which each value of x is paired with a unique value of y. |
E
|
| Function
table |
a table of x- and y-values (ordered pairs) that represents the function, pattern, relationship, or sequence between the two variables. |
M
|
| Grid
|
a network
of evenly spaces, parallel, horizontal, and vertical lines. |
E
|
| Height
|
a line segment
extending from the vertex or apex of a figure to its base and forming
a right angle with the base or basal point. |
E
|
| Hypotenuse
|
in a right
triangle, the side opposite the right angle. |
M
|
| Hypothesis
|
a proposition
or supposition developed to provide a basis for further investigation
or research. |
M
|
| Indirect
measure |
the measurement
of an object through the known measure of another object. |
M
|
| Inequality
|
a sentence
that states one expression is greater than, greater than or equal
to, less than, less than or equal to, or not equal to, another expression
(e.g., a 5 or x < 7). |
E
|
| Integers
|
the numbers
in the set {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …}. |
M
|
| Intercept
|
the value
of a variable when all other variables in the equation equal zero
(0). On a graph, the values where a function crosses the axes. |
M
|
| Intersection
|
the point
at which two lines meet. |
E
|
| Inverse
operation |
an action
that cancels a previously applied action. For example, subtraction
is the inverse operation of addition. |
M
|
| Irrational
number |
a real number
that cannot be expressed as a ratio of two numbers (e.g., ). |
M
|
| Isosceles
triangle |
a triangle
with two congruent sides and two congruent angles. |
M
|
| Labels
(for a graph) |
the titles
given to a graph, the axes of a graph, or to the scales on the axes
of a graph. |
E
|
| Length
|
a one-dimensional
measure that is the measurable property of line segments. |
E
|
| Likelihood
|
the chance
that something is likely to happen. See Probability. |
E
|
| Line
|
a straight
line that is endless in length. |
E
|
| Linear
equation |
an algebraic
equation in which the variable quantity or quantities are in the
first power only and the graph is a straight line [e.g., 20 = 2(w
+ 4) + 2w and y = 3x + 4]. |
M
|
| Line
graph |
a graph
that displays data using connected line segments. |
E
|
| Line
segment |
a portion
of a line that has a defined beginning and end (e.g., the line segment
AB is between point A and point B). |
M
|
| Mean
|
the arithmetic
average of a set of numbers. |
E
|
| Median
|
the middle
point of a set of ordered numbers where half of the numbers are
above the median and half are below it. |
E
|
| Metric
units |
the units
of measure developed in Europe and used in most of the world. Like
the decimal system, the metric system uses the base 10. Metric units
for length are milligrams, grams, and kilograms. Metric units for
volume are cubic millimeters, cubic centimeters, and cubic meters.
Metric units for capacity are milliliters, centiliters, liters,
and kiloliters. |
E
|
| Midpoint
of a line segment |
the point
on a line segment that divides it into two equal parts. |
M
|
| Mode
|
the score
or data point found most often in a set of numbers. |
E
|
| Multiples
|
the numbers
that result from multiplying a given number by the set of whole
numbers (e.g., the multiples of 15 are 0, 15, 30, 45, 60, 75, etc.). |
E
|
| Multiplicative
identity |
the number
one (1), that is, multiplying by 1 does not change a number’s
value (e.g., 5 x 1 = 5). |
M
|
| Multiplicative
inverse (reciprocal) |
any two
numbers with a product of 1 (e.g., 4 and 1/4). |
M
|
| Natural
numbers (counting numbers) |
the numbers
in the set {1, 2, 3, 4, 5, …}. |
M
|
| Negative
exponent |
used in
scientific notation to designate a number smaller than one (1) (e.g.,
3.45 x 10 -2 equals 0.0345). |
M
|
| Nonstandard
units of measure |
objects
such as blocks, paper clips, crayons, or pencils that can be used
to obtain a measure. |
E
|
| Number
line |
a line on
which numbers can be written or visualized. |
E
|
| Obtuse
angle |
an angle
with a measure of more than 90 but less than 180. |
E
|
| Odds
|
the ratio
of one event occurring to it not occurring. |
M
|
| Operation
|
any mathematical
process, such as addition, subtraction, multiplication, division,
raising to a power, or finding the square root. |
E
|
| Operational
shortcut |
a method
having fewer arithmetic calculations. |
H
|
| Ordered
pair |
the location
of a single point on a rectangular coordinate system where the digits
represent the position relative to the x-axis and y-axis [e.g.,
(x, y) or (3, 4)]. |
E
|
| Organized
data |
data arranged
in a display that is meaningful and that assists in the interpretation
of the data. See Data displays. |
E
|
| Origin
|
the point
in the coordinate plane at which the horizontal axis (x-axis) intersects
the vertical axis (y-axis). The point has coordinates (0,0). |
M
|
| Parallel
lines |
two lines
in the same plane that never meet. Also, lines with equal slopes. |
E
|
| Pattern
(relationship) |
a predictable
or prescribed sequence of numbers, objects, etc. Patterns and relationships
may be described or presented using manipulatives, tables, graphics
(pictures or drawings), or algebraic rules (functions). Also called
a Relation. |
E
|
| Percent
|
a special-case
ratio in which the second term is always 100. The ratio is written
as a whole number followed by a percent sign (e.g., 25% means the
ratio of 25 to 100). |
E
|
| Perimeter |
the distance
around a figure. |
E
|
| Perpendicular
|
a line describing
two lines or two line segments that cross to form a right angle. |
E
|
| Pi (
) |
the symbol
designating the ratio of the circumference of a circle to its diameter,
represented as either 3.14 or 22/7). |
M
|
| Pictograph
|
a data display. |
M
|
| Place
value |
the position
of a single digit in a whole number or decimal number containing
one or more digits. |
E
|
| Planar
cross-section |
the intersection
of a plane and a three-dimensional figure. |
H
|
| Plane
figure |
a two-dimensional
figure that lies entirely within a single plane. |
E
|
| Point
|
a location
in space that has no discernible length or width. |
E
|
| Polygon
|
a closed
plane figure whose sides are straight lines that are connected end-point
to end-point. |
E
|
| Prime
number |
any whole
number with only two factors, 1 and itself (e.g., 2, 3, 5, 7, 11, etc.). |
E
|
| Proof
|
a set of
steps that demonstrates the truth of a given statement. Each step
can be justified with a reason, such as a given, a definition, an
axiom, or a previously proven property. |
H
|
| Proportion
|
a mathematical
sentence stating that two ratios are equal. |
M
|
| Pyramid
|
a three-dimensional
figure whose base is a polygon and whose faces are triangles with
a common vertex. |
M
|
| Pythagorean
theorem |
the square
of the hypotenuse (c) of a right triangle is equal to the sum of
the squares of the legs (a and b), as shown in the equation c2 =
a2 + b2. |
M
|
| Quadrant
|
any of the
four regions formed by the axes in a rectangular coordinate system. |
M
|
| Radical
|
an expression that has a root (square root, cube root,
etc.) (e.g., 
is a radical). Any root can be specified by an index number, b,
in the form 
(e.g.,  ). A radical
without an index number is understood to be a square root. |
M
|
| Radical
sign |
the symbol (
) used before a number to show that the number is a radicand. |
M
|
| Radicand
|
a number appears with a radical sign (e.g., in ,
25 is the radicand). |
M
|
| Radius
|
a line segment
extending from the center of a circle or sphere to a point on the
circle or sphere. |
M
|
| Range
|
the lowest
value (L) in a set of numbers through the highest value (H) in the
set. When the width of the range is expressed as a single number,
the range is calculated as the difference between the highest and
lowest values. More advanced presentations show the range calculated
as (H – L + 1). The result of either calculation would be considered
correct. |
E
|
| Rate/distance
|
calculations
involving rates, distances, and time intervals, based on the distance,
rate, time formula (D = rt). |
M
|
| Ratio
|
the comparison
of two quantities (e.g., the ratio of a and b is a/b,
where b 0. |
E
|
| Rational
number |
a real number
that can be expressed as a ratio of two integers. |
M
|
| Ray |
a portion
of a line that begins at a point and goes on forever in one direction. |
E
|
| Real
number |
all rational
and irrational numbers. |
M
|
| Reciprocal
|
see Multiplicative
inverse. |
H
|
| Reflection
|
see Flip. |
E
|
| Reflexive
axiom of equality |
a number
or expression is equal to itself (e.g., ab = ab). |
H
|
| Regular
polygon |
a polygon
that is both equilateral and equiangular. |
E
|
| Relation
(relationship) |
see Pattern. |
E
|
| Relative
size |
the size
of one number in comparison to the size of another number or numbers. |
M
|
| Right
angle |
an angle
whose measure is exactly 90. |
E
|
| Right
circular cylinder |
a cylinder
in which the bases are parallel circles perpendicular to the side
of the cylinder. |
M
|
| Right
prism or rectangular solid |
a three-dimensional
figure (polyhedron) with congruent, polygonal bases and lateral
faces that are all parallelograms. |
M
|
| Right
triangle geometry |
finding
the measures of missing sides or angles of a right triangle when
given the measures of other sides or angles. |
H
|
| Rise
|
the change
in y going from one point of x to another (the vertical change on
the graph). |
M
|
| Rotation
|
a transformation
of a figure by turning it about a center point or axis. The amount
of rotation is usually expressed in the number of degrees (e.g.,
a 90 rotation). Also called a Turn. |
E
|
| Rule
|
a mathematical
expression that describes a pattern or relationship, or a written
description of the pattern or relationship. |
E
|
| Run |
the change
in x going from one point of y to another (the horizontal change
on the graph. |
M
|
| Scale
model |
a model
or drawing based on a ratio of the dimensions for the model and
the actual object it represents (e.g., a map). |
E
|
| Scales
|
the numeric
values assigned to the axes of a graph. |
E
|
| Scatter
Plot |
a graph
of data points, usually from an experiment, that is used to observe
the relationship between two values. |
M
|
| Scientific
notation |
a shorthand
method of writing very large or very small numbers using exponents
in which a number is expressed as the product of a power of 10 and
a number that is greater than or equal to one (1) andless than 10
(e.g., 7.59 x 105 = 759,000). It is based on the idea
that it is easier to read exponents than it is to count zeros. If
a number is already a power of 10, it is simply written 1027 instead
of 1 x 1027. |
M
|
| Sequence
|
an ordered
list with either a constant difference (arithmetic) or a constant
ratio (geometric). |
M
|
| Side
|
the edge
of a geometric figure (e.g., a triangle has three sides). |
E
|
| Similar
figures |
figures
that are the same shape, have corresponding, congruent angles, and
have corresponding sides that are proportional in length. |
E
|
| Similarity
|
a term describing
figures that are the same shape but are not necessarily the same
size or in the same position. |
E
|
| Slide
|
to move
along in constant contact with the surface in a vertical, horizontal,
or diagonal direction. Also called a Translation. |
E
|
| Slope
|
the constant, m, in the linear equation for the slope-intercept
form y = mx + b. The ratio of change in the vertical axis
(y-axis) to each unit change in the horizontal axis (x-axis) in
the form  or  . |
M
|
| Solid
figures |
three-dimensional
figures that completely enclose
a portion of space (e.g., a rectangular solid, cube,
sphere, right circular cylinder, right circular cone, and
square pyramid). |
M
|
| Spatial
relationships |
relationships
of figures existing or happening
in space. |
E
|
| Square
root |
a positive real number that can be multiplied by itself
to produce a given number (e.g., the square root of 144 is 12 or
 = 12). |
M
|
| Squiggle
|
see Break. |
M
|
| Standard
units of measure |
accepted
measuring devices and units of the customary or metric system. |
E
|
| Straight
angle |
an angle
whose measure is exactly 180. |
E
|
| Supplementary
angles |
two angles,
the sum of which is exactly 180. |
M
|
| Surface
area of a geometric solid |
the sum
of the areas of the faces of the figure
that create the geometric solid. |
M
|
| Symbolic
expression |
a symbol
or set of symbols expressing a mathematical quantity or operation
(e.g., 2x is equal to two times x). |
E
|
| Symbolic
representations of numbers |
expressions
represented by symbols (e.g., circles shaded to represent 1/4 or
variables used to represent quantities). |
M
|
| Symmetry
|
a term describing
the result of a line drawn through the center of a figure such that
the two halves are congruent. |
E
|
| System
of equations |
a group
of two or more equations that share variables. The solution to a
system of equations is an ordered number set that makes all of the
equations true. |
H
|
| Table
|
a data display. |
M
|
| Tessellation
|
a covering
of a plane with congruent copies of the same pattern with no holes
and no overlaps, like floor tiles. |
M
|
| Theoretical/expected
probability |
the likelihood
of an event happening based on theory rather than on experience
and observation. |
E
|
| Transformation
|
an operation
on a geometric figure by which
another image is created. Common transformations
Include flips, slides, and turns. |
E
|
| Transitive
property |
when the
first element has a particular relationship to a second element
that in turn has the same relationship to a third element, the first
has this same relationship to the third element (e.g., if a =
b and b = c, then a = c). Identity and equality
are transitive relationships. |
H
|
| Translation
|
see Slide. |
E
|
| Transversal
|
a line that
intersects two or more lines at different points. |
M
|
| Tree
diagram |
a diagram
in which all the possible outcomes of a given event are displayed.
|
E
|
| Turn
|
see Rotation.
|
E
|
| Unorganized
data |
data that
are presented in a random manner. |
E
|
| Variable
|
any symbol
that could represent a number. |
E
|
| Vertex
|
the common
endpoint from which two rays begin (e.g., the vertex of an angle)
or the point where two lines intersect; the point on a triangle
or pyramid opposite to and farthest from the base. |
E
|
| Vertical
angles |
the opposite
angles formed when two lines intersect. |
M
|
| Volume
|
the amount
of space occupied in three dimensions and expressed in cubic units.
Both capacity and volume areused to measure empty spaces; however,
capacity usually refers to fluids, whereas volume usually refers
to solids. |
E
|
| Weight
|
measures
that represent the force that attracts an object to the center of
Earth. |
E
|
| Whole
numbers |
the numbers
in the set {0, 1, 2, 3, 4, …}. |
E
|
| x-intercept
|
the value
of x on a graph when y is zero (0). The x-axis is the horizontal
number line on a rectangular coordinate system. |
M
|
| y-intercept
|
the value
of y on a graph when x is zero (0). The y-axis is the vertical number
line on a rectangular coordinate system. |
M
|
Copyright Statement for this Assessment and Evaluation Services Publication
Authorization for reproduction of this document is hereby granted to persons acting in an official capacity within the State System of Public Education as defined in Section 228.041(1), Florida Statutes. The copyright notice at the bottom of this page must be included in all copies.
The Administrator
Assessment and Evaluation Services
Florida Department of Education
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325 West Gaines Street
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Copyright © 2000
State of Florida
Department of State