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Glossary

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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

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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

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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

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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

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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

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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

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Grid
a network of evenly spaces, parallel, horizontal, and vertical lines.
E

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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

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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

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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

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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

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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

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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

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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

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Quadrant
any of the four regions formed by the axes in a rectangular coordinate system.
M

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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

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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

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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

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Unorganized data
data that are presented in a random manner.
E

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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

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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

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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

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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

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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

8th Grade Math Home > Teacher Resources > Secondary Mathematics Resource Booklet > Glossary