Oklahoma Administrative Code › Title 210 - State Department of Education › Chapter 15 - Curriculum and Instruction › Subchapter 3 - Oklahoma Academic Standards › Part 7 - MATHEMATICS › Section 210:15-3-61 - Definitions

Current through Vol. 41, No. 20, July 1, 2024
The following words and terms, when used in this Part,
					 shall have the following meaning, unless the context clearly indicates
					 otherwise:
"AA similarity (Angle-Angle similarity)"
means
					 if two triangles have two pairs of corresponding angles that are congruent,
					 then the triangles are similar.
"ASA congruence (Angle-Side-Angle congruence)"
means if two triangles have two corresponding angles and the side adjacent to
					 both angles congruent, then the triangles themselves are congruent.
"Absolute value"
means the absolute value of a
					 real number is its (non-negative) distance from 0 on a number line.
"Addend"
means in the addition problem 3+2+6 =
					 11, the addends are 3, 2, and 6.
"Addition and subtraction within 5, 10, 20, 100, or
					 1,000"
means addition or subtraction of two whole numbers with whole
					 number answers, and with sum or minuend in the range 0-5, 0-10, 0-20, or 0-100,
					 respectively. Example: 8 + 2 = 10 is an addition within 10, 14 - 5 = 9 is a
					 subtraction within 20, and 55 - 18 = 37 is a subtraction within 100.
"Additive inverses"
means two numbers whose
					 sum is 0 are additive inverses of one another. Example: 3/4 and -3/4 are
					 additive inverses of one another because 3/4 + (-3/4) = (-3/4) + 3/4 =
					 0.
"Algorithm"
means a finite set of steps for
					 completing a procedure (e.g. long division).
"Analog"
means having to do with data
					 represented by continuous variables (e.g. a clock with hour, minute, and second
					 hands).
"Arc (minor and major)"
means a portion of the
					 circumference of a circle with ending points A and B. Unless stated otherwise,
					 arc AB always refers to the shorter segment of the two (the minor arc).
					 Together with the major arc the two portions beginning and ending at points A
					 and B form the entire circumference of a circle.
"Arc length"
means the distance along the
					 curved line forming the arc.
"Arc measure"
means the angle formed by the
					 arc at the center of the circle.
"Area"
means a measurement of the amount of
					 space within a closed two-dimensional shape. Area is usually measured in terms
					 of "square units," in which 1 square unit is the amount of space within a
					 square that measures 1 unit by 1 unit (for a given unit of length). Example:
					 area may be measured in "square centimeters," 1 square centimeter being the
					 amount of space within a 1cm by 1cm square.
"Arithmetic sequence (progression)"
means a
					 sequence in which successive terms exhibit a common difference.
"Array (rectangular)"
means an orderly
					 arrangement of objects into a rectangular configuration (e.g. take six tiles
					 and arrange two long and three wide to form a rectangle).
"Associative property of addition"
See Table
					 1.
"Associative property of multiplication"
See
					 Table 1.
"Assumption"
means a fact or statement (as a
					 proposition, axiom, postulate) taken for granted.
"Attribute"
means characteristic (e.g. size,
					 shape, color, weight).
"Benchmark fraction"
means a common fraction
					 against which other fractions can be measured, such as ½.
"Bar graph"
means a display of categorical
					 data in which vertical or horizontal bars represent the count of a category.
					 The relative lengths of the various bars in the graph are commensurate with the
					 relative sizes of the counts of the data.
"Bivariate data"
means pairs of linked
					 numerical observations. Example: a list of heights and weights for each player
					 on a football team.
"Box plot"
means a graphic method that shows
					 the distribution of data values by using the median, quartiles, and extremes of
					 the data set. A box shows the middle 50% of the data.
"Capacity"
means the maximum amount or number
					 that can be contained or accommodated (e.g. a jug with a one-gallon capacity;
					 the auditorium was filled to capacity).
"Cardinal number"
means a number (such as 1,
					 5, 15) that is used in simple counting and that indicates how many elements
					 there are in a set.
"Cardinality"
means the cardinality of a
					 finite collection of objects is the number of objects in the set. Example: in
					 PK-Grade 1 students are still learning that "5" represents the number of
					 objects in any group of "five" objects.
"Categorical data"
means data that measures
					 the number of occurrences of a discrete set of outcomes (e.g. noticing the
					 different colors of shoes in the class and then recording the number of each
					 color).
"Chord"
means a chord is a line that connects
					 two points on a circle.
"Circle"
means the set of all points that are
					 equidistant from a given point, called the center of the circle. The set of all
					 points that lie inside the circle is called the interior of the circle.
(A)
Radius of a circle
means
				  both a segment with one endpoint on the center of the circle and the other
				  endpoint on the circle, and the length of this segment (which is necessarily
				  the same for any point on the circle).
(B)
Diameter of a circle
means
				  both a segment with endpoints on the circle that contains the center, and the
				  length of this segment.
(C)
Circumference of a circle
means the lengths of the circle if cut
				  and opened up to make a straight line segment, which can be found with C =
				  2[PI]r where r is the radius and [PI] is the irrational number "pi" (can be
				  thought of as the perimeter of the circle).
(D)
Area of a circle
means the
				  area of the interior of the circle, which can be found with A =
				  [PI]r2 where r is the radius and [PI] the irrational
				  number "pi."
"Combinations"
means a selection of objects
					 without regard to order.
"Coefficient"
means any of the factors of a
					 product considered in relation to a specific factor. Often, this will be a
					 numerical factor in a product of numbers and variables (e.g.
					 3x2 has coefficient 3).
"Commutative property"
See Table 1.
"Complement (of a set)"
means a set A is
					 typically considered to be a subset of an understood "universal set." The
					 complement of A, denoted by A/C is the set of all elements of the universal set
					 that are not members of A.
"Complementary angles"
means two angles whose
					 measures have a sum of 90 degrees.
"Complex fraction"
means a fraction A/B where
					 A and/or B are fractions (B [NOT EQUAL] 0).
"Complex number"
means numbers of the form a +
					 bi, where a, a real number, is the "real part," and b, also a real number, is
					 the "imaginary part," and i is the imaginary number. See also imaginary
					 number.
"Complex plane"
means a Cartesian plane in
					 which the point (a,b) is used to represent a + bi.
"Compose numbers"
means to compose numbers is
					 to create new numbers using any of the four operations with other numbers.
					 Example: students compose 10 in many ways (9=1, 8=2, ..., 5+5, ...). Also, each
					 place in the base ten place value is composed of ten units of the place to the
					 left (i.e. one hundred is composed of ten bundles of ten, one ten is composed
					 of ten ones).
"Compose shapes"
means joining geometric
					 shapes without overlaps to form new shapes.
"Composite number"
means any positive integer
					 divisible by one or more positive integers other than itself and 1.
"Computation algorithm"
means a set of
					 predefined steps applicable to a class of problems that give the correct result
					 in every case when the steps are carried out correctly. See also algorithm;
					 computation strategy.
"Computation strategy"
means purposeful
					 manipulations that may be chosen for specific problems, may not have a fixed
					 order, and may be aimed at converting one problem into another. See also
					 computation algorithm.
"Conditional statement"
means a statement of
					 the form, "If P, then Q," where each of P and Q and themselves statements.
					 Example: "If it rains, then the streets get wet," is a conditional statement.
					 If the conditional statement "If P, then Q," is true, then this means that it
					 is never the case that the statement P is true while the statement Q is false.
					 Example: it will never be the case that "it rained" but "the streets are not
					 wet." Related statements are:
(A)
Converse:
"If Q, then P." This may or may not be true if the
				  original statement is true.
(B)
Inverse:
"If NOT P, then NOT Q." This may or may not be true if
				  the original statement is true.
(C)
Contrapositive:
"If NOT Q, then NOT P." This is always true if the
				  original statement is true, and vice versa. Example: notice that, "If the
				  streets are NOT wet, then it did NOT rain," is logically equivalent to the
				  example statement above.
"Congruent"
means two geometric objects are
					 congruent if one can be mapped onto the other using a sequence of rigid motions
					 (rigid motions are geometric transformations that preserve lengths and
					 angles).
"Conjugate"
means the result of writing a sum
					 of two terms as a difference, or vice versa. Example: the conjugate of x - 2 is
					 x + 2.
"Conjecture"
means a statement believed to be
					 true but not yet proved.
"Constant"
means a number or sometimes a
					 letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9",
					 5 and 9 are constants. If it is not a constant it is called a variable.
"Constant of proportionality"
means given a
					 proportional relationship expressed as y=kx, the number k is often called the
					 constant of proportionality.
"Coordinate plane"
means a plane in which a
					 point is represented using two coordinates that determine the precise location
					 of the point. In the Cartesian plane, two perpendicular number lines are used
					 to determine the locations of points. In the polar coordinate plane, points are
					 determined by their distance along a ray through that point and the origin, and
					 the angle that ray makes with a predetermined horizontal axis.
"Cosine (of an acute angle)"
means, in a right
					 angle, the cosine of an acute angle is the ratio of the length of the leg
					 adjacent to the angle to the length of the hypotenuse.
"Counterexample"
means an example to show that
					 a given statement is false. Example: to disprove the statement "All right
					 triangles are isosceles," all one needs to do is produce a right triangle that
					 is scalene.
"Counting number"
means a number used in
					 counting objects (i.e. a number from the set {1, 2, 3, 4, 5, ... }). See also
					 Natural number.
"Counting on"
means a strategy for finding the
					 number of objects in a group without having to count every member of the group.
					 Example: if a stack of books is known to have 8 books and 3 more books are
					 added to the top, it is not necessary to count the stack all over again; one
					 can find the total by counting on - pointing to the top book and saying
					 "eight," following this with, "nine, ten, eleven. There are eleven books
					 now."
"Continuous graph (of data)"
means a graph is
					 continuous if it contains intervals of data points.
"Decimal expansion"
means the resulting
					 decimal number found when dividing a rational number in fraction form. May
					 include terminating and repeating decimals.
"Decimal fraction"
means a fraction (as 0.25 =
					 25/100 or 0.025) or mixed number (as 3.025 = 325/1000) in which the denominator
					 is a power of ten, usually expressed by the use of the decimal point.
"Decimal number"
means any real number
					 expressed in base 10 notations, such as 2.673.
"Decompose numbers"
means, given a number,
					 identify pairs, triples, etc. of numbers that combine to form the given
					 number.
"Decompose shapes"
means, given a geometric
					 shape, identify geometric shapes that meet without overlap to form the given
					 shape.
"Deductive reasoning"
means, informally, the
					 process of using known facts and relationships to derive new facts and
					 relationships.
"Dependent events"
means events that influence
					 each other. If one of the events occurs, it changes the probability of the
					 other event.
"Dependent variable"
means the output of a
					 function. The quantity that is affected when the input is changed.
"Digit"
means any of the Arabic numerals 1 to
					 9 and usually the symbol 0; one of the elements that combine to form numbers in
					 a system other than the decimal system.
"Digital"
means having to do with data that is
					 represented in the form of numerical digits; providing a readout in numerical
					 digits (e.g. a digital watch).
"Dilation"
means a transformation that moves
					 each point along the ray through the point emanating from a fixed center, and
					 multiplies distances from the center by a common scale factor.
"Discrete graph (of data)"
means a graph is
					 discrete if it consists of separated data points and contains no intervals of
					 data.
"Divisible"
means a non-zero integer p is said
					 to be divisible by a non-zero integer q if there exists an integer r such that
					 qxr = p.
"Domain of a relation"
means the set of all
					 the first elements or x-coordinates of a relation.
"Dot plot"
See line plot.
"Equivalent expressions"
means two expressions
					 (numerical or otherwise) are said to be equivalent if one can be obtained from
					 the other using the properties of operations, such as the commutative,
					 associative and distributive properties, as well as by representing numbers in
					 the expressions in different but equivalent forms.
"Equivalent fractions"
means two fractions a/b
					 and c/d are said to be equivalent if there exists a non-zero number n such that
					 na/nb=c/d. Equivalent fractions represent the same amount by changing both the
					 size and the number of parts of a given fraction.
"Equivalent ratios"
means two ratios a:b and
					 c:d are equivalent if there is a non-zero number k such that ka=c and kb=d.
					 Equivalent ratios can be shown to have the same unit rate.
"Expanded form"
means a multi-digit number is
					 expressed in expanded form when it is written as a sum of single-digit
					 multiples of powers of ten. Example: 643 = 600 + 40 + 3.
"Expected value"
means, for a random variable,
					 the weighted average of its possible values, with weights given by their
					 respective probabilities.
"Experimental probability"
means when trials
					 of a probability experiment are run and data is collected, the experimental
					 probability of a desired outcome is the relative frequency of that outcome as a
					 ratio of the number of such outcomes to the total number of outcomes. Example:
					 if a coin is flipped 100 times, and heads comes up 45 times, then the
					 experimental probability of heads is 45/100 or 0.45 (the theoretical
					 probability is 0.50, and if the number of trials is increased the experimental
					 probability will get closer and closer to 0.50).
"Exponent (Integer)"
means a negative integer
					 exponent denotes the reciprocal of the base raised to the corresponding
					 opposite integer. Thus x-2 =
					 1/x2.
"Exponent (Whole Number)"
means the number
					 that indicates how many times the base is used as a factor (e.g. in
					 43 = 4 x 4 x 4 = 64, the exponent is 3, indicating
					 that 4 is repeated as a factor three times).
"Exponential function"
means an exponential
					 function with base b is defined by 7 = bxt where b
					 > 0 and b is not equal to 1.
"Expression"
means a mathematical phrase that
					 combines operations, numbers, and/or variables (e.g.
					 32÷ a).
"Exterior angles (of a polygon)"
means the
					 supplement of an interior angle or a polygon that is formed by extending one of
					 the line segments determining the interior angle at a given vertex.
"Extraneous solution"
means a solution, such
					 as that to an equation, that emerges from the process of solving the problem
					 but is not a valid solution to the original problem.
"Fluency"
means easily and accurately
					 responding to calculations (Van de Walle). See Table 4.
"First quartile"
means, for a data set with
					 median M, the first quartile is the median of the data values less than M.
					 Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the first
					 quartile is 6. See also median, third quartile, interquartile range. rational
					 number and complex fraction.
"Fraction"
means a number expressible in the
					 form a/b where a is a whole number and b is a positive whole number (the word
					 fraction in these standards always refers to a non-negative number). See also
					 rational number and complex fraction.
"Frequency table"
means a representation of
					 data in which categories are listed in one column (row) of a table and the
					 number of occurrences (frequency) of each category is indicated in another
					 column (row).
"Function"
means a rule that assigns to every
					 element of one set (the domain) exactly one element of another set (the range).
					 A function is often thought of as an "input/output" rule, as in every input
					 determines an output (usually according to mathematical operations performed on
					 the input).
"Function machine"
means an input/output model
					 (often made with milk cartons, boxes, or drawn on the board) to show one number
					 entering and a different number exiting. Students guess the rule that produced
					 the second number (e.g. enter 3, exit 5, rule: add 2).
"Function notation"
means a notation that
					 describes a function. For a function f, when x is a member of the domain, the
					 symbol (x) denotes the corresponding member of the range (e.g. f(x) = x +
					 3).
"Geometric sequence (progression)"
means an
					 ordered list of numbers that has a common ratio between consecutive terms (e.g.
					 2, 6, 18, 54).
"Histogram"
means a type of bar graph used to
					 display the distribution of measurement data across a continuous range.
"Hypotenuse"
means the longest side of a right
					 triangle, necessarily opposite to the right angle. The other sides are called
					 the legs of the right triangle (longer and shorter if applicable).
"HL (Hypotenuse-Leg) congruence"
means, if two
					 right triangles have hypotenuse and one corresponding leg congruent, then the
					 triangles are congruent.
"Identity property of 0"
See Table 1
"Imaginary number"
means a number i is
					 considered imaginary if i2 = -1. See also complex
					 number.
"Independent events"
means events that do not
					 influence one another. Each event occurs without changing the probability of
					 the other event. Specifically, two events and are independent if (A AND B) =
					 P(A) * P(B).
"Independent variable"
means the input of a
					 function. The quantity whose value is changed to affect the output.
"Independently combined probability models"
means two probability models are said to be combined independently if the
					 probability of each ordered pair in the combined model equals the product of
					 the original probabilities of the two individual outcomes in the ordered
					 pair.
"Inductive reasoning"
means, informally, the
					 process of examining patterns and making conclusions based on observed
					 patterns.
"Input/Output table"
means usually a
					 two-column table (or two-row table) with one column (row) listing the inputs of
					 a rule and the other column (row) listing the corresponding outputs for each
					 input.
"Integer"
means the set of numbers that
					 contains the whole numbers and their additive inverses (opposites) (i.e. {...,
					 -2, -1, 0, 1, 2, 3, ....}).
"Intercepts (of a graph)"
means,
					 geometrically, where a graph intersects an axis in a Cartesian plane.
"Interquartile range"
means a measure of
					 variation in a set of numerical data, the interquartile range is the distance
					 between the first and third quartiles of the data set. Example: For the data
					 set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 - 6 =
					 9. See also first quartile, third quartile.
"Intersection (of sets)"
means for two sets A
					 and B, the intersection is the set of all elements that are members of both
					 sets simultaneously.
"Inverse function"
means a function (f(x)) = x
					 and f(g(x)) = x is said to be an inverse function for f. The inverse of f is
					 often denoted by f-1.
"Inverse operations"
means operations that
					 undo each other (e.g. addition and subtraction are inverse operations;
					 multiplication and division are inverse operations).
"Irrational number"
means numbers that are not
					 rational. Irrational numbers have nonterminating, nonrepeating decimal
					 expansions (e.g. square root of 2, pi).
"Length (of a segment)"
means the length of a
					 (straight) line segment is a measurement of the distance from one endpoint of
					 the object to the other. Once a unit of length is specified, the length of a
					 segment is found by placing such units end-to-end without gaps or overlaps and
					 counting how many such units are used.
"Line Plot"
means a representation of data in
					 which categories are listed underneath points on a number line, and in which
					 the number of occurrences (frequency) of each category is represented by a
					 corresponding number of marks (X's, dots) above each category's point.
"Linear association"
means a set of bivariate
					 data exhibits a linear association if a scatter plot of the data can be
					 well-approximated by a line.
"Linear equation"
means any equation that can
					 be written in the form Ax + By + C = 0 where A and B cannot both be 0. The
					 graph of such an equation is a line.
"Linear function"
means a function f is linear
					 if it can be written in the form (x) = mx + b.
"Literal equation"
means an equation involving
					 multiple variables and numbers, often that cannot be solved for an explicit
					 numerical value of any of the individual variables. In such a case one may
					 solve for one variable as an expression of the others.
"Logarithm"
means the exponent that indicates
					 the power to which a base number is raised to produce a given number. Example:
					 the logarithm of 100 to the base 10 is 2.
"Logarithmic function"
means any function in
					 which an independent variable appears in the form of a logarithm; they are the
					 inverse functions of exponential functions.
"Manipulatives"
means concrete materials (e.g.
					 buttons, beans, egg and milk cartons, counters, attribute and pattern blocks,
					 interlocking cubes, base-10 blocks, geometric models, geo-boards, fractions
					 pieces, rulers, balances, spinners, dot paper) used to represent mathematical
					 concepts, operations, and relationships.
"Matrix (pl. matrices)"
means a rectangular
					 array of numbers or variables.
"Mean (arithmetic)"
means a measure of center
					 in a set of numerical data, computed by adding the values in a list and then
					 dividing by the number of values in the list. Example: For the data set {1, 3,
					 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.
"Mean absolute deviation"
means a measure of
					 variation in a set of numerical data, computed by adding the distances between
					 each data value and the mean, then dividing by the number of data values.
					 Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean
					 absolute deviation is 20.
"Measure of central tendency"
means a
					 determination of the center of a data set meant to describe a set of data. See
					 also mean, median, mode, and percentile.
"Measure of spread (or variable)"
means a
					 determination of how much the data in a set deviates from a measure of center.
					 The most frequently used measure is standard deviation. See also standard
					 deviation, range.
"Median"
means a measure of center in a set of
					 numerical data. The median of a list of values is the value appearing at the
					 center of a sorted version of the list; or the mean of the two central values,
					 if the list contains an even number of values. Example: For the data set {2, 3,
					 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.
"Midline"
means, in the graph of a sine or
					 cosine function, the horizontal line halfway between its maximum and minimum
					 values.
"Mixed number"
means a number written in the
					 form A b/c, which is a shorthand way to represent the quantity A + b/c. A mixed
					 number may be written as a fraction greater than 1 by writing A b/c = A + b/c =
					 Ac/c + b/c = Ac+b/c.
"Model"
means a mathematical representation
					 (e.g. number, graph, matrix, equation(s), geometric figure) for real-world or
					 mathematical objects, properties, actions, or relationships.
"Modulus of a complex number"
means the
					 distance between a complex number and the origin on the complex plane.
"Multiplication and division within 100"
means
					 multiplication or division of two whole numbers with whole number answers, and
					 with product or dividend in the range 0-100. Example: 72 ÷ 8 = 9.
"Multiplication counting principle"
means if k
					 actions can be taken in N1, N2,
					 ...., Nk different ways, then there are a total of
					 N1, N2, ....
					 Nk different ways to perform those actions in
					 sequence.
"Multiplicative inverses"
means two numbers
					 whose product is 1 are multiplicative inverses of one another. Example 3/4 and
					 4/3 are multiplicative inverses of one another.
"Natural number"
means a number used in
					 counting objects (i.e. a number from the set {1, 2, 3, 4, 5, .....}). See also
					 Counting number.
"Net"
means a two-dimensional representation
					 of a three-dimensional figure constructed of polygons, such that if folds were
					 made on certain edges of the net and appropriate sides were "glued" together,
					 the resulting figure would be the original three-dimensional figure.
"Network"
means a figure consisting of
					 vertices and edges that shows how objects are connected; a collection of points
					 (vertices), with certain connections (edges) between them.
"Non-linear association"
means the
					 relationship between two variables is nonlinear if the change in the second is
					 not simply proportional to the change in the first, independent of the value of
					 the first variable.
"Nonstandard measurement"
means a measurement
					 determined by the use of nonstandard units such as hands, paper clips, beans,
					 cotton balls, etc.
"Number line diagram"
means a diagram of the
					 number line used to represent numbers and support reasoning about them. In a
					 number line diagram for measurement quantities, the interval from 0 to 1 on the
					 diagram represents the unit of measure for the quantity.
"Number sense"
means the understanding of
					 number size (relative magnitude), number representations, number operations,
					 referents for quantities and measurement used in everyday situations,
					 etc.
"Numeral"
means a symbol or mark used to
					 represent a number.
"One-to-one correspondence"
means a matching
					 of the elements of two sets such that each element from the first set is
					 matched with one and only one element of the second set, and such that each
					 element of the second set is matched with some element of the first. Early
					 grades students use this to establish the concept of cardinal use of numbers
					 (as in "5" can represent any collection of five objects; if I can match the
					 fingers on one hand to all the elements of a given set then that set has "5"
					 objects.)
"Operation"
means a general term for any one
					 of addition, subtraction, multiplication, and division.
"Order of operations"
means convention adopted
					 to perform mathematical operations in a consistent order.
(A)
Step 1.
Perform all
				  operations inside grouping symbols, and/or above and below a fraction bar in
				  the order specified in Steps 2, 3, and 4.
(B)
Step 2.
Find the value of
				  any powers or roots;
(C)
Step
				  3.
Multiply, including division, from left to right;
(D)
Step 4.
Add, including
				  subtraction, from left to right.
"Ordinal number"
means a number designating
					 the place (as first, second, or third) occupied by an item in an ordered
					 sequence.
"Outlier"
means a data point that is far
					 outside a representative range of the data set. Example: once the
					 inter-quartile range (IQR) is computed, one might calculate the interval of
					 1.5x IQR above the median and 1.5x IQR below the median and decide that any
					 data point that lies outside this range is considered an outlier.
"Parallel lines"
means lines that do not
					 intersect. Distinct lines can be shown to be parallel if and only if they have
					 equal slopes.
"Partition"
means a process of dividing an
					 object into parts or a set into (smaller) subsets.
"Pascal's triangle"
means a triangular
					 arrangement of numbers in which each row starts and ends with 1, and each other
					 number is the sum of the two numbers above it.
"Piecewise function"
means a function that is
					 defined differently on different intervals.
"Percent rate of change"
means a rate of
					 change expressed as a percent. Example: if a population grows from 50 to 55 in
					 a year, it grows by 5/50 = 10% per year.
"Perfect square"
means a number that is a
					 whole number squared, that is, a number that can be expressed as
					 n2 for n a whole number.
"Perimeter (of a polygon)"
means the total
					 length of all the edges of a polygon. Often, perimeter is thought of as the
					 distance around an object, traversed once along the edges starting from one
					 vertex and ending at the same vertex.
"Periodic phenomena"
means events that recur
					 over regular intervals, for example, ocean tides, machine cycles.
"Perpendicular lines"
means lines that
					 intersect such that all four angles that are created are congruent. Two lines
					 can be shown to be perpendicular if and only if the product of their slopes is
					 -1.
"Pi ([PI])"
means the irrational number that
					 is derived by finding the ratio of the circumference to the diameter of
					 circles. That this ratio is constant and an irrational number are important
					 concepts and challenging to prove, so they are often arrived at empirically by
					 students.
"Picture graph"
means a graph that uses
					 pictures to show and compare information.
"Place value"
means the concept that the order
					 in which digits are written in the base-10 number system determines the value
					 of that digit. Thus, in the number 245, the digit 2 is in the "hundreds place,"
					 indicating that the value of that particular 2 is actually 2 hundreds or
					 200.
"Polygon"
means a closed, two-dimensional
					 figure comprised of line segments connected end-to-end, and such that no two
					 segments cross each other. The segments are typically called sides or edges,
					 and the common endpoints of adjacent segments are called vertices (sing.
					 vertex). The space within the polygon is called its interior. The angles formed
					 by adjacent sides that lie in the interior of a polygon are called its interior
					 angles.
"Polynomial"
means the sum or difference of
					 terms which have variables raised to positive integer powers and which have
					 coefficients that may be real or complex. The following are all polynomials:
					 5x3 - 2x2 + x - 13,
					 x2y3 + xy, and (1 +
					 i)a2 + ib2.
"Polynomial function"
means any function whose
					 output is given by a polynomial expression of the input.
"Postulate"
means a statement accepted as true
					 without proof.
"Prime factorization"
means a number written
					 as the product of all its prime factors.
"Prime number"
means a whole number greater
					 than 1 whose only factors are 1 and itself.
"Probability distribution"
means the set of
					 possible values of a random variable with a probability assigned to
					 each.
"Properties of equality"
See Table 2.
"Properties of inequality"
See Table 2.
"Properties of operations"
See Table 1.
"Probability"
means the study and measure of
					 the likelihood of an event happening.
"Probability model"
means a probability model
					 is used to assign probabilities to outcomes of a chance process by examining
					 the nature of the process. The set of all outcomes is called the sample space,
					 and their probabilities sum to 1. See also uniform probability model.
"Proof"
means a method of constructing a valid
					 argument using deductive reasoning.
"Proportion"
means an equation that states
					 that two ratios are equivalent (e.g. 4/8 = ½ or 4 : 8 = 1 : 2).
"Pyramid"
means a three-dimensional shape
					 constructed from a polygon (called the base) and triangles that have one edge
					 matching the edges of the base and such that the triangles share a common
					 vortex.
"Pythagorean theorem"
means for any right
					 triangle, the sum of the squares of the lengths of the legs equals the square
					 of the lengths of the hypotenuse.
"Quadratic equation"
means an equation that is
					 equivalent to ax2 + bx + c = 0, where a [NOT EQUAL]
					 0.
"Quadratic expression"
means an expression
					 that contains variables raised to whole number exponents no higher than
					 2.
"Quadratic function"
means a function that can
					 be represented by an equation of the form y = ax2 +
					 bx + c, where a, b, and c are arbitrary, but fixed, numbers and a [NOT EQUAL]
					 0. The graph of this function is a parabola.
"Quadratic polynomial"
means a polynomial
					 where the highest degree of any of its terms is 2.
"Quadrilateral"
means a polygon with 4 sides.
					 Important classes of quadrilaterals:
(A)
Trapezoid
A quadrilateral in
				  which at least two sides are parallel.
(B)
Parallelogram
A
				  quadrilateral in which opposite sides are parallel.
(C)
Rhombus
A parallelogram in
				  which opposite sides are congruent (have the same length).
(D)
Rectangle
A parallelogram
				  that has at least one right interior angle.
(E)
Square
A rectangle that has
				  all sides congruent.
(F)
Kite
A quadrilateral that has two pairs of congruent adjacent
				  sides.
"Quotient"
means the result of a division
					 problem. Also, given whole numbers n and m with n>m, if we write n=mq+r with
					 0=r<m, then say q is the quotient and r is the remainder.
"Radical"
means the v symbol, which is used to
					 indicate square roots or nth roots.
"Random sampling"
means a small group of
					 people or objects chosen from a larger group or population by a process giving
					 equal chance of selection to all possible people or objects.
"Random variable"
means an assignment of a
					 numerical value to each outcome in a sample space.
"Range (of a relation)"
means the set of all
					 the second elements or y-coordinates of a relation is called the range.
"Range (of a data set)"
means the difference
					 between the maximum and minimum values of a data set, a measure of the spread
					 of the data.
"Ratio"
means a relationship between
					 quantities such that for every a units of one quantity there are b units of the
					 other. A ratio is often denoted by a:b, and read "a to b."
"Rational expression"
means a quotient of two
					 polynomials with a non-zero denominator.
"Rational number"
means a number expressible
					 in the form a/b or -a/b for some fraction a/b. The rational numbers include the
					 integers.
"Real number"
means an element of the set of
					 numbers consisting of all rational and all irrational numbers.
"Rectangular array"
means an arrangement of
					 mathematical elements into rows and columns.
"Rectangular prism"
means a three-dimensional
					 object constructed from three pairs of parallel rectangles (called faces in
					 this context) that share common edges so as to form an enclosed space and such
					 that opposite rectangles are congruent. The vertices of the rectangles are the
					 vertices of the prism, and the sides of the rectangles are called edges. A cube
					 is a rectangular prism in which each fact is a square of the same size as the
					 other faces.
"Rectilinear figure"
means a polygon, all
					 angles of which are right angles.
"Recursive pattern (or sequence)"
means
					 patterns in which each number is found from the previous number by repeating a
					 process (e.g. Fibonacci numbers).
"Reflection"
means a type of transformation
					 that flips points about a line, called the line of reflection. Taken together,
					 the image and the pre-image have the line of reflection as a line of
					 symmetry.
"Real numbers (set of)"
means the set of all
					 rational and irrational numbers.
"Relation"
means a collection of ordered pairs
					 of real numbers.
"Relative frequency"
means the empirical
					 counterpart of probability. If an event occurs N1
					 times in N trials, its relative frequency is
					 N1/N.
"Remainder Theorem"
means if f(x) is a
					 polynomial in x then the remainder on dividing f(x) by x - a is f(a).
"Repeating decimal"
means a decimal in which,
					 after a certain point, a particular digit or sequence of digits repeats itself
					 indefinitely. See also terminating decimal.
"Right angle"
means, informally, an angle
					 whose measure is 90 degrees. Formally, if two congruent copies of a given angle
					 are supplementary (that is, they form a straight line when one matches an edge
					 of one copy with one edge of the other), then the given angle is said to be a
					 right angle. (We can then define the measure of this angle to be 90 degrees and
					 measure other angles in terms of a right angle.)
"Rigid motion"
means a transformation of
					 points in space consisting of a sequence of one or more translations,
					 reflections, and/or rotations. Rigid motions are here assumed to preserve
					 distances and angle measures.
"Rotation"
means a type of transformation that
					 turns a figure about a fixed point, called the center of rotation.
"SAS congruence (Side-Angle-Side congruence)"
means if in two triangles two corresponding sides and the angles formed by
					 those sides are congruent, then the triangles are congruent.
"SSS congruence (Side-Side-Side congruence)"
means if two triangles have corresponding sides that are congruent, then the
					 triangles are congruent.
"Sample space"
means in a probability model
					 for a random process, a list of the individual outcomes that are to be
					 considered.
"Scale factor"
means for similar shapes, the
					 common ratio of corresponding side lengths is called the scale factor.
					 Informally, it is the multiplicative amount by which the lengths of one shape
					 are "blown up" or "shrunk down" to obtain the other shape to which it is
					 similar.
"Scatter plot"
means a graph in the coordinate
					 plane representing a set of bivariate data. Example: the heights and weights of
					 a group of people could be displayed on a scatter plot.
"Scientific notation"
means a widely used
					 floating-point system in which numbers are expressed as products consisting of
					 a number between 1 and 10 multiplied by an appropriate power of 10 (e.g. 562 -
					 5.62 x 102).
"Secant (of a circle)"
means a line that
					 intersects a circle at two points.
"Sequence"
means a set of elements ordered so
					 that they can be labeled with consecutive positive integers starting with 1
					 (e.g. 1, 3, 9, 27, 81). In this sequence, 1 is the first term, 3 is the second
					 term, 9 is the third term, etc.
"Set model (for fractions)"
means the use of a
					 discrete set of objects to represent the whole and a subset of those objects to
					 represent a fraction. Example: since 3 of the 15 students in class are wearing
					 blue shirts, 3/15 of the students are wearing blue shirts.
"Significant figures (digits)"
means digits
					 included in a measurement that purposely indicate the precision of the
					 measurement. Example: writing a measurement at 3.50 seconds instead of 3.5
					 seconds indicates that the measurement is accurate to the hundredths
					 place.
"Similar (shapes)"
means two geometric shapes
					 are said to be similar (to each other) if one can be mapped onto the other by a
					 sequence of similarity transformations.
"Similarity transformation"
means a rigid
					 motion followed by a dilation.
"Simultaneous equations"
means two or more
					 equations containing common variables.
"Sine (of an acute angle)"
means the
					 trigonometric function that for an acute angle is the ratio between the leg
					 opposite the angle when the angle is considered part of a right triangle and
					 the hypotenuse.
"Slope (of a line)"
means a measure of the
					 steepness of a line in a Cartesian plane, found by determining the constant
					 change in the y-coordinate per 1-unit change in the x-coordinate.
"Spatial sense"
means the ability to build and
					 manipulate mental representations of 2- and 3-dimensional objects and
					 ideas.
"Standard deviation"
means a measurement of
					 how much each value in the data differs from the mean of the data.
"Statistics"
means the study of data.
"Stem-and-leaf plot"
means a frequency
					 distribution made by arranging data in the following way (e.g. student scores
					 on a test were 96, 87, 77, 93, 85, 85, and 75 would be displayed as: 9]6,3;
					 8]7,5,5; 7]7,5).
"Subitize"
means instantly knowing "how many."
					 Recognizing a number without using other mathematical processes.
"Substitution"
means the substitution of one
					 expression for an equivalent expression, used when rewriting expressions as
					 equivalent ones or solving equations. It is based on the transitive property of
					 equality, which states, "If A=B, and B=C, then A=C."
"Summary statistics"
means a collection of
					 statistics () that describe the data set. Example: the range, mean, and
					 standard deviation of a given data set indicate certain features of the data
					 set and hence are summary statistics.
"Supplementary angles"
means two angles whose
					 measures have a sum of 180 degrees.
"Supposition (act of supposing)"
means making
					 a statement or assumption without proof.
"Surface area (of a rectangular prism)"
means
					 the total measure of the area of the faces of a rectangular prism.
					 Equivalently, the total area of a net for the prism.
"Tangent"
means meeting a curve or surface in
					 a single point if a sufficiently small interval is considered; (of an acute
					 angle) the trigonometric function that, for an acute angle, is the ratio
					 between the leg opposite the angle and the leg adjacent to the angle when the
					 angle is considered part of a right triangle.
"Tape diagram"
means a drawing that looks like
					 a segment of tape, used to illustrate number relationships. Also known as a
					 strip diagram, bar model, fraction strip, or length model.
"Terminating decimal"
means a decimal is
					 called terminating if its repeating digit is 0. Every terminating decimal is
					 the decimal form of some rational number. See also repeating decimal.
"Third quartile"
means, for a data set with
					 median M, the third quartile is the median of the data values greater than M.
					 Examples: for the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the third
					 quartile is 15. See also median, first quartile, interquartile range.
"Transformation"
means a prescription, or
					 rule, that sets up a one-to-one correspondence between the points in a
					 geometric object (the pre-image) and the points in another geometric object
					 (the image). Reflections, rotations, translations, and dilations are particular
					 examples of transformations.
"Transitivity principle for indirect
					 measurement"
means, if the length of object A is greater than the length
					 of object B, and the length of object B is greater than the length of object C,
					 then the length of object A is greater than the length of object C. This
					 principle applies to measurement of other quantities as well.
"Translation"
means a type of transformation
					 that moves every point in a graph or geometric figure by the same distance in
					 the same direction without a change in orientation or size.
"Transversal line"
means a line that crosses
					 two or more other lines is called a transversal.
"Triangle"
means a polygon with three sides.
					 Important classes of triangles:
(A)
Equilateral triangle
a triangle with all sides
				  congruent.
(B)
Right
				  triangle
contains an interior angle that is a right angle.
(C)
Scalene triangle
a triangle
				  with no side congruent to another.
(D)
Isosceles triangle
a
				  triangle with two congruent sides.
"Trigonometric function"
means trigonometric
					 functions (sine, cosine, tangent, and their reciprocals) are commonly defined
					 as ratios of two sides of a right triangle.
"Trigonometry"
means the study of
					 trigonometric functions.
"Uniform probability model"
means a
					 probability model which assigns equal probability to all outcomes. See also
					 probability model.
"Unit fraction"
means a fraction with a
					 numerator of 1, such as 1/3 or 1/5.
"Unit of measurement"
means, when measuring a
					 given attribute of an object, a "unit" is defined in terms of which all other
					 measurements are determined. That a given unit is fixed is a concept to be
					 learned by young students (e.g. we wouldn't measure the length of a room in
					 hands because your hand is different from mine, and we wouldn't measure the
					 length of a room using cm and inches at the same time).
"Union (of sets)"
means, for two sets A and B,
					 the union A[UNION]B is the set of all elements that are members of one or both
					 of the sets.
"Variable"
means a quantity that can change or
					 that may take on different values; a symbol (often a letter of the alphabet,
					 sometimes including the Greek alphabet) that represents a number in a
					 mathematical expression.
"Venn diagram"
means a data display in which
					 (typically) circles are used to represent categories and in which the
					 overlapping of two (or more) circles indicates data that lies in each category
					 in the overlap.
"Visual fraction model"
means a diagram or
					 representation to show the relative size of a fraction, for example, a tape
					 diagram, number line diagram, or area model.
"Volume (of a 3D object)"
means a measurement
					 of the amount of space within a closed three-dimensional shape. Volume is often
					 measured in terms of "cubic units," in which 1 cubic unit is the amount of
					 space within a cube that measures 1 unit by 1 unit by 1 unit (for a given unit
					 of length). Example: volume may be measured in "cubic centimeters," 1 cubic
					 centimeter being the amount of space within a 1cm by 1cm by 1cm cube. Note that
					 since one can measure the volume of a liquid by placing said liquid into a 3D
					 shape, volume has historically been measure in various units such as cups,
					 fluid ounces, and liters. Not that 1 cubic centimeter is equal to 1 milliliter,
					 one way to connect such fluid units to cubic units.
"Whole numbers"
means the numbers 0, 1, 2, 3,
					 etc.