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Oklahoma Administrative Code (Last Updated: March 11, 2021) |
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TITLE 210. State Department of Education |
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Chapter 15. Curriculum and Instruction |
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Subchapter 3. Oklahoma Academic Standards |
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Part 7. MATHEMATICS |
SECTION 210:15-3-55. Definitions
Latest version.
- The following words and terms, when used in this Part, shall have the following meaning, unless the context clearly indicates otherwise:"AA similarity" or "Angle-Angle similarity" means if two triangles have two pairs of corresponding angles that are congruent, then the triangles are similar."ASA congruence" or "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" 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" means a sequence in which successive terms exhibit a common difference. Also known as "arithmetic progression"."Array" 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 Appendix A."Associative property of multiplication" See Appendix A."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 = 2πr where r is the radius and π 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 = πr where r is the radius and π 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. 3x has coefficient 3)."Commutative property" See Appendix A."Complement" means, in the context of a set, that 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 is not equal to 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" means, in a right triangle, 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" 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 = 3 25/1000) 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" 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" means "line plot"; as defined in this section."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 xraised to the power of negative 2 = 1/x squared."Exponent (Whole Number)" means the number that indicates how many times the base is used as a factor (e.g. in 4 cubed = 4 × 4 × 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. 3 ÷ a)."Exterior angles" means the supplement of an interior angle of 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. See Appendix D."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", and "interquartile range" as defined in this section."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" means an ordered list of numbers that has a common ratio between consecutive terms (e.g. 2, 6, 18, 54). Also known as "geometric progression"."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 Appendix A."Imaginary number" means a number i is considered imaginary if i = -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) x 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" 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" means, in the context of a straight line segment, 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" means a rectangular array of numbers or variables. The plural is "matrices"."Mean" or "Arithmetic mean" 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" 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 n for n a whole number."Perimeter" 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 (π)" 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: 5x - 2x + x - 13, xy + xy, and (1 + i)a + ib."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 Appendix B."Properties of inequality" See Appendix B."Properties of operations" See Appendix A."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 ax + bx + c = 0, where a is not equal to 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 = ax + bx + c, where a, b, and c are arbitrary, but fixed, numbers and a is not equal to 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 √ 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 "Recursive 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" 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 N times in N trials, its relative frequency is N/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" or "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" or "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 × 10)."Secant" 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" means, in the context of fractions, 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" 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" 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" 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" 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" means making a statement or assumption without proof."Surface area" means, in the context of rectangular prisms, 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, "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" 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.