Mathematics Curriculum Framework - November 2000
Appendix III: Glossary
Algorithm A finite set of steps for completing a procedure, e.g., long division. (H)
Analog Having to do with data represented by continuous variables, e.g., a clock with hour, minute, and second hands. (W)
Analytic geometry The branch of mathematics that uses functions and relations to study geometric phenomena, e.g., the description of ellipses and other conic sections in the coordinate plane by quadratic equations.
Box-and-whisker plot A method for displaying the median, quartiles, and extremes of a set of data, using the number line. (H)
Calculus The mathematics of change and motion. The main concepts of calculus are limits, instantaneous rates of change, and areas enclosed by curves.
Capacity 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.
Capture-recapture experiment A type of experiment used to estimate a population. On the first day a certain number, M, of the population, N, is captured and tagged or marked. On the second day another sample, n, of the population is captured including the recapture of some R of those already tagged. The population can be estimated using the formula
Cardinal number A number (as 1, 5, 15) that is used in simple counting and that indicates how many elements there are in a set.
Cartesian plane or Euclidean plane A coordinate plane with perpendicular coordinate axes.
Closure property A set of numbers, such as the integers, is closed under a particular operation if performing the operation on numbers in the set results in another number in that set. For example, the set of non-zero integers is closed under multiplication, but is not closed under division: the product of two non-zero integers is again a non-zero integer, but their quotient need not be an integer.
Complex number A number that can be written in the form a ++ bi where a and b are real numbers and
i = √-1.
Convenience (haphazard) sampling The collection of data from readily available sources, without emphasis on methodological rigor.
Coordinate plane A plane in which two coordinate axes are specified, i.e., two intersecting directed straight lines, usually perpendicular to each other, and usually called the x-axis and y-axis. Every point in a coordinate plane can be described uniquely by an ordered pair of numbers, the coordinates of the point with respect to the coordinate axes.
Counting number A number used in counting objects, i.e., a number from the set 1, 2, 3, 4, 5,....
Decimal number Any real number expressed in base 10 notation, such as 2.673.
Deductive reasoning A type of reasoning wherein the conclusion about particulars follows necessarily from general or universal premises. (W)
Digit a) Any of the Arabic numerals 1 to 9 and usually the symbol 0; b) One of the elements that combine to form numbers in a system other than the decimal system.
Digital 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 A type of transformation of the plane that fixes a point C (the center of the dilation) and maps any other point P to the point P' characterized as follows: the segment CP' has the same direction as the segment CP, and has length k times the length of the segment CP, where k is a positive constant (the scale factor of the dilation).
Discrete mathematics The branch of mathematics that includes combinatorics, recursion, Boolean algebra, set theory, and graph theory.
Dot product For vectors A = <Xa, Ya> and B = <Xb, Yb>, the dot product A•B = (xa)(xb ) + (ya) (yb).
Expanded notation A way of representing a number that shows the sum of each digit multiplied by the appropriate positive power of ten and the units digit, e.g., 3451 as 3 x 1000 + 4 x 100 + 5 x 10 + 1 or as 3 x 103+ 4 x 102 + 5 x 10 + 1.
Exponent 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.
Fibonacci numbers The sequence of numbers beginning with 1, 1, in which each number that follows is the sum of the previous two numbers, i.e., 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....
Function A mathematical relation that associates each object in a set with exactly one value.
Fundamental Counting Principle If event M can occur in m ways, and after it has occurred, event N can occur in n ways, then event M followed by event N can occur m·n ways.
Fractal A curve or shape so irregular that its dimension (according to the technical definition of dimension) is a fraction, rather than an integer. Many interesting examples of fractals have the property of being self-similar, in the sense that portions of the fractal are similar in shape to magnified parts of itself at arbitrarily high rates of magnification.
Geometric or figural pattern A sequence of symbols or geometric figures.
Geometric sequence (progression) An ordered list of numbers that has a common ratio between consecutive terms, e.g., 2, 6, 18, 54....(H)
Inductive reasoning a) The type of reasoning that uses inference to reach a generalized conclusion from particular instances; b) In mathematics, demonstration of the validity of a law concerning all the positive integers by proving that it holds for the integer 1 and that if it holds for an arbitrarily chosen positive integer k it must hold for the integer k+1; also called mathematical induction. (W)
Integer A number that is either a whole number or the negative of a whole number.
Irrational number A number that cannot be expressed as a quotient of two integers, e.g., √2. It can be shown that a number is irrational if and only if it cannot be written as a repeating or terminating decimal.
Iterative pattern or sequence A sequence or pattern formed by repeating the same procedure. For example, the Fibonacci sequence.
Line graph A set of data points on an X-Y grid, possibly with consecutive points connected by line segments.
Line of best fit A straight line drawn through or near to as many data points as possible on a scatterplot.
Line plot A number line with dots or other marks above it to show the number of times an event occurs. (H)
Linear equation 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 programming A mathematical method of solving practical problems (as the allocation of resources) by means of linear functions where the variables involved are subject to constraints. (W)
Matrix, pl. matrices A rectangular array of numbers or variables.
Measure of central tendency Either the mean, median, or mode of a distribution, i.e., one of the possible notions of an average.
Network a) A figure consisting of vertices and edges that shows how objects are connected, b) A collection of points (vertices), with certain connections (edges) between them.
Numeral A symbol or mark used to represent a number.
Numeric pattern A pattern composed of numerals.
Order of Operations 1. Do all of the operations inside parentheses, and/or above and below a fraction bar in the proper order, 2. Find the value of any powers or roots, 3. Multiply and divide from left to right, 4. Add and subtract from left to right. (H)
Ordinal number A number designating the place (as first, second, or third) occupied by an item in an ordered sequence. (W)
Partition A process of dividing an object into parts.
Pascal's triangle 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. (H)
| || || || || ||1|| || || || || |
| || || || ||1|| ||1|| || || || |
| || || ||1|| ||2|| ||1|| || || |
| || ||1|| ||3|| ||3|| ||1|| || |
| ||1|| ||4|| ||6|| ||4|| ||1|| |
|1|| ||5|| ||10|| ||10|| ||5|| ||1|
Pictogram (pictograph) A graph that uses pictures to show and compare information. (H)
Probability A number between zero and one that describes the likelihood that a given event will take place. For example, the probability of throwing a six with a single throw of one die is 1/6, and the probability of throwing two sixes with a single throw of two dice is 1/36.
Proof A method of constructing a valid argument, using deductive reasoning.
Proportion An equation that states that two ratios are equivalent, e.g., 4/8 = 1/2 or 4 : 8 = 1 : 2.
Pythagorean theorem For any right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse.
Random sampling A smaller 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. (H)
Random variable A variable that is itself a function of the result of a statistical experiment in which each outcome has a definite probability of occurrence; also called variate. (W)
Ratio A comparison of two numbers or quantities, e.g., 4 to 7 or 4 : 7 or 4/7.
Rational number A number that can be written as the ratio of an integer to a counting number; or more formally, a number that can be expressed as a ratio a/b where a and b are integers and b ≠ 0, e.g., 0.5, 3/5, -3, 8, 3-9/10.
Real number A number from the set of numbers consisting of all rational and all irrational numbers.
Recursive pattern or sequence A pattern or sequence wherein each successive term can be computed from some or all of the preceding terms by an algorithmic procedure.
Reflection A type of transformation that flips points about a line, called the line of reflection. Taken together, the image and the preimage have the line of reflection as a line of symmetry.
Rotation A type of transformation that turns a figure about a fixed point, called the center of rotation.
Sample space In probability, the set of all outcomes of a given experiment, e.g., the sample space for tossing two coins is (H,H), (H,T), (T,H), (T,T). (H)
Scatter plot Two sets of data plotted as ordered pairs in the coordinate plane. (H)
Winning Olympic High Jump
Scientific notation 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. (W)
Sequence, progression 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, and so on. (W)
Transformation A prescription, or rule, that sets up a one-to-one correspondence between the points in a geometric object (the preimage) and the points in another geometric object (the image). Reflections, rotations, translations, and dilations are particular examples of transformations.
Translation A type of transformation that moves every point by the same distance in the same direction, e.g., in a geographic map, moving a given distance due north.
Valid a) Well-grounded or justifiable; being at once relevant and meaningful, e.g., a valid theory; b) Logically correct. (W)
Variable A letter used to represent one or more numbers in an expression, equation, inequality, or matrix. (H)
Vector A quantity that has magnitude and direction. A vector is typically represented by a directed line segment, whose length represents the magnitude and whose orientation in space represents the direction. (W)
Venn diagram A diagram that is used to show relationships between sets. (H)
Vertex-edge graph A graph consisting of points with connections in which the points are called vertices and the line segments are called edges.
Whole number A number that is either a counting number or zero.
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