  Mathematics State Curriculum Glossary Absolute value: A number's distance from zero on a number line (e.g., the absolute value of 2 and the absolute value of -2 are both 2, i.e., |2| = 2 and |-2| = 2). Additive inverse: Two numbers are additive inverses of each other if their sum is 0 (e.g., since -4 + 4 = 0, then -4 and 4 are additive inverses of each other). Algebraic expression: Numeral and/or variable joined by any combination of the four basic operations (+, -, x, /) and involving any power(s) of numeral and/or variable (e.g., 3-8, 7x4, 4+X, Y/2, N-2, 3(4+8)-7, Y2-2). Area: The size of a region measured in number of square units. Arithmetic sequence: A sequence with a constant difference between consecutive terms (e.g., 2, 5, 8, 11,... is an arithmetic sequence with a constant difference of 3). Associative Property: A property of addition or multiplication in which the regrouping of the addends or factors does not change the outcome of the operations [i.e., (a + b) + c = a + (b + c) and (ab)c = a(bc)]. Attribute: A characteristic of an object, such as color, shape, or size. Bar graph: A graphical display representing data in different categories or groups. The length of a rectangle or bar is used to represent the numerical amount. Box and whisker plot: A graphical display which shows the median, quartiles, and extremes of a set of data but does not display any other specific data values. Capacity: The maximum amount that can be contained by an object. Often refers to measurement of liquid. Cardinal numbers: The counting numbers (1, 2, 3...). Circle graph: A graphical display that shows data as parts of a whole circle. Circumference: The distance around a circle; the formula for circumference of a circle is pi times the diameter (C = TTd). Closed figure: The boundary of a simple 2-dimensional region, including shapes with straight and curved sides. Commutative Property: A property of addition or multiplication in which the sum or product stays the same when the order of the addends or factors is changed (i.e., a + b = b + a and ab = ba). Concrete: Physical objects used to represent mathematical situations. Congruency: Geometric figures having the same size and shape; all corresponding parts of congruent figures have the same measure. Conjecture: A preliminary statement or hypothesis that something is true; a statement may later be confirmed or disproved through observation or testing. Coordinate geometry: The algebraic study of geometry through the use a coordinate plane or system. Coordinate plane: A 2-dimensional system in which the coordinates of a point are its distances from two intersecting perpendicular lines called axes. The formal name for this system is Cartesian coordinate system. Counting techniques: Methods to determine the number of possible outcomes of an event. Some of the methods are tree diagram, list, rules for multiplication, combinations, and permutations. Curve fitting: The sketching of a line or curve to best describe a relationship between two variables on a scatter plot. Deductive reasoning: The process of reasoning that starts from statements accepted as true and applied to a new situation to reach a conclusion (e.g., if 5+4 = 9, and 6+3 = 9, then 5+4 = 6+3). Diagonal: For a polygon in the plane, any line segment joining non-adjacent vertices. For a polyhedron in space, a line segment joining two vertices not in the same face. Dilation: A transformation which produces a figure similar to the original by proportionally shrinking or stretching the figure. Dimensional analysis: A method of converting units within a measurement system. Direct proof: The proof of a proposition by accepting the hypothesis of the proposition and arguing to the conclusion. Distributive Property: A property which establishes a relationship between multiplication and addition such that multiplication distributes across the addition [i.e., a(b+c) = ab + ac]. Divisibility (rules of) : Special tests to determine if a particular integer is a factor of a given number, (e.g., a number is divisible by 10 if it ends in a 0). Elapsed time: The amount of time between a beginning time and an ending time. Equally-likely outcomes: Events in a sample space that have the same probability of occurring. Equation: A mathematical sentence of equality between two expressions (e.g., N + 50 = 75 or 75 = N + 50 means that N + 50 must have the same value as 75). Equivalent: Numbers or expressions that have the same value. Estimation: The process of finding a number close to an exact amount. Euclidean geometry: The geometry (plane and solid) based on Euclid's postulates. Experimental probability: A probability calculated from the results of an experiment. Explicit relationship: A sequence rule using the number of the term to define the function [e.g., in the sequence 3, 6, 9,..., the explicit rule is f(n) = 3n where n is the number of the term and f(n) is the value of the term]. Exponent: A number which is placed to the right of and above another number (base). The value of the exponent determines how many times the base is used as a factor (e.g., 34 = 3 x 3 x 3 x3; {3 is the base and is used as a factor 4 times} the exponent is 4). Exponential form: A way of writing numbers using bases and exponents [e.g., 425 = (4 x 102) + (2 x 101) + (5 x 100)]. Exponential function: A function whose general equation is a y=abx or y=abkx, where a, b, and k stand for constants. Face: A plane surface of a three-dimensional figure. Factor: The numbers or terms multiplied in an expression. Formula: An equation that states a fact or rule (e.g., A= w). Frequency table: A display to show how often items, numbers, or a range of numbers occur. Function: A relationship in which every value of x has a unique value of y (e.g., the relation y = 2x + 1 is a function because for every different x, there is one and only one y). Function notation: A notation that describes a function. For a function ƒ, when x is a member of the domain, the symbol ƒ(x) denotes the corresponding member of the range [e.g., an equation of a function might be ƒ(x) = x+3]. Geometric sequence: A sequence with a constant ratio between two consecutive terms (e.g., 1, 2, 4, 8, 16,... is a geometric sequence with a ratio of 2). Graph: A pictorial representation of information or relationships between numbers. Histogram: A graphical display representing continuous data in different categories or groups. Indirect measurement: A measurement which is found by using a formula or other strategy and not actually measuring something (e.g., finding the height of a tree without actually holding a ruler next to it). Indirect proof: A proof that begins by assuming the denial of what is to be proved and then deducing a contradiction from this assumption. Inductive reasoning: A type of type of mathematical reasoning which involves observing patterns and using those observations to make generalizations. Inequality: A mathematical sentence in which the value of the expressions on either side of the relation symbol are unequal. Relation symbols include >, <, , , or (e.g., x < y, 7 > 3, n 4). Inference: A conclusion drawn from data. Integer: A set of whole numbers and its opposites (i.e. …..-3, -2, -1, 0, 1, 2, 3, ….) Inverse operations: Two operations that "undo" each other (e.g., addition and subtraction). Line graph: A graphical representation using points connected by line segments to show how something changes over time. Line of best fit: A line drawn on a scatter plot to estimate the relationship between two sets of data. Line plot: A graph using marks (e.g., X, ·) above a number on a number line to show the frequency of data. Linear function: A function with no exponents other than one and with no products of the variables (e.g., y=x+4, y= -4, and 3x-4y = 1/2 are linear functions); in a rectangular coordinate system, the graph of a linear function is a line. Manipulatives: Tools, models, blocks, tiles, and other objects which are used to explore mathematical ideas and solve mathematical problems. Matrices: Rectangular arrays of numbers arranged in rows and columns. Mean: In a collection of data, the sum of all the data divided by the number of data. Measures of central tendency: Numbers which tend to cluster around the "middle" of a set of values. Three such numbers are mean, median, and mode. Median: The middle number (or the mean of the two middle numbers when necessary) in a collection of numbers that is arranged in order from least to greatest. Mode: The number(s) that occur(s) most often in a collection of data. Model: To represent or show mathematical ideas and relationships and real-world situations using objects, pictures, graphs, tables, functions, and other methods. Multiple: The product of a whole number and any other whole number. Multiplicative inverse: Two numbers are multiplicative inverses of each other if their product is 1 (e.g., since 4 x 1/4 = 1, 1/4 and 4 are multiplicative inverses). Numerical perspective: A mathematical idea expressed as a number or numbers. One-dimensional: A figure that has length but no width or height. Ordinal numbers: Numbers used to express order (e.g., 1st, 2nd, 3rd). Outcome of an activity: One of the possible events in a probability situation. Parallel(ism): Lines that lie in the same plane and never meet. Also, planes lying in space that never meet. Patterns: Regularities in situations such as those in nature, events, shapes, designs, and sets of numbers (e.g., spirals on pineapples, geometric designs in quilts, the number sequence 3, 6, 9, 12, . . . ). Percent: A special ratio that compares a number to 100 and uses the % sign (e.g., 1/2 = 50% and 2/3 = 66 2/3%). Perimeter: The distance around a geometric shape. Perpendicular(ity): Lines in the same plane which intersect to form a right angle. Pictograph: A graphical representation that shows numerical information by using picture symbols. Place Value: The value of a digit as determined by its position in a number (e.g., in the number "11" the one is worth either 10 or 1, depending on the position). Population: A group of people, objects, or events that fit a particular description. Power: A number expressed using an exponent (e.g., the number 53 is read five to the third power or five cubed). Power function: A function with a variable base and a constant exponent [e.g., f(x) = axb]. Precision: The smallest place value to which an approximate number or measurement is expressed (e.g., if pi is represented as 3.14, then its precision is .01). Prime number: A whole number greater than 1 that can only be divided evenly by itself and 1 (e.g., 17). Prism: A three-dimensional figure with parallelogram faces and two parallel, congruent bases. Probability: The number of favorable outcomes compared to the number of possible outcomes of an experiment. A number from 0 to 1 which indicates how likely something is to happen. Probability of an event: A number that measures the likelihood that the event will occur. Properties of operations: Mathematical principals that are always true (e.g., commutative, associative, distributive, inverses). Proportion: An equation of the form a/b=c/d which states that the two ratios are equivalent. Pythagorean Theorem: The sum of the squares of the lengths of the two legs (a, b) of a right triangle is equal to the square of the length of the hypotenuse (c). The formula is a2 + b2 = c2. Quadratic function: A function of the second degree [i.e., a function of the form f(x) = ax2 + bx + c]; in a rectangular coordinate system, the graph of a quadratic function is a parabola. Radical: Another name for the roots of numbers, such as the square root of 5 or \/5. Range of data set: The difference between the greatest and the least numbers in a set of data (e.g., the range of 2, 7, 13, and 17 is 15). Rate: A ratio comparing two different units (e.g., miles per hour). Ratio: A comparison of two whole numbers by division. Rational number: A real number that can be written as a quotient of two integers a/b, where b does not equal 0; a repeating or terminating decimal, integer, fraction, or whole number. Real number: Any number that is either rational or irrational. Recursive relationship: A function rule which uses the value of the preceding term in the definition. Reflection (flip): A transformation which produces the mirror image of a figure (i.e., flipping a figure across a line). Representations: Different ways to show the same mathematical concepts (i.e., ¼, .25, 25%) Rotation (turn): A transformation obtained by rotating a figure around a fixed point (i.e., turning a figure about a point). Sample space: The set or collection of all possible outcomes of a probability experiment. Scale: Choice of increments and range of numbers on an axis. Scale drawing: A scaled representation of physical objects or drawings. Scatter plot: A graphical representation consisting of ordered pairs possibly showing a relationship between two variable quantities. Scientific notation: Representation of a number as the product of a number between 1 and 10 and a power of 10; used especially for very small or very large numbers (e.g., 6,900,000 = 6.9 x 106 or .00069 = 6.9 x10-4). Sequence: A function whose domain is the set of natural numbers. Similarity: Two or more figures having the same shape but not necessarily the same size. Simulation: A representation of a situation or problem with a similar but simpler model or a more easily manipulated model in order to determine experimental results. Spatial reasoning: The ability to interpret and make drawings, form mental images, and visualize movement or change in those images. Statistical investigation: A procedure for obtaining data and drawing conclusions or making decisions on the basis of available data. Stem and leaf plot: A method of organizing data for the purpose of comparison where the "leaf" is the number in the smallest place value and the "stem" includes the numbers in the larger place values. Surface area: The sum of the areas of the faces of a solid figure. Symbolic perspectives: Mathematical ideas expressed using numeric and/or non-numeric representations. Symmetry: A figure has symmetry if there exists some line or point through which all points of the figure can be reflected to generate another point on the figure. System of linear equations: Two or more equations that are conditions imposed simultaneously on all the variables, but that may or may not have common solutions (e.g., x+y=2, and 3x + 2y = 5). Theoretical probability: A probability calculated from mathematical counting techniques. Three-dimensional: An object that has length, width, and height. Transformation: A rule for moving every point in a plane figure to a new location. Translation (slide): A transformation that slides a figure a given distance in a given direction. Trigonometric ratio: A comparison of the measures of the lengths of two sides of a right triangle expressed in fractional or decimal form; there are six trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) associated with any angle. Trigonometry: The study of right triangle measurements and ratios, useful for calculating indirect measurements. Two-dimensional: A figure that has length and width but not height (i.e., a plane figure such as a rectangle or circle). Valid argument: An explicit demonstration or proof that has been shown to be true. Validate: To give evidence that a solution or process is correct. Variable: A letter or symbol which represents one or more numbers. Vertex (vertices): The points where two line segments come together (corners). Visual perspective: A mathematical idea expressed as a picture, graph, or table. Volume: The amount of space enclosed in a three-dimensional figure, measured in cubic units. Whole numbers: The numbers in the set {0, 1, 2, 3, …}. 