MATH ACADEMIC VOCABULARY

ACADEMIC VOCABULARY THAT WE NEED TO GET THROUGH

The purpose of this glossary is to help the user better understand and implement the Mathematics Standard. It is not intended to be a study guide for the AIMS and is not a comprehensive list of all mathematics terms.

The definitions in the glossary are general in nature. For specific information about grade level expectations, consult the explanations and examples column in the grade level documents.

absolute value function

accuracy (mathematical)

addition principle of counting

adjacency matrix

adjacent vertices

algebraic expression

algebraic form/notation

alternate exterior

alternate interior

altitude of a geometric figure

angle

appropriate measure

area

arithmetic sequence

associative property

attribute of a figure

attribute of a function or graph

axis (axes: plural) (in two-dimensions)

base of a polygon

benchmark fraction

bias

binomial theorem

box and whisker plot

Cartesian coordinate system

chord of a circle

chromatic number

coloring of a graph

coloring of a picture or map

common algorithm

common denominator

common irrational numbers

common multiple

commutative property

comparative language

complementary angles

complementary events

complex fraction

complex solution

composite figure

composite number

composition of function

compound interest

compound probability

compound probability experiment

computational estimation

computational fluency

concrete materials

concrete situation

conditional probability

conditional statement

Conjugate Root Theorem

connected vertex-edge graph

exterior angles

interior angles

consecutive vertices

constant (of an expression)

constant (rate of change)

contextual situation

conversion factor

coordinate plane

coordinates of a point

correlation coefficient

corresponding angles

counting number

counting problem

cube

cube root

cubic function

De Moivre’s theorem

deductive proof

deductive reasoning

degree of a polynomial

degree of a vertex

degree of accuracy

density property

dependent events

dependent variable

Descartes Rule of Signs

digit

dimensional analysis

distance formula

distortion in data display

distribution of data

distributive property

divisibility rules

documentary stamps

domain of a function

durables (consumer)

edge (vertex-edge graph)

edge of a polyhedron

efficiency (mathematical)

equilateral polygon

equivalent

Euclid’s 1st Postulate

Euclid’s 2nd Postulate

Euclid’s 3rd Postulate

Euclid’s 4th Postulate

Euclid’s 5th Postulate

Euclidean geometry

expanded notation

experimental (empirical) probability

explicit formula

explicit sequence

exponential form

exponential function

exponential growth

face of a polyhedron

factorial notation

Fibonacci sequence

flexibility (mathematical)

foci (of an ellipse)

Four Color Theorem

fractional part

frequency table

front-end estimation

function(algebraic)

function notation

Fundamental Theorem of Algebra

geometric model

geometric pattern

geometric probability

geometric sequence

geometric solid

graphic organizer

greatest common factor

grouping symbols

growing pattern

Hamilton circuit

higher order polynomial

identity element

identity property of

imaginary numbers

implicit formula

improper fraction

independent events

independent variable

indirect measurement

Individual retirement account (IRA)

inductive reasoning

input/output machine

inscribed angles

intercepted arc

interquartile range

inverse function

inverse of a statement

inverse operation

inverse relationship

irrational numbers

irregular polygon

isosceles triangle

iterative pattern/ sequence

lateral surface

Law of Large Numbers

least common multiple (LCM)

line of best fit

line of reflection

line of symmetry

linear equation

linear expression

linear function

logarithmic function

lowest common denominator (LCD)

mathematical argument

mathematical fluency

meaningful context

measurable attribute

measures of center

measures of spread

monomial expression

multi-line graph

multiple of a number

multiplication principle of counting

multi-variable equation

natural numbers

necessary information

negative number

neighboring vertices (of a vertex-edge graph)

net of a polyhedron

non-contextual problem

non-Euclidean geometry

non-random sample

non-routine problem

non-standard shapes

a number’s distance from zero on a number line (e.g., the absolute value of is 4, the absolute value of 4 is 4; symbolically,

a rule that defines a relationship between two sets of numbers that for each value of the independent variable set there is only one value in the dependent value set where

, where ; for all values of x

the extent to which a solution or measurement matches a standard or expected result

an angle with measure between zero degrees and ninety degrees

a number used in the mathematical operation of addition (e.g., 6 + 8 = 14, 6 and 8 are addends)

a mathematical operation that combines two or more numbers to calculate a sum

a principle that allows for the efficient counting of the total number of ways a task can be accomplished when each part of the task consists of counting items from separate groups that do not overlap. For example, how many triangles are in the figure below? The task is to recognize there are three types of triangles (small, medium, and large) where each group does not overlap with another group; i.e., where each type of triangle appears as a member of one and only one group.

elementary school: If you want to count the total number of triangles in the figure above, count the number of small-sized triangles (8), count the number of medium-sized triangles (4), and count the number of large-sized triangles (1) and add them together (8 + 4 + 1 = 13). So there are a total of 13 triangles in the figure.

If you have a task that can be accomplished through counting a collection of items among disjoint groups, and you count m items in the first group, n items in a second group, and g items in a third group (etc.,) then you can efficiently count the total number of items in the task by using the addition principle of counting. In this example, we would add m plus n plus g or (m + n + g).

high school: let A1 and A2 be separate events that may occur at the same time with n1 and n2 possible outcomes for each event, respectively; then the total number of possible outcomes for the two events occurring are n1 + n2.

the arrangement of rows and columns labeled by graph vertices , with a 1 or 0 in position according to whether or not

and are adjacent. For a simple graph with no self-loops, the adjacency matrix must have zeros on the diagonal while the adjacency matrix for an undirected graph is symmetric al

vertices joined by an edge or neighboring vertices in a vertex-edge graph

a group of numbers, symbols, and variables that express a single or series of mathematical operations (e.g.,

an algebraic description written in terms of numbers, symbols, and variables

a set of step-by-step instructions for completing a task that can be generalized to other tasks, problems, or situations

angles formed by one or more transversals intersecting two lines whose interiors are not between two lines and on different sides of the transversal (e.g.,

angles formed by one or more transversals intersecting two lines whose interiors are between the two lines and on different sides of the transversal (e.g.,

a perpendicular segment from a base to a vertex or between bases

a measure of one half the difference between the largest and smallest value of a function

a device for the measurement of time that has numbers 1 to 12 around a face, with an hour, minute, and second hand that shows a continuous sweep of time

a process of dividing a composite into its parts for the purpose of examination

a geometric figure consisting of the union of two rays that share a common endpoint (vertex)

a line, line segment, or ray that divides an angle into two congruent parts

the measure (in degrees or radians) of the arc formed by two rays with a common endpoint (vertex)

a purchased investment contract between a person and an insurance company that defines payments to the insurer, in lump sum or in a series of payments, in exchange for benefits paid back to the insured at a designated date or series of dates

the reasonable use of an attribute, unit, or tool within the context of a problem (e.g., using a ruler to measure dimensions of a tissue box but not the dimensions of a building, using meters as the unit measure for the dimensions of a house but not the dimensions of a picture frame)

the degree of accuracy required for a mathematical task (e.g., approximating the lengths of lumber in framing carpentry requires less accuracy then the lengths of molding in finish carpentry)

a value or quantity that is close to, but not the same as, the desired value or quantity for a specified purpose

a two dimensional space measured by the number of non-overlapping unit squares or parts of unit squares that can fit into the space

an ordered set of items in which the difference between each consecutive item is constant

possible order of a set of events or items

a rectangular arrangement of objects or elements organized into rows and columns, or a set of objects or elements organized into a specific pattern

addition: changing the grouping of terms in a sum without changing the sum

multiplication: changing the grouping of factors in a product without changing the product

a line that a graph approaches

a property or common feature of a sets of objects or elements

a characteristic or distinct feature

the result of the sum of all the numbers in a data set divided by the number of elements in that data set

one of two perpendicular number lines used to form a coordinate system

a representation of the length of either vertical or horizontal bars used to enumerate and compare data

exponent: a term used to indicate a factor for repeated multiplication (e.g., in 47, 4 is the base)

logarithm: the quantity a in the equation

the face of a geometric figure that identifies its type

a side of a polygon that is perpendicular to its height

a commonly known point of reference from which measurements may be made (e.g., four quarters make a whole)

a commonly known fraction that serves as a meaningful reference point for measurement comparison

sampling: a segment of data that is not representative of the original set of data

statistical: an effect which deprives a statistical result of representativeness by systematically distorting it

an algebraic expression consisting of two terms (e.g., , )

a description of the coefficients of the expansion of the binomial raised to the nth power

to divide an object or term into two congruent parts

a point, segment, line, ray or plane which divides a segment, angle or figure into two parts of equal measure

a method for displaying the median, quartiles, and extremes of a data set

a fee in the form of a commission charged to the buyer by the brokerage firm for acting on behalf of the investor with the bond, commodities, or stock market

an action, process, or result of a mathematical computation

the amount of space in units or cubes that can fit into a solid (note: also referred to as volume)

a plane containing points identified by their distance from the origin in ordered pairs along two perpendicular lines referred to as axes (note: also referred to as coordinate plane and rectangular coordinate plane)

an agency or action that produces an effect

a metric scale for the measurement of temperature based on the properties of water

an angle whose vertex is the center of a circle and whose sides (rays) are radii

a segment whose endpoints are on a given circle

fewest number of colors needed to color a vertex-edge graph

a set of points in a plane that are equidistant from a given point called the center

a display of data as sections of a circle that represent all the data (note: formerly called pie graph or pie chart)

a path in a graph that starts and ends at the same vertex

a fraction of the circumference of a circle

the point where the three perpendicular bisectors of the sides of a triangle meet

the total distance around a closed curve like a circle

the number part of a term and variable combination (e.g., the coefficient for 7x is 7)

lines or shapes that have all points in common

points that lie on the same line

assigning colors to the vertices of a vertex-edge graph so that adjacent vertices are assigned different colors

assigning colors to the regions of a picture or map so that regions that share a common border are assigned different colors

The number of ways of choosing or selecting k unordered outcomes from n possibilities.

a set of step by step instructions that are well known by most practitioners and are frequently used (e.g., borrowing, carrying)

a number divisible by all of the denominators in a set of fractions

a whole number that divides without remainder into two or more non-zero numbers

a grouping of well known real numbers that cannot be expressed as a ratio of two integers

a whole number multiple of two or more given numbers (e.g., 48 is a common multiple of 2, 3, and 4)

addition: the addition of terms in any order obtains the same sum (e.g., , )

multiplication: the multiplication of terms in any order obtains the same product (e.g., , )

words used to describe the differences in terms and objects (e.g., bigger, smaller, less than, more than, not equal to)

any two angles whose measures have a sum of ninety degrees

two events whose probabilities of occurring sum to one; mutually exclusive events (e.g., when flipping a coin, getting a head and getting a tail are complementary events)

a vertex-edge graph in which every vertex is adjacent to every other vertex

a fraction that has a fractional numerator, denominator, or both (e.g., )

a number that can be written in the form where a and b are real numbers and i is an imaginary number (e.g., 2+3i which is equivalent to

a solution to a problem or equation that is not a real number

to create by putting together

a geometric figure that is composed of two or more simple polygons

a number that has factors other than one and itself

a function comprised of more than one function arranged such that the output of one function becomes the input of the next function

a percentage of an amount that accrues based on the product of the interest rate and the sum of the principal and any previously earned interest

the likelihood that an event will occur based on whether another event has occurred

an organized process that examines the likelihood of two events occurring simultaneously, or the likelihood of one event occurring, instead of other possible outcomes, in conjunction with another event

the method of determining an approximate solution to a numerical problem

the efficient automatic recall of addition, subtraction, multiplication, and division facts; the efficient and automatic recall and use of standard algorithms for addition, subtraction, multiplication, and division

to determine or calculate by mathematical means

the then clause in an if-then conditional statement; a statement based on a reasonable judgment of two or more proposals

physical objects and manipulatives used for the purpose of instruction to represent mathematical situations

a condition derived from real-world examples and applications (note: also called contextual situation)

the likelihood that an event will occur based on an event that has already occurred

a statement with a hypothesis and conclusion in the form, if hypothesis, then conclusion (e.g., if a closed figure has exactly three sides, then the figure is a triangle)

a three-dimensional figure generated by rotating a triangle about one of its legs to form a solid with one circular base

vertex-edge graphs can be used to model entities which are in conflict

having the same shape and exactly the same size

the intersection of a plane and two right conical surfaces that have the same vertex and whose angles are opposite rays (e.g., ellipse, parabola, hyperbola, circle)

an unproven statement based on observations

if a+bi is a root for polynomial P, then a-bi is also a root for polynomial P

a vertex-edge graph is connected if there is a path between all pairs of vertices (if a path does not exist between all pairs of vertices then the graph is disconnected)

to follow in order one after the other

angles formed when one or more transversals intersect two parallel lines, that are not located between the two parallel lines, and are located on either side of a transversal

angles formed when one or more transversals intersect two parallel lines, that are located between the two parallel lines, and are located on either side of a transversal

vertices that share a side of a polygon

the attribute of being unchanging, consistent, and regular

a term with a degree of zero

a fixed incremental increase or decrease over an interval

arithmetic: the formation of a conclusion or the derivation of a result by joining or organizing forms

geometry: to draw a geometric figure using appropriate tools to meet a given set of constraints

real-life scenarios or circumstances that illustrate mathematical problems (note: also called concrete situation)

a conditional statement that is the logical equivalent to the original statement exchanging the hypothesis with the conclusion and negating both of them

a conditional statement that exchanges the hypothesis (if) and conclusion (then) components of an if-then statement

the ratio of two equal quantities that are measured in different units

a polygon with each interior angle measuring less than 180 degrees and whose diagonals lie inside the polygon

a plane containing points identified by their distance from the origin in ordered pairs along two perpendicular lines referred to as axes (note: also referred to as Cartesian coordinate system and rectangular coordinate plane)

an ordered pair of real numbers that locate a point in a plane

the relationship between two or more data sets or variables

a value between 1 and -1 that determines if two lines have a linear relationship

a pair of angles that occupy the same location at each intersection when two lines are intersected by one or more transversals (e.g.,

in a right triangle, the ratio of the length of the leg adjacent to a given acute angle to the length of the hypotenuse

an example used to contradict or disprove a given statement

a number from the set of numbers consisting of 1, 2, 3, 4, 5, 6, … (note: also referred to as natural numbers)

a type of problem that determines the number of arrangements, possibilities, or outcomes of events

a plane section that intersects a solid

exponents: the third power of a number

geometry: a regular 3-dimensional figure having six congruent square faces

one of only three equal factors of a given number (e.g., the cube root of 27 is 3, 3 x 3 x 3 = 27

a rule containing the cube of a variable (e.g., f(x)=x3)

a vertex-edge graph where the vertices can be arranged in a circle so that each vertex is adjacent to the vertices that come before and after it

a 3-dimensional figure composed of two congruent and parallel circular regions joined by a curved surface

quantitative and/or qualitative information within a context gathered through observation, questioning, and/or measurement

a defined group of quantitative and/or qualitative information within a context gathered through observations, questioning, and/or measurement

a method to find the exponential value of an imaginary number; given any nonzero complex number z and any integer n, the nthpower of z, rCiS(θ)=r(cos θ+isin θ) is ZM = (r(cos θ + isin θ))M = rM((cosnθ + isinnθ) = rM CiS(nθ)

a demarcation mark used in a base ten numbering system to designate values that are less than one

to break down into smaller units to simplify computation

a formal use of deductive reasoning using logical steps in the form of axioms, theorems, and given information

a series of logical steps in which a conclusion is drawn directly from a set of statements (premises) that are assumed to be true

algebra: the degree of a term is the sum of the powers of each variable in the term

geometry: a unit of measure based on dividing a circle into 360 equal parts, and used to measure angles, arcs and rotations

temperature: the unit of measure for temperature

the degree of the highest term of the polynomial

the number of edges that meet at a vertex in a vertex-edge graph

a standardized mathematic set of rules for rounding using significant figures that allows for the consistent handling of different scales of measurement

the bottom part of a fraction that indicates the number of equal parts into which the whole is divided (e.g., 4 in the fraction ¾)

the ratio of the amount of matter in an object compared to its volume; calculated as mass (m) per unit volume (v)

a statement that says there is always a rational number between any two rational numbers

two events such that the likelihood of the outcome of the second event is affected by the outcome of the first event

the output variable in a function which depends on the value of the input or independent variable

a mathematical method for the determination of both positive and negative zeros of a function; let P(x) be a polynomial with real coefficients: the number of positive zeros of P is either equal to the number of variations

in sign of P(x) or less than this by an even number, and the number of negative real zeros of P is either equal to the number of variations in sign of P(−x) or less than this by an even number

a sequential organizational method from biggest to smallest, greatest to least, latest to earliest

a line segment joining two non-adjacent vertices of a polygon

a line segment that joins two points on a circle and passes through the center of the circle

the result obtained using the operation of subtraction

the ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, used in a base ten numeration system

a device for telling time that shifts between discrete states instead of continuous variation

a transformation that either enlarges or reduces a geometric figure proportionally using a scale

measurement: measure of distance in a specific direction (e.g., length, width, depth)

space: the number of coordinates needed to specify a location in space

a use of proportional analysis as a problem-solving strategy for the conversion of measurement units

a series of items linked by edges that are directed with an initial and terminal vertex (note: also referred to as digraph)

a fixed line perpendicular to the axis of symmetry and that lies the same distance from the vertex as the focus, but in the opposite direction

a fee assessed that is equal to 1% of the amount of a loan (e.g., one point on a $100,000 mortgage is equal to $1,000)

a condition in which the number of possibilities are separated from each other and are distinct

a contemporary branch of mathematics that is used in business, industry, and daily life; topics include combinatorics, iteration and recursion, and vertex-edge graphs

the positive value for the length of the shortest line segment joining two points

a general method or rule to measure the distance between two points that are identified by ordered pairs (e.g.,

the use of incorrect proportion, design variation in comparison of data sets, lack of context, or insignificant use of data in direct comparison with meaningful data

the values that a variable has across a spread of data

a rule or method that states that every term inside grouping symbols may be multiplied by a term outside grouping symbols to yield an equivalent expression

the value to be divided in a division problem

the ability to divide one whole number by another whole number without a remainder

a set of general rules that may be used to determine whether or not a number is evenly divisible by another number

2: if the number is even it is divisible by 2

3: if the sum of all of the digits is divisible by three, the number is divisible by 3

4: if the number formed by the last two digits is divisible by 4, the number is divisible by 4

5: if the last digit is a 0 or 5, the number is divisible by 5

6: if a number is divisible by both three and two, it is divisible by 6

7: if the difference of last digit doubled and the rest of the digits is divisible by seven, the number is divisible by 7 (e.g., 343: 34 – 6 = 28)

8: if the last three digits of a number are divisible by 8, the number is divisible by 8

9: if the sum of the digits is divisible by nine, the number is divisible by 9

10: if the last digit of the number is 0 it is divisible by 10

the opposite operation of multiplication that separates items or values into equal parts with or without a remainder

the value by which another quantity is divided in a division problem

a state tax, in the form of stamps, that must be paid when ownership of a property passes from one owner to another

the set of values for the independent variable (input value) of a function

a mathematical operation that calculates a scalar product using two vectors and real numbers (e.g., for vectors

A= <Xa, Ya> and B=<Xb, Yb> the dot product A·B=(xa)(xb ) + (ya) (yb))

a portion of the full amount paid at the time of purchase or delivery

a product such as an automobile or appliance that has a life expectancy of at least three years

the abbreviation for for example; precedes a non-exhaustive list of examples provided as options; other examples may be appropriate but not included (compare to i.e.)

an edge or arc that connects two vertices in a vertex-edge graph or network

a line segment where two faces of a polyhedron intersect

the ability to determine a method for solution quickly and with little effort

the measure of actual time between two distinct events

an item or term contained within a set of items or terms

the set of all points in which the sum of the distances between focal points is a constant

a series of marks, “…”, to indicate the continuance of a pattern or sequence

a set, signified by the symbol Ø, to indicate that the set contains no items or elements (note: also called the null set)

a description of the performance of a function as it increases or decreases without boundaries

a point that demarks the beginning and the end of a line segment, the initial point of a ray, or the end of an arc

a term that indicates the same amount, measure, or quantity as another amount, measure, or quantity

a mathematical statement divided by an equal symbol that states the two values or expressions have the same value

a polygon in which all sides are congruent

two expressions or statements that always have the same truth value

an approximate and reasonable answer that is close to the exact answer without actually calculating the exact answer

a line segment may be drawn joining any two points

any line segment can be extended indefinitely in a line

given a line segment, a circle can be drawn having the segment as a radius and one endpoint as a center

all right angles are congruent

only one straight line may be drawn between a given line and a point that is not on that line (note: also called the Parallel Postulate)

the study of geometry based on definitions, undefined terms (point, line and plane), and the assumptions of Euclid

a path in a vertex-edge graph that starts and ends at the same vertex and does not retrace any edges

a path in a vertex-edge graph that travels every edge exactly once and the starting vertex differs from the ending vertex

the use of one or more mathematical operations to calculate the value of an expression for a given input

a function that meets the mathematical rule

a natural number that is divisible by two without a remainder

a vertex in a vertex-edge graph whose degree is even

outcomes during a probability activity

elementary: the display of digits to show the place value of each digit

secondary: the display of an expression without parentheses

the average value distribution for a random variable

a ratio formed by the comparison of the number of times an event occurs in an experiment to the number of times the experiment is completed

a statement that is expressed without ambiguity

an equation in which the dependent variable is written in terms of the independent variable (e.g., y=2x+3, f(x)=x5-7, or I=Prt)

a group of terms arranged in a predictable way (pattern) with a rule that is used to generate the nth term of the pattern

a number placed to the right and above (superscript) a non-zero base that indicates the operation of repeated multiplication

a mathematical representation of a term raised to a power or terms grouped and raised to a power (e.g., 5x3 or (5x+7)2/5)

an equation format written as where the base, a, is a constant real number greater than zero but not equal to one.

the increase in a quantity over time represented by y = a·bx where a > 0 and b > 1

(e.g., ; each time x is increased by 1, y increases by a factor of 2)

a mathematical phrase containing one or more terms linked by operation symbols

any data or information in a problem that is not necessary to determine a solution or to answer a question

to infer a value for an unknown variable in an interval using known values in a defined interval

a maximum or minimum value of a function on a given interval

each polygon that combines to construct a three-dimensional solid

a collection of related addition and subtraction facts, or multiplication and division facts, made from the same numbers (e.g., [7+2=9, 2+7=9, 9-7=2, 9-2=7} and {7X2=14, 2X7=14, 14÷7=2, 14÷2=7}

noun: the value that can be divided into another value with no remainder

verb: rewrite a number or polynomial as a product of numbers, simpler polynomials, or of polynomials and monomials

the product of all integers from a given number down to the number one

the format and symbol (!) used to represent a factorial

decomposing, through division, a complicated expression into the most simple expressions possible, that when multiplied yields the original expression

the U.S. customary or standard scale measure of temperature

the equal opportunity for the occurrence of all possible events or being equally divided

a recursive sequence in which every number is the sum of the two preceding numbers

extending credit or purchasing on contract

a set of items or values that is limited to a countable number of elements

a student’s ability to recognize strategies necessary to complete a mathematical task, and a student’s ability to apply learned strategies to alternative mathematical tasks

the efficient automatic recall of addition, subtraction, multiplication, and division facts; the efficient and automatic recall and use of standard algorithms for addition, subtraction, multiplication, and division

two fixed points on an ellipse from which the sum of the distances of all other points on the ellipse is a constant

a fixed point from which all other points are equidistant

a general mathematical equation that relates two or more terms or values

given any plane or spherical surface separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color

a rough or fragmented geometric shape that can be subdivided into parts, each of which is (approximately) a reduced-size copy of the whole

a number written in the form of a ratio where the top number is referred to as the numerator and the bottom number is referred to as the denominator

a part of a whole or a part of a group

the number of occurrences of an event within a specified interval

a collection of data organized to display the number of events in a specified interval or multiple intervals

a classification of patterns on two-dimensional surfaces that repeat in one direction

using the leading, or left-most, digits to make an estimate quickly and easily (e.g., when asked to estimate the sum of 594, 32, and 221 an original estimate would be 5+0+2 hundreds or 700)

a rule that defines a relationship between two sets of numbers in that for each value of the independent variable set there is only one value in the dependent variable set

an equation in the form of to show the output value of a function, f, for an input value x

an nth degree polynomial has n solution(s), real or complex

the ability to apply a solution method to many different problems and situations

a representation of a geometric figure or concept

a design representation of nonfigurative shapes including, lines, rectangles, and polygons

the likelihood of an event occurring based on geometric relationships such as area, surface area, or volume (e.g.,

if an arrow hits the target, the probability of hitting the red (shaded) bulls eye is

a finite or infinite progression of real numbers where each element is equal to the previous term multiplied by a constant referred to as the common ratio

a 3-dimensional shape bounded by surfaces (e.g., rectangular prism, pyramid, cylinder, cone, and sphere)

a representation of an algebraic equation applied to a coordinate grid

a visual tool designed to represent data in a format that improves understanding (e.g., Venn diagram, concept web, K-W-L chart)

the largest natural number or monomial that divides into different natural numbers or terms without a remainder

a variety of symbols of inclusion; parentheses, brackets, braces, or bars (i.e., ( ) , [ ] , {} , , | | )

patterns that show an arithmetic or geometric change between pairs of elements in the pattern (e.g., numbers in decreasing order; buildings in decreasing size; or 3, 5, 8, 12, ……)

a path in a vertex-edge graph that begins at a vertex, passes through every vertex exactly once, and returns to the original vertex

a path in a vertex-edge graph that starts as some vertex in the graph and visits every other vertex of the graph exactly once.

a perpendicular segment from a base to a vertex or between bases (note: also called altitude)

a polygon with six sides

an expression with a degree equal to or greater than two

a vertical bar graph with each bar representing a certain interval of data

parallel to or in the plane of the horizon; in a coordinate grid, the x-axis is a horizontal line

a set of all points on a plane such that the difference between the distances from the plane to the foci is a constant, and is created by the intersection of the plane and the cone

the longest of the three sides of a right triangle; the side opposite the right angle in a right triangle

the if clause in an if-then conditional statement

abbreviation for that is; precedes a specific list of items in which all of the items should be used (compare to e.g.)

a number when used in an operation with a given number leaves the given number unchanged

addition: the rule that recognizes that a given number remains unchanged after the addition of a zero

multiplication: the rule that recognizes that a given number remains unchanged after multiplication with the number one

a figure produced as the result of one or more transformations

the square root of a negative number expressed using i ()

assumed or indirectly stated; inferred

an equation in which the dependent variable and independent variable are not separated by the equal sign, or in which the dependent variable is written in terms of the independent variable (e.g., 2x+y=3,= or

a fraction in which the numerator is greater than the denominator

a monetary charge levied by an authority for public purposes that is based on monies made from employment, business, or capital gains

two events in which the outcome of the second event is not affected by the outcome of the first event

the input value for a function

a measurement determined without the direct application of measurement tools

a deductive reasoning strategy that uses contradiction or elimination to rule out all possible conclusions except the original statement which must be true

an account that allows the holder to delay paying income tax and reduces the amount of taxes owed on the funds deposited

a reasoning process in which a conclusion is drawn from several observations

a statement relating two or more quantities or values that are not equal using words or symbols (≠, <, >, <, >)

a conclusion drawn from given information, many times in the form of data

the set in which the number of elements cannot be counted

a method used to build functions by applying a rule to an input value which generates an output value

an angle with its vertex on the circle and with sides (rays) that are chords of the circle

the set of real numbers consisting of the whole numbers and their opposites ¼ -2, -1, 0, 1, 2 ¼

general: an integer

calculus: a function used for the calculation of the area under a curve

the point at which a line or curve crosses a given axis

that part of a circle that lies between two segments, rays, or secants that intersect the circle

a method for the estimation of the value of a function using the known values of a number above and below the unknown value

a measure of variability, that is resistant to outliers, determined by the difference between the first and third quartiles

a set of numbers or values between, and in some cases including, two given values

a function ƒ(y) = x, denoted by ƒ-1(x) such that the domain of the function ƒ(x) becomes the range of the inverse function ƒ-1(x), and the range of ƒ(x) becomes the domain of ƒ-1(x) ; the function will only have an inverse function if it is a one to one relation

a rectangular array of values with columns and rows which when multiplied by the original array of values results in an array of values with a one for every diagonal element from the top left to the bottom right and a zero for all other elements in the array

a conditional statement obtained by negating both the hypothesis and the conclusion of a given conditional statement

a related but opposite process (i.e., multiplication is the inverse of division)

additive: a number when added to a given number results in a sum of zero (note: also called identity property of addition)

multiplicative: a number when multiplied to a given number results in a product of one (note: also referred to as the identity property of multiplication)

a set of real numbers that cannot be expressed as a ratio of two integers (i.e., )

a polygon whose interior angles are not equal and/or its sides are not equal in length

a triangle that has two or more congruent sides (note: equilateral triangles are a subset of isosceles triangles)

the repetition of a pattern or sequence

a pattern/sequence generated by using an initial value and repeatedly applying the same rule

to prove or show to be true or valid using logic and/or evidence

a quadrilateral with two distinct pairs of congruent adjacent sides and no congruent opposite sides

a 2-dimensional surface that is not a base of a 3-dimensional figure

the sum of the lateral faces of a three-dimensional figure

a law that allows for the calculation of the measurement of a side or angle of a triangle given other values for the triangle; for any ΔABC:

the larger the sample the closer the experimental probability will approximate the theoretical probability

a description of the relationship between the angles of a triangle and the opposite sides of the same triangle; for any ΔABC:

the smallest value for which two or more values are factors (e.g., the LCM of 3, 4, and 6 is 12, the LCM of and

the value, if one exists, that the dependent variable approaches as the independent variable approaches a given value

a straight set of points that extends infinitely in opposite directions (note: this is an undefined term in Euclidean geometry)

a representation used to show change over an interval, with the data points connected by line segments

a line drawn on a scatter plot to estimate the linear relationship among the data

the line that behaves as a mirror such that after a figure is reflected across the line all the points on the line are left unchanged by the reflection (transformation)

a line that divides a figure into two congruent parts that are mirror images of each other

a sketch of data in which check marks, or other marks above a number line, shows the frequency of each value

two points or endpoints and all the points on the line between the endpoints

an equation containing one or more terms in which the variable(s) is/are raised to the power of one but no higher

a collection of numbers, symbols, operations, and two or fewer variables with a degree of one

a function that has a constant rate of change and can be modeled by a straight line

a model for growth that adds a fixed amount to each time period

a metric unit of capacity that is equal to the volume of a cube that measures ten centimeters on a side

a power to which a positive number base greater than one must be raised to generate a given number

functions that involve logarithms and are the opposite of the exponential function

a system of reasoning used to validate arguments

a rational and varied systematic series of steps based on sound mathematical procedures in order to arrive at the solution

the least common multiple of the denominators of every fraction in a given collection of fractions

size or quantity

a wide variety of physical materials or objects that students use to foster the learning of abstract ideas in mathematics (note: also referred to as concrete materials)

the amount of matter a body contains

the justification of a particular solution, algorithm, or method using logic, evidence, and mathematically sound reasoning

the use of mathematical strategies with efficiency, accuracy, and flexibility

a rectangular array of numbers or letters arranged in rows and columns

the number with the greatest value in a set of numbers; the greatest vertical value in a graph

a measure of center where the sum of a set of numbers is divided by the number of elements in the set (also referred to as the average)

the real world application of a mathematical concept

a common feature of a set of objects or numbers that can be measured

numbers that communicate the “center” or “middle” of a set of data (i.e., mean, median, and mode)

an indication of the dispersion or variation of data values including range, quartiles, interquartile range, standard deviation, and variance

a measure of center that identifies a value such that half the data is above the value and half the data is below the value when the data is listed in order

a measurement system based on the base-ten numeration system (e.g., meter, liter, gram)

a point on a line segment halfway between the two endpoints

the difference between the upper and lower quartiles

the number with the smallest value in a set of numbers; the least vertical value in a graph

the number from which you are subtracting

to cause to become less severe

a number represented by a whole number next to a fraction, and is equal to the sum of the whole number and the fraction

a measure of center that is the value or values that occur(s) most frequently in a given set of numbers

an object, drawing, graph, expression, or equation that represents a given context

algebra and functions: choice of an equation or function to represent a given context

geometry: use of physical objects or manipulatives to show a geometric situation

an algebraic expression consisting of a single term that does not require any addition or subtraction (e.g., 5y)

a representation consisting of two or more line graphs that correspond to discrete data sets

a number into which a given number may be divided with no remainder

the operation of repeated addition

a principle that allows for the efficient counting of the total number of ways a task is accomplished when some number of parts follows a first part of the task. For example, how many outfits can you make using three shirts, two pants, and four shoes? The task is to make an outfit with three parts (a shirt selection, a pants selection, and a shoes selection).

elementary school: If you want to count the total number of ways a task can be completed that is accomplished through a series of parts, and you can select m ways to complete the first part, n ways to complete the second part, and g ways to complete the third part (etc.,) then you can efficiently count the total number of ways to accomplish the task by using the multiplication principle of counting. In this example, we would multiply m times n times g or (m • n • g) In the example above, we can count the total number of outfits by 3 x 2 x 4 or 24 outfits.

high school: let A1 and A2 be events with n1 and n2 possible outcomes, respectively; then the total number of outcomes for the sequence of the two events is n1 • n2high school: let A1 and A2 be events with n1 and n2 possible outcomes, respectively; then the total number of outcomes for the sequence of the two events is n1 • n2

an equation with three or more variables that can be graphed in three or more dimensions

the set of real numbers consisting of 1, 2, 3, 4, 5, 6, … (note: also referred to as counting numbers)

the values and statements required to find the solution to a problem

statements meaning not or the opposite of; for any given statement , its negation is the statement , ~ (not ) whose truth value is the opposite of the truth value of

a real number that is less than zero

vertices that share an edge (note: also referred to as adjacent vertices)

a two-dimensional representation of the surface of a three-dimensional figure

A network or vertex-edge graph consists of a collection of vertices and edges where each edge connects two of the vertices

a problem given without an application/story

a geometry that contains an axiom which is equivalent to the negation of the Euclidean parallel postulate (e.g., Riemannian geometry is a non-Euclidean geometry using the statement, “If

is any line and is any point not on

, then there are no lines through that are parallel to ” as its parallel postulate (also called elliptic geometry); and Hyperbolic geometry is a non-Euclidean geometry using the statement, “If

is any line and is any point not on

, then there exists at least two lines through that are parallel to ” as its parallel postulate

a sample selected using a biased method

word problems that include a model of a real life situation, focus on higher levels of interpretation,

are organized with no obvious solution, and that may require multiple problem solving strategies

geometric figures that are not in common usage but fulfill a given definition (e.g.,

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