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absolute value- The distance from zero. A number which has no sign.

abundant number - any number whose sum of its factors, excluding itself, is greater than itself.

acute angle - An angle which measures less than 90 degrees.

addend - the number to be added.

Addition Property - The rule stating that adding equals (of any value) to both sides of an equation or inequality will not change the relationship.

additive inverse - The opposite number on the number line which when added to a given number sums to 0.

adjacent angle - an angle which shares a common ray (or side) to the angle given.

adjacent side - the ray or side of an angle. In a right triangle, that side is called a leg. When one side is adjacent to another side they are both sides of the same angle.

algorithm - a procedure or set of rules which when applied in steps will result in the solution to a type of mathematical problem.

alternate exterior angles - A special angle pair formed by a transversal cutting two parallel lines; the angles appear on opposite sides of the transversal and outside the parallel lines. They are congruent.
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alternate interior angles - A special angle pair formed by a transversal cutting two parallel lines; the angles appear on opposite sides of the transversal and inside the parallel lines. They are congruent.
Picture

altitude of a triangle - A line segment which attaches the vertex or top angle to the base by forming right angles. In an obtuse triangle, the altitude must be drawn to the base, as extended. An altitude of a triangle is, by definition a perpendicular line segment. The altitude measures the height of a triangle. In a right triangle, the altitude is one of the legs. When a triangle is rotated the altitude changes, as does the base and vertex angle.

angle - Two rays which share a common endpoint will form an angle. Types of angles: Acute angle: less than 90 degrees. Obtuse angle: greater than 90 degrees, but less than 180 degrees. Right angle: measures 90 degrees. Straight angle: measures 180 degrees. Reflex angle: measures more than 180 degrees. Rotating a radius within a circle will map out all of these angles as the radius travels through a distance of 360 degrees from its initial starting point. A central angle is the angle formed by any two radii in a circle. Picture. 

angle bisector - A ray drawn from the vertex of an angle through the center which will subdivide the angle into two congruent angles.

angle pairs - Related angles in sets of two. There are several kinds of angle pairs with which you should be familiar: Complementary angles total to 90 degrees. Supplementary angles total to 180 degrees. Corresponding angles are formed by a transversal which will cut two parallel lines. These angles are on the same side of the transversal. In this case one angle is a translation type of transformation or "slide" of the other. Corresponding angles are congruent. Vertical angles are formed by the intersection of two lines. They lie opposite each other at the point of intersection. Vertical angles are also congruent. Congruent angles are angles which have the same measure in degrees. Picture

arc - A part of the circle measured in the same number of degrees as the angle formed by two radii attached to the endpoints of the arc.
 Picture

area - The amount of space, or the region within a two-dimensional, closed figure. It is measured in square units.

Some common formulas for area are:

Area of a parallelogram, rectangle, rhombus or square:  A= BH

Area of a square: A=s2

Area of a trapezoid: A= 1/2H(b1 +b2)

Area of a circle: A=pr2

Area of a triangle: A=1/2bh

arithmetic sequence - A special sequence where a constant is added to or subtracted from numbers in the sequence to arrive at the next consecutive number.  Example. 

Associative Property for addition or multiplication - A truism that states that the way addends or factors (the numbers in the addition or multiplication problem) are grouped or regrouped will not change the sum or product so long as only addition or multiplication is used singularly on the entire set of numbers. The associative property applies to all real numbers including signed numbers, but it cannot be used for subtraction or division problems.

average - Also known as the the arithmetic average or mean. The average of an ordered range of numbers tends to be in the middle of the group of numbers. It is therefore also known as a central tendency. Other measures of central tendency are the median and the mode. The arithmetic average or mean is arrived at by taking the sum of the numbers in the set and dividing by the number of items in that set.

average deviation - A statistic which measures how much the average of all the absolute values of the differences between measurements and the mean compares to the actual mean.

axes - x and y. In the coordinate system the perpendicular lines drawn through the origin. Singularly, they are referred to as the x and y axis. See also origin.   Picture.

 base - 1. A side of a geometric figure which lies flat on the bottom of the figure. In a two-dimensional shape, the location of the base is arbitrary, but in three-dimensional space figures, usually the base is a specific shape which lies parallel to a plane of reference. Some figures have two parallel bases.     Picture

2. In a numeration system the base tells us, in terms of place value, how many times greater each value to the left is in terms of the place value to the right. The place value is multiplied by the digit to find its value. In our base 10 system every place value to the left is 10 times as great as the place value to the right. Alternately, we can find the value of any digit by multiplying the digit shown by the base raised to the power of the exponent related to the place value. The number 101 in base 2 would mean 1 x 22 + 0 x 21 + 1 x 20.

3. In a shortcut system of denoting repeated multiplication of the same number, the number which is being multiplied. See also exponent.

bias - Influence on results. A biased sample is not fair.

binary operation - A logical operation between two numbers which will result in one answer. The operation may be complex. Max which finds the maximum number between two numbers is an example of a binary operation.

binary system - A number system depending on base 2.

bisect - To divide evenly into two congruent parts.

bisector - A line or ray which acts to bisect a figure.

box and whisker graph (plot)- A special graph which pictorially shows the median, upper and lower quartiles, and extreme points of a distribution.   Picture

capacity - The measure of how much can be held within a container.

cardinal number - A count of items in a set.

Cartesian coordinate - One of the values in an ordered pair of numbers on a two dimensional grid.

Cartesian coordinate graph - The grid which measures locations of points as an ordered (x,y) pair. The values in the pair are each called coordinates.

central angle - In a circle the angle at the center representing a portion of the circle set off by two radii.   Picture

chance- 1. The possibility  or likelihood of an event occurring, strictly by luck.   2. An opportunity which has an unknown likelihood of success. 

chord - A line segment which connects any two points on a circle. A diameter is the largest chord in a circle.  Picture

circle - A set of points mapping out a closed curve around a fixed point which is the center, all equidistant from that point.

circumference - The distance along the circle from a given point back to the same point. Circumference in a circle is similar to the perimeter of a polygon.     Picture

circumscribe - To place figure A around figure B so that the vertices of  figure B touch the sides of figure A.  A polygon may be circumscribed about a circle so that the sides touch upon the circle.  Examples

closed figure - A set of points in two dimensional space which, either straight or curved, will end where they begin and enclose a region or regions. A simple closed curve only has one region - the line drawn does not intersect at any point.    Examples

closure property - The rule that states that for a given operation on a set of numbers the result of the operation will yield a number which is in the original set. For instance, multiplication of all real numbers is closed since the result will always be a real number, but division of integers is not closed since some results are fractional and not integers.

cluster - An imaginary grouping of close ordered pairs on a grid which makes them appear to be more compact than pairs outside the cluster.  Picture

coefficient - A number placed before a letter or letters in an algebraic expression which will be multiplied by the numbers represented by the letters or powers of the letters which follow. In the expression 4X2, 4 is the coefficient.

coincide - To follow the same route or path. Two lines coincide when they have an unlimited number of points of intersection.

collinear - Being on the same line.

combination - A special arrangement where no repeats are allowed for all possible arrangements. A repeat is a choice of the same items in a different order. The notation used for combinations is: nCr , for n objects chosen r at a time.

commission - A kind of wage earned on sales pegged to the amount of the sales, usually in the form of a percent.

common denominator - When a smaller unit fractional part which can divide evenly a group of related fractions is identified, the lower portion of that fractional part. Since 1/3 and 1/4 can both be broken up into slices of 1/12, 12 is the common denominator.

common factor - a number which will divide evenly all the numbers in a set. All whole numbers have the common factor of 1. Another common factor between 12 and 8 is 4.

common multiple - Given separate listings of all the multiples of a set of numbers, those which are the same on each of the listings are known as common multiples. The least common multiple is the smallest number which is evident on all the listings. Common multiples for 3 and 4 would be 12, 24, 36, etc., but the least common multiple between 3 and 4 is 12.

Commutative Property - The truism that states that the order of a group of numbers which have the same operation, either addition or multiplication, will not change the result. Division or subtraction is not commutative. For instance: a + b = b + a; ab=ba. Also: If a + b +c = a constant, then a+c + b also equals the same constant.

compass - 1. A tool used for drawing arcs or circles. 2. A navigational tool which shows direction on a map. Picture

compatible numbers - Numbers which will divide more easily. We use rounding to create compatible numbers.

complementary angles - An angle pair totaling to 90 degrees.

complex fraction - A fraction which has more than one denominator. When we divide a whole number by a fraction, a fraction by a fraction or a fraction by a whole number, the full operation shown as a fraction is considered complex.

composite number - A number which has more factors (whole number divisors) than itself and one.

concave polygon - A polygon which has an angle or angles which are greater than 180 degrees. Parts of the figure appear to point inward toward the center. Diagonals drawn may be outside the figure.   Picture

cone - A solid figure which has a base as a circle and a curved surface tapering to one fixed point or vertex. A polyhedron with only one flat surface or face.     Picture

congruent - Exactly equal. Having the same size and shape. Congruent shapes have equal measures. There exists congruent line segments, angles, polygons, geometric shapes, and other objects or pictures.     Picture

congruent angles - Angles which have the same measure.

constant - A letter within an expression, equation or inequality which can take on one value only, the value of which will be ultimately known. Since constants are represented by letters, they are often confused with variables.

conversion - The act of changing a value to an equivalent form. Conversion ratios are ratios of equal numbers and components which can be used to multiply a value to achieve an equivalent value. For instance, since 1 foot = 12 inches, the conversion ratio 1foot/12inches can be used to multiply by any number of inches to change them to feet. Conversely, 12inches/1foot can be used to change feet to inches. The measurement to be converted must appear in the denominator.

convex polygon - A polygon which has all interior angles less than 180 degrees. The sides and vertices of the figure appear to point away from the center.     Picture

coordinate graph - See Cartesian coordinate graph.    

coordinate plane - The surface on which a grid is drawn with vertical and horizontal axes known as the x and y axes. The points within the grid are ordered pairs. See also Cartesian coordinate.    Picture

coordinates - The ordered pair of numbers which represent a location on an x-y grid. (4,3) are coordinates. Though each of the numbers in the parentheses are known as coordinates, the first number is the abscissa and the second number is the ordinate. See Cartesian coordinate.   Picture

coplanar - Lying in the same plane.     

corresponding angles - 1. An angle pair formed by cutting two parallel lines with a third intersecting line known as the transversal. These angles are on the same side of the transversal. In this case one angle is a translation type of transformation or "slide" of the other. Picture Corresponding angles are congruent.   2. When comparing two polygons, the matched angles which are exact copies from one to another of the polygons. Picture

corresponding part - A matched part of a congruent figure, either angle or side. Corresponding parts of congruent figures are congruent.

corresponding sides - Matched sides in polygons which are congruent.  These can be found between two corresponding angles.

cosine - One of the trigonometric functions describing an angle in a right triangle, which is a ratio of the measure of the side adjacent to the given angle compared to the measure of the hypotenuse.   Picture

counting number - One of the members of the set starting with the number one and increasing in value by 1 in order. This set is infinitely large.

cross products - In a proportion, the product of any number on the top and any number on the bottom. Since cross products in a proportion are equivalent, we can use the cross products to prove that two ratios are equal and form a proportion.

cross section - The face of a solid which has been cut by a plane.      Picture

cube - 1. The cube of a number is the number multiplied by itself and itself again. 2. A three dimensional shape in the form of a box with 6 equal flat faces in the form of squares.   Picture

curve - A finite set of points moving in a changing direction.   Picture

customary measurement - Units of measurement in the English System commonly used in the United States such as feet, pounds, miles, and ounces. Link to FunSchool Customary Measurement Dictionary.

cylinder - A polyhedron with two congruent parallel bases in the form of circles and a curved surface which is perpendicular to both bases.    Picture

data - Pieces of information or numbers.

decagon - A 10 sided polygon.   Picture

decimal - A number arrived at by dividing a whole numbers by powers of ten.

decimal System - A base 10 system in which every cardinal number shown in a place value takes on the value of the digit times a power of ten. Starting from the single digit's place which has a value of the digit times 100, the value of each digit to the left is 10 times as great. To the right of that number, each digit has a value 10 times less.

 

Power of ten

 

104

 

103

 

102

 

101

 

100

 

 

 

10-1

 

10-2

 

Place value

 

ten-thousands

 

thousands

 

hundreds

 

tens

 

ones

 

.

 

tenths

 

hundredths
deductive reasoning - Using known facts and intuitive or proven rules together to reach a conclusion.

degree - 1. A part of a circle or circles expressed as some fraction or multiple of 360 used for measuring angles. 2. A unit used to measure temperature.

denominate number - A number used in connection with a unit of measure such as the number 4 in 4 inches.

denominator - The divisor or bottom part of a fraction. It denotes the total number of parts available to that fraction. The numerator indicates the number of parts used.    Picture

density property - The situation existing whereby, between any two numbers on a number line, another point may be located and defined as another value. There are an unlimited number of values between any two values.     

dependent events - In probability, when the outcome of one event influences other concurrent or following events, the events are said to be dependent.

deviation - The amount of volatility in a distribution as measured by the differences between points in the distribution and the mean.

diagonal - A line segment drawn from one vertex of a polygon to a nonadjacent vertex.  Picture

diameter - In a circle, a line segment drawn from one point on the circle through the center to a point opposite. There are an unlimited number of diameters which may be drawn in a circle.      Picture

difference - The result arrived at by subtracting one number from another.

digit - A whole number between 0 to 9 used to represent the part value of a larger number. For instance, in the number 49, 4 is a digit in the 10's place. Digits are used to write numerals.

dilation - The transformation process of reducing or enlarging a figure into a similar figure.   Picture

direct variation - If in a relationship between two variables multiplying or dividing by a constant will leave the relationship the same then the numbers are said to be in direct variation. For instance if doubling the number of hours will double the pay then hours and pay are in direct variation. In direct variation the numbers may be shown in equal ratios. (y/x = k, where k is a constant). In indirect variation the numbers behave differently; muliplying one variable will change the other variable in the opposite direction (xy=k).

discount - The amount of reduction in the price of a good or service.     Example

disjoint set - In comparing the members of two or more sets, those members which are not on more than one listing.    Picture

distance - A measurement of how far one point is from another. In traveling, the distance traveled is always equal to rate x time (d=rt).

distribution - In statistics, the listing of numbers or arrangement of the numbers showing the relative positions of data points, describing the nature of the numbers being studied.    The set:  {3,5,7,9,10,14,22,36,48,57,80,99} could represent a distribution of numbers.

Distributive Property of multiplication over addition- A truism which states that the total arrived at by multiplying by the addends separately and then adding them is the same as the total arrived at by multiplying by the sum. The regions formed by multiplying can be considered areas. When a rectangle is subdivided, the areas formed by multiplying the parts is the same as the original area. Since subtraction is addition of signed numbers and division can be depicted by multiplying by the reciprocal, the distributive property will also hold for division or addition of signed numbers.   Picture   Examples

dividend - The number to be divided.    Picture

divisibility - The ability to divide numbers "evenly" so that there is no remainder.

divisibility rules - Shortcuts for determining (without performing the entire division) whether a given number can be divided by another number without resulting in a remainder. The common rules are as follows:

 

 

Number

 

Rule

 

2

 

The number to be divided is even.

 

3

 

The sum of the digits is divisible by 3. You may first subtract multiples of 9 before testing. You may also first delete combinations of digits which sum to 9.

 

4

 

The number represented by the last two digits of the larger number is divisible by 4.

 

5

 

The number ends in 0 or 5.

 

6

 

When testing, the rules for 2 and 3 both apply.

 

8

 

The number represented by the last three digits of the larger number is divisible by 8.

 

9

 

The sum of the digits is divisible by 9. You may first subtract multiples of 9 before testing. You may also first delete combinations of digits which sum to 9.

 

10

 

The last digit is zero. Also when the rules for 2 and 5 jointly apply.

division - A shortcut method of counting the number of repeated attempts at subtraction to reduce a number to zero, or some fractional amount of the original number (also known as the remainder).    Picture

Division Property - The rule stating that dividing both sides of a relationship by the same constant will keep the relationship intact. Though the Division Property clearly applies to equations, dividing inequalities by negative numbers reverses the relationship. Therefore, the division property doesn't really apply to inequalities, but must be modified for use by inequalities.   Example

divisor - In a division problem, the number which is being repeatedly subtracted from the number being divided. A factor of a number.  Picture

dodecahedron - A polyhedron that has twelve congruent faces in the form of pentagons.  Picture

domain - The set of items associated with one of the parts of a function or relation. The domain set normally applies to the values available to the first, independent variable. Example: In the relation {(4,3), (2,4), (3,8)} the numbers 4,2, and 3 are part of the domain.

edge - The line segment where two faces of a polyhedron meet.   Picture

elements - Members of a set.

empirical probability - A probability arrived at by comparing the outcomes in an experiment with all the possible outcomes in a sample or population. See also experimental probability.

empty set - Also known as the null set. A set which has no elements.  Example:  N={ } 

endpoint - The final point which is visible on a line segment or ray. Note that a line segment has two endpoints while a ray only has one.

equation - A true statement which states that two quantities (expressions) will have the same value. The quantities which may be in the form of any combination of numbers, variables and/or powers are joined by an equal sign. An equation acts as a "balanced scale" where measuring the quantities on both sides of an equal sign on a scale, would result in the scale adjusting to equal heights.

equilateral - Having all equal sides. Polygons are equilateral when all of the sides have equal measures.

equivalent expressions - Expressions which, when evaluated using the same substitutions, have the same value.

equivalent fractions - Fractions which have the same value or can be depicted by the same size region based on the same size whole.  Picture

equivalent numbers = Numbers which can be converted, but not changed in value, to make them equal.

equivalent ratios - Ratios which have the same value. Two equivalent ratios make up a proportion.

equivalent sets - Sets having the same number of elements. The elements need not be exactly the same in each set.  Example:  {4,5,6} and {2,3,4} are equivalent sets because they both have 3 elements.  

estimate - A rough "guess" as to a count or the result of an operation or series of operations. An approximation in a problem.

estimation - The process of a using estimates to arrive at a solution.

Euclidean geometry - The basis of geometry devised by Euclid in his book on The Elements which bases the representation of our universe on certain premises or postulates.

evaluate - Literally, to find the value of an expression by substituting known values for the variables.

even number - One of the members of the set of whole numbers which, when divided by 2, leaves no remainder.

event - 1. An outcome of an experiment or trial.  2. An alternative situation.

expanded notation - The form of a number which shows the place value of each digit as a power function using the base and exponent associated with the place value. The number 567 in expanded notation would be 5 x 102 + 6 x 101 + 7 x 100. Expanded notation differs from scientific notation, because in expanded notation each digit is treated separately in determining its value, while in scientific notation, the value of the entire number is expressed as a multiple of base 10. Sometimes expanded notation is written without using bases or exponents, in which case the number 567 would simply be 500 + 60 + 7.

experimental probability - Also known as empirical probability. Finding a probability by analyzing results of repeated attempts of a situation or experiment. The outcomes may or may not be random. The probability is arrived at by a ratio which compares the number of successful outcomes to the total number of trials (also known as the sample space).

exponent - In the shorthand representation of a repeated number of multiplication of the same number, the number of times that the number is multiplied by itself. The exponent is shown in superscript. In the number 64, 4 is the exponent and 6 is known as the base. The number, if expanded, would be 6 x 6 x 6 x 6.

Exponent Property - The rule which indicates that the result of modifying equivalent parts of an equation by using the same power or root will not change the relationship. Be aware that taking the square root of an equation results in two inverse solutions . Example: if x2 = 16 then x = -4 or +4.

exponential growth - In a graph of a relationship, where the increase of one variable is related by an exponent to the increase of the other. An example of an equation showing exponential growth could be in the form of y = ax2, where a is a constant.

expression - A grouping of numerals, variables and exponents with operations to arrive at one result without indicating how the total value relates to other predefined quantities or expressions.  For example,   3X + 7  is an expression.  Note that it is not set equal to, greater than, or less than any quantity.

exterior angle - In a polygon, the angle formed on the outside by extending one of the sides.   Picture

extremes - 1. In a proportion, the top left number and the bottom right number.  Picture    2. In an ordered distribution of numbers, the values which are highest and lowest. When points in the distribution are plotted on a scattergram, the extremes may appear as outliers.
Picture

face - A flat surface area of a solid geometric figure.   Picture

factor - A whole number divisor of a number.    

factor tree - A branch type picture which depicts smaller and smaller factors until prime factors are shown at the bottom. Since there are alternate choices to factors chosen on each line, not all of the composite factors of a number may be visible. All composite factors though can be arrived at by multiplying combinations of the prime factors shown.  Example

factorial - The result of an operation which continually multiplies a number by 1 less until the number multiplied is 1. 4 factorial, denoted by 4! means 4 x 3 x 2 x 1.

fair event - An event that has a likelihood of occurring that is equal to all other possible alternative events.

Fibonacci Sequence - A famous sequence which uses any two consecutive numbers to arrive at the next number in the sequence. The sequence starts with two 1's.   {1,1,2,3,5,8,13, 21, etc}

finite Set - A set which contains a known quantity of members or elements.   

flip - A common name for a translation which involves reflection. The image is turned over about a given line so that a mirror image appears. In this transformation, the size and shape remain the same. The orientation, though will change.    Picture

formula - A way of symbolically showing an algorithm or procedure using variables.

fraction - A operation of division depicted as one number over another, separated by a bar. A portion of a whole where the denominator indicates the number of parts in the whole and the numerator indicates the number of parts used in the portion.    Example

fractional number - A number which can be shown as a fraction. Note that all decimal numbers are by their nature fractional numbers since they can be changed to fractions.

frequency - The number of times that a number or item appears on a listing of data.

frequency graph - A pictorial representation of various intervals, or specific numbers, and frequencies for the data used. A frequency graph looks like a bar graph, but the bars are connected.   Picture

frequency table - A chart which shows the frequencies for specific numbers or intervals of numbers from a data listing. It is an organized way to group the data, usually arrived at by first tallying like numbers or numbers which appear within the chosen intervals. This can also be used to count the number of times certain events occur.     Picture

front-end rounding - An estimation process by which the digits to the right of a numeral within a number are replaced by zeros. See also rounding.

function - A relationship between two sets of data, one of which is the input data of the independent variable and the other of which is the output data of the dependent variable. A function can be shown as a set of ordered pairs of independent and dependent numbers where the same independent variable may not be linked with two different dependent variables. Example:  {(4,3), (-4,3), (4,4)} may be a function, whereas {(4, 3), (4, -3), (4,4)} can't be a function.

functional relationship - A relationship where one variable has a unique link to a second variable.

Geometric sequence - A special sequence where each next number in the sequence is arrived at by multiplying or dividing the preceding number by a constant.  Example:  {4,20,100,500,2500, etc.}

Geometry - The study of two-dimensional and three-dimensional representations of figures and shapes. It is a method of depicting real-world relationships between points, lines, rays, angles and planes.   See link.

Golden Ratio - A relationship discovered by the Greeks expressed as the ratio of 1.61 to 1. This relationship occurs when certain measurements in nature and in architecture are compared. Like Pi, it is considered a geometric constant.   

gram - A standard metric measurement unit for a small mass. In measuring mass, it measures "how much" of a substance there is. It does not measure weight, as many people believe, since weight is the effect of gravity acting on mass.

graph - An orderly representation of data in the form of a picture, usually on a grid.

greatest common factor - (see also factor) In listings of the factors of two or more numbers, the largest number to appear on all the lists. In some cases the Greatest Common Factor, also known as GCF, may be one of the smaller numbers for which a factor listing has been compiled. The GCF may be recognized with experience without actually compiling the lists. Example: The GCF of 6, 12 and 18 is 6 since 6 will appear as a factor in a factor listing for 6, 12 and 18 and it will be the biggest number to appear on all three listings. Note that every number has itself as a factor.

grid - A series of parallel horizontal and vertical line segments, equally spaced, which make up equal size squares.     Picture

half-turn - A rotation of 180 degrees.     Picture

height -  In a geometric figure, the distance as measured by a  perpendicular drawn to any of the bases of the figure. 

hemisphere - Half of a sphere.   Picture

heptagon - A polygon having 7 sides.    

hexagon - A polygon having 6 sides.

histogram - A special bar graph which depicts a frequency distribution.  Picture

horizontal - Lying in a side to side position parallel to the bottom of a given orientation or base line.

hypotenuse - In a right triangle the side which lies opposite the right angle. It is the longest side of a right triangle. If the measure of the other sides, or legs, of the triangle are known, the measure of the hypotenuse can be determined using the Pythagorean Theorem.  Picture

icosahedron - A polyhedron with 20 flat faces in the form of triangles.  Picture

identity element - That which when added to or multiplied by a number results in the same number. In addition the identity element is 0. In multiplication it is 1. Adding or multiplying by an inverse number will result in an amount equal to the identity element. 

Identity Property of 0 or 1. The property that states that adding 0 or multiplying by 1 will result in the same number.

imaginary numbers - A set of numbers which are multiples of negative roots. These numbers have no basis of measurement within Euclidean Geometry.   Examples

improper fraction - A fraction wherein the numerator is equal to or larger than the denominator. An improper fraction can be changed to a whole or mixed number.

independent events - In probability, two or more events in which the outcome of one in no way influences the outcomes of the others.

indirect measurement - Using formulas and properties to find the measurement of objects without resorting to measuring tools.

indirect or inverse variation - If, in a relationship, multiplying one variable by a constant will result in the other variable being divided by the same constant, then the numbers are in indirect variation. The product of the variables will always equal a constant. For example, the number of hours you watch television may have an inverse affect on your grades. This would be represented where H=hours, and G= grades as HG= k, k being a constant.

inductive reasoning - Expanding upon given facts by interpolation or by forecasting to come to a conclusion.

inequality - A relationship between two expressions or values which are not entirely equal to one another.   Examples

infinite - Unending. There is no limit. The limit is so small or large so as to be indeterminable.

infinite set - A set of items or numbers which has so many members that they can not be counted or whose number of elements is so large as to be indeterminable.

infinity - A location, number or boundary which has infinite qualities.

input - A number which is associated with the independent variable of a function.

inscribe -  To place figure A into figure B so that the vertices of figure A touch upon the sides of figure B.   A polygon may be inscribed within a circle, such that the vertices are on the circle.   Examples. 

integer - A whole number or it's opposite. The set of integers includes all positive counting numbers, the negatives of those numbers and zero.

interest - The cost of money paid for the privilege of waiting to receive the money in return. The amount earned on a loan or deposit. The amount which earns the interest is called the principal.

interior angle - One of the angles within a polygon.   Picture

interpolation - Extending a model to predict further outcomes.

intersecting lines - Lines in the same plane which cross.   Picture

intersection - The point at which two lines, rays, line segments or planes cross or meet.

intersection of sets - Those elements which are in common to more than one set.  Example

interval - 1. The specification of the range of numbers used within a section of a graph. 2. A section of a chart with a range of numbers.

inverse - Additive or multiplicative. The number which when added or multiplied by a given number results in the identity element. Also the operation which is opposite. Subtraction is the inverse operation of addition, while division is the inverse operation of multiplication.

inverse variation - See indirect variation.

irrational number - A number, or symbol standing for a number, which can be changed to a decimal which neither terminates or repeats. Any number which can not be shown as a fraction, whether proper or improper.  Example

isosceles triangle - A triangle which has two equal (congruent) sides. As a result, the base angles will also be congruent.   Picture

kite - A quadrilateral which has two adjacent pairs of sides which are equal. A kite has one line of symmetry.    Picture

lateral - Literally, on the side. A lateral face is one which is not considered one of the bases.

latitude - A measure of distance north or south of the equator in degrees. Lines of latitude are parallel to the equator.

Least Common Denominator - Also known as the LCD. When trying to compare fractions, the smallest multiple denominator shown as a unit fraction representing the largest size piece which will divide each of the fractional pieces evenly. Once the LCM of each of the denominators tested is known, then that is equivalent to the LCD.

Least Common Multiple - When listing common multiples of numbers the first number to appear on all the lists. See also Common Multiple. The LCD is arrived at by finding the LCM for the denominator parts of the fractions.

legs - In a right triangle, the sides which are not opposite to the right angle. The side opposite the right angle is, of course, the hypotenuse.  

like fractions - Fractions which have the same denominator.

line - A set of close points extending endlessly in opposite directions.  Picture

line of best fit - An approximation of where a line may be drawn on a scatter plot to go through most of the centers of clusters of data, thus subdividing the points into approximately two regions of equal numbers of data.

line of reflection - An imaginary line placed in the center of two symmetric images or figures. Corresponding points on the congruent "mirror images" are equidistant from that line.    Picture

line of symmetry - An imaginary line, like the line of reflection which will divide any image or group of images into two corresponding parts, each of which is a congruent "mirror image" of the other. If you folded a paper containing the image or images on this line, they would exactly fit on each other. Picture

line symmetry - A figure is said to exhibit line symmetry if it can be folded somewhere within the figure on an imaginary line of symmetry resulting in two mirror images.  For example, the letters B, C   and D have horizontal line symmetry, the letters A,  M and Y have vertical line symmetry, and the letters H, I, and X have both. 

line plot - A graph which shows repeated numbers as points or crosses above a number line.  Picture

line segment - A portion of a line. Since a line segment is finite, it has two endpoints.   Picture

linear equation - An expression of a function or relation, which, if plotted on a coordinate graph, would be in the form of a straight line. The equation, by it's nature has no exponents or powers. Linear equations in X and Y are in the form of Y=mX +b, where m stands for the slope of the line, when plotted, and b is the y-intercept.

linear measure - The measurement of the distance between points. Also known as the length.

liter - A standard measurement unit in the metric system for measuring liquid capacity.  It is roughly the size of a quart. 

logic - Using reasoning, either inductive or deductive, to arrive at a conclusion from partial information.

longitude line - An imaginary line running North and South around the globe and measured in degrees east or west from the main longitudinal line known as the Prime Meridian.  Picture

lower quartile - In an ordered data distribution, the midpoint value between the lowest, extreme value and the median.  It makes no sense finding this point for ungrouped data and the actual calculation for grouped data is laborious. 

lowest terms - A fraction is said to be in lowest terms when it is not possible to find any number which will divide the numerator and denominator evenly.

magnitude - Size of a number relative to a number line. The property which measures how big or small a number is.

mean - Also known as the arithmetic average or average. The mean tends to be in the middle of an ordered distribution of numbers, much like the median, so that both are called measures of central tendency. It is one singular measure which is typical of all the data, by nature of it being in the center. The mean is computed by taking the sum of all the numbers in the listing of data and then dividing by the total number of items in the listing. It is inappropriate to average means, unless the two listings being averaged have the same number of items. For this reason the mean of more than one listing sorted together is the weighted average of the individual listings.

means - In a proportion, the bottom left number and the top right number.  Example

measure of central tendency - One of the statistical measures which includes mean, median and mode. Each of these tends to be in the center of an ordered distribution.

measurement - The process of determining the mass, capacity, area, time or distances of unknown quantities or situations. Measurement answers the questions "how much?", "how many?" "how far?" or "how long". There are presently two measurement systems used in the world, customary measurement (Also known as the English System) and metric measurement. Customary measurement is little used in most parts of the world. Link to FunSchool  Measurement Dictionary.

median - 1. A measure of central tendency of an ordered listing of data. The middle number of an ordered set of data, or, in an distribution of an even number of items, the middle or average of the two middle numbers.   In ungrouped data the median is the (n+1)/2 number.   In grouped data, it is simply the n/2 number.    2. A line drawn from a vertex in a triangle to the middle of the opposite side. The median of a trapezoid connects the two midpoints of the lateral sides (non parallel, non bases) of the figure.  Picture

mental math - Using estimation, algorithms, and a common sense approach to find the solutions to mathematical problems without using pencil and paper or electronic instruments.

meridian - A line of longitude.

meter - A standard measure in the Metric System for distance equal to just over a yard.

metric system - A system of measurement based on the base 10 system. Units for similar types of measurement are related by prefixes such as kilo (1000 times), deci (1/10), centi (1/100) and mili (1/1000). Link to FunSchool  Measurement Dictionary.

midpoint - A place on a line segment which divides the line segment into two congruent halves.  Picture

mixed numeral - A number which can be represented in two parts as a whole number and a simple fraction or decimal number.  Ex:  3 1/2  can be shown as the whole number "3" and the fraction "1/2" or ".5". 

mode - In an ordered distribution of numbers, the number which appears the most frequently.

multiple - A number arrived at by repeatedly adding the original number, or by multiplying it by a whole number.

multiplication - A shortcut method of adding repeatedly.

Multiplication Property - A rule that states when we multiply a relationship (such as an equality or inequality) by a constant, the relationship remains unchanged. Note, that although this is entirely true for equations, when inequalities are multiplied by negatives, the relationship is reversed.

multiplicative inverse - See also inverse. The reciprocal of a number. A number which when multiplied by the given number results in the identity of 1.

mutually exclusive events - Events which can't occur simultaneously.

natural number - Basically, a counting number.

negative - Opposite. Negative numbers have subtraction signs in front of them denoting that they are less than zero. The more negative a number the smaller the number.

negative correlation - A relationship shown on a scatterplot where an increase in one variable results in a subsequent decrease in the other.    Picture

negative integers - the subset of integers which have negative signs in front. They are all opposites of whole numbers.

negative slope - A slope where the line on which the slope is based goes from the upper left to the lower right of the grid.   Picture

net - a flat representation of all of the faces of a solid figure, which can be cut out and attached to form the figure.   Picture

nonagon - A nine-sided polygon.  Picture

number - A symbolic representation for a quantity or count.

number line - A listing of numbers horizontally at appropriate intervals depending on quantity represented. The points along the line correspond to real numbers, whether they be positive, negative, fractional, or even irrational.     Picture

number sentence - Basically, an equation without variables.   Ex:   3 +4 = 7

numeral - A symbol used to represent the number of units in a place value of a number.   For instance, the 5 in 56 is a numeral representing 5 tens. 

numeration system - An organized set of numbers, operations and relationships such that standard arithmetic may be utilized.

numerator - The top part of a fraction. The number of parts of the whole used for the fraction.  Picture

numerical or number expression - An expression which has only numbers and no variables.  For example,   6(3+2) is an expression, although somewhat complicated.   This is equivalent to  6x3 + 6x2 which is also an expression.  

obtuse angle - An angle with a measurement more than 90 degrees, but less than 180 degrees.   Picture

obtuse triangle - A triangle having an obtuse angle.

octagon - An eight-sided polygon.     Picture

octahedron - A polyhedron with eight faces, each in the form of triangles. Picture

odd number - Any whole number which is not evenly divisible by 2. An odd number may be represented by 2n -1 where n is any whole number.

open sentence - Any equation or inequality containing variables. Example: 4x +3>5 is an example of an inequality which is an open sentence.

opposite -1.   On a number line,  a number which is in a different direction by the same distance from zero. Example:  The opposite of +5 is -5.   2. The negative of something.  Example: The opposite of yes is no.   3.  A direction which is the exact reverse of the original direction.  Example.  The opposite of north is south. 

order of operations - PEMDAS - The agreed upon order in which operations are completed to work out a problem. Parentheses are done first, followed by exponents, then multiplication and division in order from left to right, followed by addition and subtraction, also in order from left to right. A fraction bar is an operation left for last.

ordered pair - Two numbers which represent vertical and horizontal components on a Cartesian coordinate plane. The numbers show the distance from the center of the grid known as the origin.

ordinal number - The number which names the position or place of an number. For example "seventh" is an ordinal number.

origin - 1. The point (0,0) on a Cartesian coordinate grid.

outcome - 1. The way something can happen in a probability experiment. A possible result.  2. The result of an experiment that offers alternative results. 

outlier - A data point which is not indicative of most of the members of the distribution, by virtue of it being too large or too small.     Picture

output - The number associated with the independent variable of a function.  Picture

palindrome - A number or word which can be read the same backwards as forwards.

parallel lines - Lines which can never meet. They are by definition equidistant at all locations along the lines.  Picture

parallel planes - Planes which do not intersect.   Picture

parallelogram - A quadrilateral with two pair of opposite sides equal and parallel.  Picture

Pascal's Triangle - An arrangement of numbers in the form of a triangle starting with 1 and having a number below equal to the sum of the two numbers above it. This device, is used to demonstrate various sequences and patterns, but each line can be used to find combinations in probability.  Picture

pentagon - A five-sided polygon.  Picture

per - A word which often is associated with a fraction bar in a ratio or the dots of a ratio. It is one way of making the comparison between two parts of a ratio.

percent - A representation of a fraction in hundredths. A part of one hundred.

percent change - A ratio between the amount of change over the original expressed as a percent.

percentage - The relationship between two numbers where one is a percent of the other. Baseball percentages are given in thousandths instead of hundredths.

percentiles - The delineation of a set of ordered data in terms of 100 equal parts.

perfect square - A square number whose factors (roots) are integers.

perimeter - The measurement of the distance around the outside of a figure or space. Also the actual boundary limits of a open area.

period - A grouping of three numerals separated by commas in a large number. Visualizing numbers from the right, we experience the units' period, then the thousands' period, the millions' period, billions' period and so on.

permutation - An arrangement which considers all possible outcomes including those which have the same items, but in a different order.

perpendicular - Meeting exactly at right angles.   

perpendicular bisector - A line which is perpendicular to another line and which divides it into two equal measures.

perpendicular lines - Intersecting lines in the same plane which meet at right angles.  Picture

Pi - The Greek letter which represents the irrational number which is the ratio between the circumference and the diameter of any circle.

pictograph - A graph which has pictures by legend representing  quantities of items.

place value - A position of a numeral in a number which implies the value of the numeral.

plane - A never-ending flat surface area.

plane figure - A geometric shape which only has two dimensions and lies in one plane.

point - A position in a plane represented by a dot. In actuality, a point has no dimensions and can not be seen.  Picture

polygon - A simple closed figure with straight sides.   Picture

polyhedron - A three dimensional shape with intersecting flat faces. It is also known as a type of solid or space figure since it encloses a three-dimensional region. Though a cylinder, for instance, is a type of space figure, it is not a polyhedron since it has some curved surfaces.  Picture

population - 1. All of the items in a set from which a sample can be chosen.  2. All of  the items, people or things  under consideration in an experiment or survey.

positive correlation - A relationship in data where a line of best fit would rise from the lower left to the upper right of the scatter plot.     Picture

positive integer - A number which is a member of the set of whole numbers being greater than or equal to zero.

power - An expression which contains an exponent.

precision - An expression of the accuracy of a measurement.

Prime Meridian - An imaginary line going north and south through Greenwich, England agreed upon to be 0 degrees longitude.

prime factor - A factor of a number which is a prime number.

prime factorization- A method by which a number is subdivided into all of its component prime factors.

prime number - A number which only has two factors, namely itself and one. A prime factor of a number is one of the factors which is a prime number.

principal - The amount loaned out or invested to earn income.

principal square root - The positive square root of a number. Note that each non-negative number will have two roots, one positive, one negative with the same numerical value.

prism - A polyhedron with at least 2 parallel, congruent, flat faces. The lateral faces are in the form of parallelograms.   Picture

probability - Possibility. The chance that an event or events will occur, usually expressed as a fraction or percent. Probabilities are, by their nature between or equal to 0 and 1. A zero probability means an event is impossible, while a probability of 1 means certainty.

product - The result arrived at when numbers are multiplied together. The numbers so multiplied are called the factors.

profit - What is left over after all expenses are subtracted from all income. The amount of money earned by a company or individual.

proportion - An equation consisting of two equivalent ratios or fractions. A proportion can also be stated as an analogy: A:B=C:D where B and C are considered means while A and D are extremes. In a true proportion, the product of the means always equals the product of the extremes.

protractor - A tool used for measuring angles in degrees.   Picture

pyramid - A polyhedron with triangular sides which taper to one vertex and a base which is in the form of a polygon. A triangular pyramid has a triangular base. It is also called a tetrahedron.  Picture

Pythagorean Theorem - A proven premise which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. Usually the theorem is stated by formula as a2 + b2 = c2 where the letters a and b arbitrarily represent the measurements of the legs and c is the measurement of the hypotenuse.   Picture

quadrant - A fourth of a grid which is the region between the two axes of a Cartesian Coordiate Graph.
Picture

quadratic equation - An equation in the form of y=ax2 +bx + c, where a, b and c are constants.

quadratic formula - The formula used to solve for all types of quadratic equations.  

quadrilateral - Any of the types of four-sided polygons. Types of quadrilaterals include parallelograms, trapezoids, kites, rhombi, rectangles and squares.  Picture

quarter turn- A rotation of 90 degrees.    Picture

quartiles - The breaks which divide a set of ordered data into 4 equal amounts of items.    

quotient - The answer to a division problem.   Picture

radical - 1. A number which is arrived at by finding two or more equal factors for the number which appears inside the radical or root sign. 2. The number which represents the root of another number.

radical sign - The symbol which represents an operation of finding equal factors for a number. When the radical sign appears without any subscript number attached, it is assumed to be the square root function.
Picture

radius - A line drawn from the center of a circle to a point on the circle depicting the distance from the inside to the outside. There are an infinite number of radii in a circle.   Picture

random - Chosen by chance. Unbiased and naturally occurring without any intentional selection. Random samples lead to fairly predictable outcomes in experiments.

random number table - A table of values which has been set up by a computer so that every number has an equal likelihood of having been generated by the computer and there are no intentional patterns or relationships in the table.

range - 1. The difference between the greatest and smallest numbers in an ordered set of numbers. 2. The set of numbers which can be used to substitute for a dependent variable in an equation. The solution set in a problem is chosen from the range.

rate - A special ratio which compares two related values such as distance and time. Most rates are shown as unit rates where the denominator is 1. The rate of speed is found by dividing distance by time.

ratio - A comparison between two numbers normally expressed as a fraction.

rational number - A number which can be converted to a fraction. Note that any repeating or terminating decimal is by nature a rational number, since it can be converted to a fraction.

ray - A set of close points beginning at a fixed point and extending endlessly in a straight direction. Picture

real numbers - The set of numbers which include all values and representations of values, whether rational or irrational, which can be shown on a number line. When a distance is associated with a real number, it can be measured either directly or indirectly. Numbers which are not real are called imaginary numbers and they do not represent actual measurements within Euclidean Geometry.

reciprocal - The multiplicative inverse of a number. When a number is represented as a fraction, we arrive at the reciprocal by switching the numerator and denominator. The product of two reciprocals is 1.

rectangle - A parallelogram with a right angle. (Actually, it will have 4 right angles and opposite sides equal and parallel)    Picture

rectangular prism - A box having 6 rectangular faces.   Picture

reflection - A transformation, usually on a grid, in which the new figure appears to be a mirror image being congruent but having the opposite orientation. Also commonly known as flip.  Picture

reflex angle - An angle with a measurement greater than 180 degrees but less than 360 degrees. Picture

region - A space enclosed by line segments as boundaries which will form a simple closed curve.  
Picture

regular polygon - A polygon whose sides and angles are congruent.   A square is a good example of a regular polygon.  A rhombus would not be regular, since it does not have congruent angles. 

regular polyhedron - A polyhedron whose faces are all congruent polygons.  A tetrahedron is a good example of a regular polyhedron. 

relation - A correspondence between two sets of numbers or data, usually expressed as ordered pairs.

remainder - When carrying out the process of division, the number which will be left when you have divided the dividend by the divisor the maximum number of times.

rename - 1.To change the numerator and denominator of a fraction by a constant multiplier in order to change the appearance of the fraction without changing its value. 2. To change a mixed number to an improper fraction or vice versa.

repeating decimal - A decimal number which has the same numeral or sequence of numerals continuing infinitely at the end.

rhombus - A parallelogram with all equal sides.   Picture

right angle - An angle which has a measure of exactly 90 degrees.  A right angle is commonly marked with a box at the vertex.  

right triangle - A triangle which has one right angle.  Picture

Roman numerals - Symbols used by the Romans for counting and representing numerals and their place value.   Ex:  XXIV   stands for the number 24. 

root - The factor which multiplied a specified number of times will result in the number from which you want to extract the factor. The square root is one of two equal factors of the number in question. A cube root would be one of three equal factors of the number in question.  For example, the number 125 has a root of 5 since 53 is 125.   The square root of 25 is 5. 

rotation - Also known as a turn. A transformation of a figure, usually on a grid, in which each point in the figure is moved along an arc around a fixed point for a fixed number of degrees.   Picture

rotating - The process of producing a rotation figure.

rotational symmetry - A circumstance exhibited by two figures, one of which has been transformed into the other by rotating through an angle less than 360 degrees.

rounding - An estimation process whereby a numeral in a specified place value of a number is changed by increasing or decreasing it's value by 1 unit, based on whether the next digit to the right is under 5 or 5 and over. In the case of under five, the digit value is decreased. In the case of 5 and over, the digit value is increased. In the special case of front-end rounding, also known as truncation, the digits to the right of the number are simply disregarded by zeroing them out.

sample - A subset of items chosen from a population. A random sample is one that is chosen so that each choice has an equal likelihood of ending up in the sample.

sample space - All of the possible outcomes as indicated by an exhaustive listing or tree diagram.

scale drawing - A drawing of an object such that the distances are reductions or enlargements by a constant amount, and proportionate to the original object. A scale model is a three-dimensional representation of the same type of scaling process.

scale model - See scale drawing.

scalene triangle - A triangle which has no equal sides, and therefore no equal angles.  Picture

scaling factor - In a proportionate relationship involving similar figures, the common multiplier which can be applied to both the numerator and denominator of one ratio to produce an equivalent ratio which relates to the corresponding sides of a dilation of a figure.

scatter plot or scattergram - The representation of a distribution of data numbers as a series of ordered pairs or points on a grid. The pattern may show clusters of data as well as extreme values known as outliers.

scientific notation - A way of representing a number as a power of 10. The first significant digit is used, with all other digits changed to a decimal. It is then multiplied by 10 to the power necessary to change the number back to its original form.

sector -  A wedge that represents a portion of a circle, much the same as a piece of a pie.  

semicircle - Half of a circle.

sequence - A pattern of numbers, objects or pictures in which a rule is consistently followed in progressing from one item to the next.

set - A collection of numbers, letters, figures, objects or things. Each item is called an element.

signed numbers - Positive and negative numbers. Note that signed numbers also include fractional numbers with signs and zero.

significant digits - The non-zero digits of the number which represents a measurement. In scientific notation, the decimal must appear after the first significant digit.

similar - Having the same shape, but not the same size. In similar figures, the corresponding angles are the same and the corresponding sides are in proportion.  Picture

simple closed curve - A closed curve which encloses only one region. The lines which make up the curve do not intersect.  Picture

simple interest - Interest which is computed by using a set rate over a fixed amount of time as a one-shot computation on principal.

simplest form - A fraction which has been reduced such that numerator and denominator are not concurrently divisible by anything greater than 1 is said to be in simplest form.

simulation - A modeling of an experiment or process.

sine ratio - In a right triangle the ratio which compares the measurement of the side opposite a given angle with the hypotenuse. A sine ratio exists only in connection to a particular angle of the triangle.
 Picture

skew lines - Lines in different planes which do not intersect.  Picture

slide - The common expression for a translation. Movement of a figure on a grid in a horizontal, vertical or diagonal direction.   Picture

slope - The steepness of a line as measured by the rise over the run. A ratio which compares the vertical component with the horizontal component of a line on a grid.   Picture

solid figure - Any geometric three dimensional shape.

solution Set - The elements represent the solutions to the problem or number sentence.

space figure - A solid figure enclosing a three-dimensional region or space. See Link.

speed - Also known as rate of speed. See rate.

sphere - A space figure in which every point on the outside is equidistant from the center of the figure.
 Picture

square - A rectangle with all equal sides or a rhombus with right angle. A square has 4 congruent sides and 4 congruent angles. The diagonals drawn in a square, are perpendicular bisectors of each other.  Picture

square number -A number arrived at by multiplying two equal numbers. The numbers need not be integers, but it is not appropriate to consider numbers other than integers and decimal numbers as being square numbers. Normally this term is analogous to a perfect square, but there are square numbers like 1.21 which are not perfect squares.

square root - One of two equal factors of a number. A number which multiplied by itself yields the number from which the root is to be extracted. Visually, if you imagine a square with an area inside, the side of the square which results in that area would be the positive square root. Note that there are actually two square roots of a positive number, one positive and one negative. Negative numbers do not have square roots as real numbers, but are considered imaginary.

standard - A measurement guide which is agreed to be the absolute example of a particular unit of measure and upon which other instruments of measurement will be based.

standard form - Expression of a number in the usual manner without resorting to any expansion of parts of the number.

standard measurement - Also known as customary measurement.

standard deviation - The amount of variation displayed by a distribution of numbers which compares the dispersion of the numbers to the location and magnitude of the mean.

statistic - A number which relates an observation about a set of data, or compares more than one set of data. It can measure the center or dispersion of a set of data, or it can compare two related statistics from two sets of data. You can, for instance, test two means to see if it is likely that they originate from the same population. Commonly used statistics are the mean, median, mode, range, variation and standard deviation.

Statistics -1. The study of interpreting data and relationships within a set of data, or between related sets of data, by using formulas, charts and graphs. 2. Plural for statistic.

stem-and-leaf plot - A graph which shows all of the numbers in a distribution by showing the first part coupled with the rest. Example: The numbers 11,12, and 13 might be shown with a stem of 1 and leaves of 1,2 and 3.   Picture

straight angle - An angle with a measure of precisely 180 degrees.    Picture

string - Any sequence of numbers treated as one unit.

subset - A smaller grouping within a set of numbers. The grouping can contain all, some or none of the elements in the original set.

subtraction - The process of taking away one number from another to arrive at a result called a difference.

Subtraction Property - A rule that states that in a relationship, either equality or inequality, subtraction of equals from both sides does not change the relationship.

sum - The result when two or more numbers are added.

supplementary angles - An angle pair which together total to 180 degrees.  Picture

surface area - A measurement of all of the areas of all of the faces of a space figure.

survey - A procedure whereby information about a topic or population is obtained through a questionnaire.

symmetry - The condition which exists when the parts of a figure appear to correspond in such way that two opposite, extreme points are the same distance from the center or imaginary line. Parts of this figure will appear as either reflections or rotations.    Picture

symmetric figure - A shape which exhibits symmetry. Line or point symmetry will divide this figure into two or more congruent parts. In the case of point symmetry, the figures will be rotations. In the case of line symmetry, the figures will be reflections.

tangent - 1. A line drawn to the outside of a circle, touching at only one point.  Picture    2. In a right triangle, the Tangent is the ratio which relates the side opposite an angle to the side adjacent, for a given angle. Knowing a tangent ratio allows someone to determine the angle measure by comparing to a table value or by using a scientific calculator, since the ratio is constant for any size triangle.    Picture

term - One of the numbers in a sequence.

terminating decimal - A normal decimal number which has a finite number of digits.

tessellation - A drawing resulting from tiling a plane completely without allowing any spaces, overlaps or gaps between the figures used.     Picture   Example Lesson and Information. 

tetrahedron - A polyhedron with 4 flat, congruent, equilateral, triangular faces.   This is one of the regular polyhedrons.  Picture

theoretical probability - See empirical probability.

topology - The branch of mathematics which studies transformation of solid objects by stretching, folding, shrinking or otherwise distorting parts of the figure resulting in an equivalent shape.

transformation - A change in a figure by movement or by size. Transformations may be translations, rotations, dilations, reflections or a combination or these.

translation - A transformation which moves in one direction in a plane, either horizontally, vertically or diagonally.   See slide. 

transversal - A line which can be drawn across and intersecting two or more parallel lines.  Picture.

trapezoid - A quadrilateral which has one pair of parallel sides. Each of these sides is called a base.
      Picture

tree diagram - A method of depicting all possible outcomes or arrangements using a branching network of line segments.   Picture

trial - One experiment resulting in one outcome.

triangle - A three sided shape (polygon) within a plane. There are several types of triangles, classified, based on sides or angles.   Picture

According to sides triangles may be :

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equilateral - Has all equal sides
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isosceles - Has at least two equal sides.
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scalene - Has no equal sides.

Based on angles, triangles may be called:

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right - Has a right angle.
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acute - Has all angles less than 90 degrees.
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obtuse - Has one angle greater than 90 degrees.

trigonometry - The branch of mathematics which uses indirect measurements and relationships in similar, congruent and right triangles to arrive at solutions to problems.

truncate - To cut off. To disregard some of the parts of the figure or measurement.

turn - The common name for a rotation transformation.  Picture

union of sets - A set containing all of the elements (combined) common to two or more sets.  Picture

unit - 1. The one's place. 2. Pertaining to the number 1. 3. A unknown standard of measurement.

unit rate - A rate where the second number is 1.     For instance, miles per gallon means miles per one gallon.  

upper quartile - In an ordered distribution of numbers, the midpoint value between the median and the upper extreme number.   It actually makes little sense to find the upper quartile of ungrouped data and finding it for grouped data requires laborious calculations.  Example

variable - A letter within an expression, equation or inequality which takes on different number values in different circumstances. Often, constants represented by letters may be considered variable even though they have one value when solved.

variation - A measure of the volatility or dispersion of a distribution.

Venn diagram - A picture which, by using circles, represents the relationship between two of more sets of numbers.     See union or intersection for examples of Venn diagrams. 

vertex - The endpoint from which two rays emanate to form an angle.  Picture

vertex angle - In a triangle, the angle which is opposite the base.    Picture

vertical - Having an up and down direction in a plane. It is perpendicular to any line which is considered horizontal.

vertical angles - An angle pair formed by two intersecting lines and lying opposite the common vertex. Vertical angles are, by definition, congruent.    Picture

volume - A measurement of the capacity of a solid figure measured in cubic units.
Some of the common formulas for volume are as follows:

Volume of a rectangular solid - V=LWH

Volume of a cone - V=1/3BH

Volume of a cylinder - V= Bh or V=pr2h

Volume of a pyramid - V= 1/3BH

Volume of a sphere - V= 4/3pr3

whole number - One of the members of the set of counting numbers or the number zero.

X- Axis - In a Cartesian Coordinate System, the numbered line drawn horizontally through the origin.

Y-Axis - In a Cartesian Coordinate System, the numbered line drawn vertically through the origin.

zero - A symbol used to define "no value". It is also used as a placeholder within a number to indicate the absence of a value associated with that digit.

zero as an exponent - Anything raised to a zero power is 1.

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REVISED  May 4, 2002.