abacusAn abacus is an ancient device that is used for

arithmetic calculations.

abscissaThe abscissa is the x-axis of a coordinate

system. The numerical value of the abscissa tells you the distance from the origin along the x-axis. The abscissa is

the first number, x, in the coordinates of a point (x,y).

|-3|=3absolute value

The absolute value of a number is the distance from the origin on a number line. For example, the absolute

value of 2 is 2 (written |2|=2). The absolute value of -2 is

also 2 (written |-2|=2).

abundant numberAn abundant number (also called a redundant number) is number (an integer) for which the sum of its proper factors (divisors) is greater than the number itself. For example, 12 is an

abundant number because the proper divisors of 12 are 1, 2, 3, 4, 6, which add up to 16, which is greater than 12. Compare with perfect number,

deficient number.

acute angleAn acute angle is less

than 90 degrees.acute triangle

All three interior angles of an acute triangle are acute (less than 90 degrees).

addendThe addend is one of the numbers that is being

added in order to find a sum.

1+1=2

2+3=5

additionAddition is the summing of

numbers to determine their total.

0additive identity

The additive identity is the number zero because zero

plus any number is equal to the original number. For example, 2+0=0+2=2.

algebraAlgebra is the study of generalized arithmetic. In

algebra, unknown numbers can be represented by letters in order to solve equations. For example, 4 + x = 10 is

true for x=6. Algebra (originally called al-jabr) was invented in the Middle East by Abu Ja'far Muhammad ibn Musa Al-Khwarizmi (born in Baghdad about AD

825) during the Middle Ages.

algorithmAn algorithm is series of steps

or rules used for solving a problem. For example, the standard method for doing

long division problems is an algorithm.

alphaAlpha is the first letter in the Greek alphabet. Alpha often

denotes the first term in a series or the brightest star in

a constellation.

angleAn angle is the amount of rotation it would take to put one intersecting line on top of another.

AngstromAn Angstrom is equal to one ten billionth (1 x 10-10) of a

meter. This unit of measure is named for the Swedish

physicist Anders J. Ångström.

angular distanceAngular distance is the measure of an arc (a segment of the circumference of a circle). Angular distance measures the proportion of a circle that the arc in question consists of.

Angular distance is expressed in degrees, radians, arc minutes (one-sixtieth of a degree), or arc seconds (one-sixtieth of a

minute). For example, latitude is the angular distance north or south of the equator measured in degrees, and longitude is the

angular distance east or west of the prime meridian (which goes through Greenwich, England), measured in degrees.

arcAn arc is a segment along

the circumference of a circle, or the part of any

curve between two points.

areaThe area of a region is the number of square units contained within the region. For example, the area of a square with a sides of length s is A = s2. The area of a rectangle is A = length*width. The area

of a parallelogram is A = base*height. The area of a triangle is (1/2)base*height. The area of a . The

area of a circle is A = >πr2

1+1=2

7-4=3

arithmeticArithmetic is the study of addition,

subtraction, multiplication, and

division.

arithmetic meanThe arithmetic mean of a set of

numbers (also called the average) is equal to the sum of the numbers

divided by the number of numbers. For example, for the data

set {1, 2, 3, 6}, the mean is (1+2+3+6)/4 = 12/4 = 3.

arithmetic sequence (or arithmetic progression)

An arithmetic sequence, also called an arithmetic progression, is an

ordered list of numbers where each term is obtained by adding (or

subtracting) a constant amount to the previous term. For example, the

arithmetic sequence 0, 2, 4, 6, 8, 10, ...

is the sequence of numbers starting with 0 where the terms increase by 2

in turn.

(a + b) + c =a+ (b + c)

(a x b) x c =a x (b x c)

associative propertyThe associative property for an operation states that changing the grouping of the

numbers does not change the result of the operation. For example, addition and

multiplication have the associative property. Subtraction and division do not have the

associative property.

asymmetricalSomething that is

asymmetrical is not symmetrical - it does not

have symmetry. For example, the figure above

is asymmetrical.

asymptoteAn asymptote is a straight line that defines the limits of a curve (such as a hyperbola). In the picture above, the dashed lines are

asymptotes of the hyperbola.

averageAlso called the arithmetic mean,

the average of of a set of numbers is the sum of the numbers divided

by the number of numbers. For example, the average of 1,4,6,9 is

(1+4+6+9)/4=5.

axiomAn axiom is a statement that is assumed or accepted to be true as a starting point for

proving other things.

axisAn axis is an imaginary straight line around which an

object, like a planet, turns. For example, the Earth's axis is a line that goes through the North and South Poles.

axis of symmetryAn axis of symmetry is a line about which

something is symmetrical. For example, the diameter of a circle is an axis of symmetry.

bar codeBar codes store a series of

encoded numbers - they can be read by laser scanners. There are bar codes on most things that are for sale in stores and many other items that need to be tracked (like

bar graphA bar graph is a type of graph that visually displays information using

baseThe base is the bottom of a

geometric figure, like the bottom of a cone. The base is defined as

baseIn a number system, a base is the number

upon which the system is based. For example, the numbers used in everyday life are base 10 numbers - each place value is a power of 10. Numbers can be written in any integer base, two or greater. In base two, each place value

is a power of 2 (and only the numbers 0 and 1 are used). In base 8, each place value is a

power of 8 (and only the numbers 0 through 7

train cars). a series of bars or rectangles. the side opposite a vertex. are used).

1,000,000,000

billionA billion is a thousand million or ten

to the ninth power. The Earth is billions of years old and there are

billions of stars in the sky.

binary number systemThe binary number system is a way of expressing

numbers in base two. Each place value is a power of 2 (in our ordinary base ten system, each place value is a power of 10). Only the numbers 0 and 1 are used in this system. For example, in the binary number system, 11 represents

the number 3, and 101 represents the number 5.

2x + 3y

binomialA binomial is a

polynomial expression that has two terms, like 3x2

+ 4yz.

bisectTo bisect is to divide into two equal (congruent) parts. For example, if you bisect a 90 degree angle, you divide it into two 45 degree angles.

bisectorA bisector is is a line or ray that divides something (an angle, line segment or arc) into two equal (congruent) parts.

CC equals 100 in

Roman numerals.

calculatorA calculator is a

machine that solves math problems.

calculusCalculus is a branch of mathematics that was developed separately by

Gottfried Wilhelm Leibniz and Isaac Newton in the 1600s. Calculus is used to calculate motion and areas (and many other things). Differentiation and

integrations are two major areas of calculus.

calendarA calendar divides the

year into periods and lets you know what day it is.

cardinal numberA cardinal number is a

whole number that tells you

"How many?".

Even Odd≤ 5 0,2,4 1,3≥ 5 6,8,10 5,7,9

Carroll diagramA Carroll diagram (named for the

mathematician/author Lewis Carroll) is a rectangular chart that is used to sort items with respect to one, two or three

binary (yes/no) categories.

carryWhen you carry in

addition, the sum of the numbers is ten or more,

and the ten's place is "carried" to the next

place.

Cartesian coordinatesA Cartesian coordinate system is a rectangular coordinate system with two axes (x is the horizontal axis and y is the

vertical axis). Every point on the plane can be located by an ordered pair (x,y), which notes its distance from the x-axis and

from the y-axis. The axes meet at the origin, the point (0,0). It is named for René Descartes.

centCent is another word for penny.

center of massThe center of mass is the location at which the entire

mass of an object (or set of objects) may be considered for purposes of calculations. It is the

point of the average weighted position in space of an object (or a collection of objects).

centiCenti is a prefix that

means one-hundredth. For example, a centimeter is

one hundredth of a meter.

centroidThe centroid is the point at which a

geometric figure balances. The centroid of a triangle is the point at which the three

medians intersect.

chordA chord is a line segment that connects

two points on a circle. The longest chord on a circle is the diameter of the

circle.

circleAll of the points on a circle are the same distance from the center of the circle (that distance is called the radius

of the circle).

circle graphA circle graph (also called a pie chart) is a

diagram that is useful for displaying information about the percentages or parts

of a whole.

circumferenceThe circumference is the

distance around an object. The circumference of a circle of

radius r is 2πr .

clockA clock tells

you what time it is. coin

A coin is a piece of metal money.

collinearPoints that are

collinear are on the same line.

a x b = b x a

commutative propertyThe commutative property states that for some operations, you can change the order of the terms and not change the outcome of the operation. For example, a x b = b x a and a + b = b + a. The commutative property holds for addition and multiplication; it

does not hold for subtraction or division.

compassA compass is a device that

always points north. A compass is also a device

that draws circles.

compatible numbersTwo compatible numbers form a

division fact. For example, since 72 divided by 9 is 8, 72 and 9 are

compatible numbers (so are 72 and 8).compass rose

A compass rose is a design on a map that shows direction. It points which way is north, south, east,

complementary angle

A complementary angle is an angle that, when

added to another angle, equals 90 degrees.

west, and some intermediate directions on the map.

complex fractionA complex fraction is a

fraction that has a fraction in the numerator, denominator,

or both.

complex numberA complex number is a number that can

be written in the form a + bi, where a and b are real numbers and i is the square root

of -1 (an imaginary number ).

composite numberA composite number is a number that has more than two factors. For example, 6 is a composite number

because it has four factors (1, 2, 3, 6). 5 is not a composite number because it has only 2 factors, 1 and

5.

computerYou are using a computer right

now.

concentric circles

Concentric circles are circles that have the same center point.

conditionalA conditional (also called an if-then

statement or an implication) is a statement of the form, "if p then q" - p is

called the antecedent, p is called the consequent. The conditional "if p then q" is false only when p is true and q is false.

coneA cone is a shape that has a point at the center

and a circular cross-section throughout (it looks like two infinitely-long ice cream cones with the vertices touching). The volume of a

single portion of a cone is πr3L/3 (where r=radius of cone at the larger end, L=length

of the cone).

congruentCongruent means having the same shape and size. For example, two

triangles are congruent if they have the same interior angles and same side

length. Two line segments are congruent if they are the same length.

conjectureA conjecture is

an educated guess.

connect-the-dotsWhen you do a connect-

the-dots puzzle, you draw a line from number to

number to make a picture.

conic sectionA conic section is set of points that

results from the intersection of a cone and a plane. Some conic sections

include a point, ellipse, circle, parabola, and hyperbola. coordinates

Coordinates are an ordered pair of numbers that show the location of a point on the x-y plane. Every point on the plane can be located by a pair of coordinates (x,y), which notes its

distance from the x-axis and the y-axis.

consecutiveConsecutive means in order.

For example, 1 and 2 are consecutive whole numbers; 6 and 8 are consecutive even

numbers.

cosecantCosecant (abbreviated csc) is a

trigonometric ratio, corresponding to the length of the hypotenuse divided by

the length of the opposite side of the right triangle. Cosecant is equal to

1/sine.

cosineCosine (abbreviated cos) is a

trigonometric ratio, corresponding to the length of the adjacent side

divided by the length of the hypotenuse of the right triangle.

cotangentCotangent (abbreviated cot) is a

trigonometric ratio, corresponding to the length of the adjacent side divided by the length of the opposite side of the right triangle. Cotangent is equal to

1/tangent.

counting numberThe counting numbers are

the positive whole numbers, 1, 2, 3, 4, 5... .

crescentA crescent is the shape of the moon shortly before and after

the time of the new moon.

cubeA cube is a solid geometric figure with six square faces.

The volume of a cube is s3 (where s=length of a side of the cube). The surface area of a cube is 6s2 (where s=length of

a side of the cube).

cubedCubed means raised to the

third power, like x3. For example, 2 cubed = 2 x 2 x 2

= 8.

cube rootThe cube root of a number, n, is a

number whose cube is that number. For example, the cube root of 8 is 2, since 2 x 2 x 2 = 8. In general, the

cube root of n is a if a3=n.

cubic equationA cubic equation is an equation whose highest

degree term is 3. For example, 5x3 - 8x2 + 2xy = 4 is a cubic

equation.

curveA curve is

a wavy line.

cylinderA cylinder is a 3-dimensional figure with a long tube-like body and congruent, parallel bases. A right-circular cylinder has a base that is perpendicular to the axis of the cylinder (it is like a can of food). The

volume of a right-circular cylinder is πr2L (where L=length of cylinder, r=radius of cylinder). The surface area of a cylinder is 2πrL (where

L=length of cylinder, r=radius of cylinder).

decagonA decagon is a

ten-sided geometric

figure.

deciDeci is a prefix that

means one-tenth. For example, a decimeter

is one tenth of a meter.

1.33

decimalA decimal is a base 10 number that is written with a decimal point in

it. For example, 1.1, 10.43, and 0.01 are

decimals.

decimal pointA decimal point is a dot that separates the a number into the whole number part (on the left of the decimal point) and the fraction (to the right of the decimal point). For

example in 21.46, 21 is the whole number and .46 (forty-six hundredths) is the fraction.

deficient numberA deficient number is number (an integer) for

which the sum of its proper factors (divisors) is less than the number itself. For example, 9 is a

deficient number because the proper divisors of 6 are 1 and 3 which add up to 4, which is less than

9. Compare with abundant number, perfect number.

degreeA degree is a measure of

temperature or angle. There are 360 degrees in a circle. Each

degree is divided into 60 minutes, represented by the apostrophe

symbol, '. 1°=60'.

denominatorThe denominator is the bottom number

in a fraction.

DescartesRené Descartes ( March 31, 1596 - February 11, 1650) was a French mathematician and philosopher. Descartes invented the Cartesian

coordinate system and many principles of philosophy.

diagonalA diagonal is a line that joins two non-consecutive vertices

of a polygon.

diameterThe diameter is the longest

distance from one side of a circle (or a sphere) to the other.

diamondA diamond is a four-sided figure (a

quadrilateral) whose sides are all the same length. People play baseball on a diamond-

shaped field.

diceDice are cubes with numbers on each side that are used in games.

A single one is called a die.

differenceThe difference is the answer in

a subtraction problem.

digitA digit is a single numeral

within a number. For example, the number 153 is

a 3-digit number.

dimeA dime is a coin worth ten cents.

directrixThe directrix is a line that helps generate a parabola or hyperbola. For example, a parabola is a set of points (P) such that the distance from the directrix to P is equal to the distance from P to the focus F.

dividendThe dividend is the number

that is divided (in long division). The dividend

divided by the divisor is the quotient (plus a remainder).

divisionDivision is an operation that divides a number into portions. Any number divided by one is equal to the original number.

You cannot divide any number by zero. Division is the inverse of multiplication. In long division, the dividend is divided by

the divisor, resulting in a quotient plus a remainder. The ÷ symbol is called an obelus.

divisorThe divisor is the number that the dividend is divided by (in long division). The dividend divided by the divisor is the quotient (plus a remainder).

dodecagonA dodecagon is a

twelve-sided polygon (figure).

dodecahedronA dodecahedron is a twelve-sided geometric solid

whose faces are pentagons.

dollarA dollar is worth 100

cents.dominoes

Dominoes is a game played with tiles that have dots on them.

dotA dot is a tiny speck

or point.

************12

dozenDozen is another word for twelve.

ee

e is a transcendental number that is equal to approximately 2.71828182845904523536028747135266249... e is an irrational, non-

repeating decimal and is the base of the natural logarithm. The symbol e honors the Swiss mathematician Euler (e is sometimes called Euler's number).

eightEight is the number

between seven and nine. Spiders have eight legs. Stop signs have eight sides. An eight-sided

figure is called an octagon.

18eighteen

Eighteen is the number between seventeen and nineteen. An eighteen-

sided polygon is called an octadecagon.

80eighty

Eighty is the number between

seventy-nine and eighty-one.

11

***********

elevenEleven is the number between

ten and twelve. Eleven is ten plus one. An eleven-sided figure is

called a hendecagon or an undecagon.

ellipseAn ellipse looks like a flattened circle. It consists of all the points in a

plane that satisfy the following: a+b=(twice the length of the semi-major axis), where a is the distance from one focus to the point on the ellipse, and b is the distance from the other focus to the same point on

the ellipse.

{ }

empty setThe empty set (also called the null set)

is the set that has no elements.

enneadecagonAn enneadecagon is a

nineteen-sided polygon.

=equal

When two things are equal they are exactly the same in

number, quality, or amount.

1+1=2

3-x=2

equationAn equation is a mathematical

statement that contains an equal sign, like ax + b = c.

equatorThe equator is an imaginary circle

around the Earth or any orb, halfway between the North and South Poles.

equilateral triangleThe sides of an equilateral triangle are all the same length and all the interior

angles are 60 degrees.

Escher, M.C.Maurits Cornelis Escher (June 17, 1898-March

27, 1972) was a Dutch artist known for his woodcuts of interlocking geometric patterns

and impossible constructions.

0, 2, 4, 6, 8, 10, ...

even numberAn even

number is divisible by

two.

!exclamation point

In mathematics, the exclamation point means factorial. The factorial of a number is equal to the number times

all the positive whole numbers less than it. For example, 5!= 5x4x3x2x1=120

xn

exponentAn exponent is a power that

a number is raised to. For example, in 23, the exponent

is 3.

exponential notationExponential notation (also called scientific notation) is a short-hand way of expressing very small or

very large numbers; this system avoids using a lot of zeros by using powers (exponents). In scientific notation, there is a number between 1 and 10 multiplied by a power of ten. For example,

the number 250 written in scientific notation is 2.5 x 102. For another example, the number 0.000052 written in scientific notation is 5.2 x 10-5.

expressionAn algebraic expression consists of one or

more variables, constants, and operations, like 3x-4. Each part of an expression that is added or subtracted is called a term For example, the

expression 4x2-2x+7 has three terms.

factorThe factor of a number is a number that divides that

number exactly. For example, the factors of 6

are 1, 2, 3 and 6.

factor treeA factor tree is a graphical representation in tree form that shows the factors of a

specific number.

!factorial

In math, the exclamation point means factorial! The factorial of a number is equal to the number times all the positive whole

numbers less than it. For example, 5!= 5x4x3x2x1=120.

FahrenheitFahrenheit is a measure of temperature that is abbreviated F. Water freezes at 32°F and boils

at 212°F.

1, 1, 2, 3, 5, 8, 13...

Fibonacci numbersThe Fibonacci numbers are a sequence of numbers

generated by adding the previous two numbers to get the next number, starting with two ones. Fibonacci numbers were named for the Italian mathematician Leonardo da

Pisa, aka "Fibonacci" (c.1175-1250).

15***************fifteen

Fifteen is the number after fourteen (14) and before

sixteen (16). A fifteen-sided polygon is called a

pentadecagon.

50**************************************************

fiftyFifty is the number after forty nine (49) and before fifty one (51). A

fifty-sided figure is called a pentacontagon.

firstThe first person or thing comes before the others. First is abbreviated 1st.

fiveFive is the number

between four and six. We have five fingers on each hand. A pentagon is a five-sided figure.

focusA focus (plural foci) is one of the central points of a conic section, such as an ellipse, hyperbola, or

parabola.

(ax + b)( cx + d)

FOILFOIL is an acronym that stands for First, Outer, Inner,

Last. It refers to a method of multiplying two binomials, like (ax + b)( cx + d). To multiply, you must multiply each term out, including the first terms (ax times cx), the inner terms (b times cx), the outer terms (ax times d), and the last terms (b times d). For example, (2x + 3)( 4x + 5) =

8x2 + 10x + 12x + 15 = 8x2 + 22x + 15.

footA foot is a unit of

measurement that is equal to twelve inches or

one third of a yard.

F=maformula

A formula shows a mathematical relationship between expressions.

40****************************************

fortyForty is the number after thirty nine (39)

and before forty one (41).

fourFour is the number after three (3) and before five (5). A quadrilateral is a geometric figure that has four sides.

14**************

fourteenFourteen is the number after thirteen (13) and before fifteen (15). A fourteen-sided polygon

is called a tetradecagon.

fractalFractals are patterns

within patterns within patterns.

1/2fraction

A fraction is a part of a whole, like a half, a third, a quarter, etc. For example, half of an apple is a fraction of an apple. The top number in a fraction is

called the numerator; the bottom number in a fraction is called the denominator.

GAUSS, J. C. F.Johann Carl Friedrich Gauss (April 30, 1777-Feb. 23, 1855) was

a great German mathematician, physicist, and astronomer. Gauss did important work in number theory, analysis,

differential geometry, statistics, magnetism, and the motion of planetoids.

GCFThe Greatest Common Factor (GCF) [also called the

Greatest Common Divisor or GCD] is the largest positive integer that is a factor of two or more numbers.

For example, the GCF of 14 and 21 is 7. It can be written GCF(14, 21) = 7.

GCDGreatest Common Divisor

(GCD) means the same thing as Greatest Common

Factor (GCF).

geometryGeometry is the mathematical

study of points, lines, angles, and solids.

globeA globe is a small,

spherical model of the Earth.

Goldbach's ConjectureGoldbach's Conjecture states that every even integer greater than 2 can be expressed as

the sum of two prime numbers. It was first noticed by the mathematician Christian Goldbach in 1742. It has yet to be proven or disproven.

googolA googol is the number 10100 (10 raised to the 100th power or 1 followed by 100 zeros=

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000). A googol is much larger than the number of atoms in the Universe.

googolplexA googolplex is the number 10 raised to the googol power:

10(googol) or 10(10100) (1 followed by a googol of zeros). A googolplex is much larger than the number of atoms in the

Universe.

golden ratioThe golden ratio is (1 + square root of 5)/2 =

1.61803399... Many people say that a rectangle with the height to width ratio being the golden ratio is a pleasing

shape.

graphA graph is a diagram that

shows relationships between things.

great circleA great circle is an imaginary circle

on the surface of a sphere whose plane passes through the center of

the sphere.

>greater than

The mathematical symbol > means "greater than." When one number is greater than a second number, the

first one is bigger than the second. For example, 4 is greater than 2, or 4 > 2.

GCFGreatest Common Factor

The Greatest Common Factor (GCF) is the largest positive integer that is a factor of two or more

numbers. For example, the GCF of 14 and 21 is 7. It can be written GCF(14, 21) = 7.

GCD

Greatest Common DivisorThe Greatest Common Divisor (GCD) is

another was of writing the Greatest Common Factor (GCF).

Greek AlphabetThe Greek alphabet has 24 letters, alpha, beta, gamma, delta, epsilon, zeta, eta, theta, iota, kappa, lambda, mu, nu, xi, omicron, pi, rho, sigma, tau, upsilon, phi, chi, psi, and omega. The Bayer system in astronomy uses Greek letters to denote stars by their relative brightness in each constellation (in order of decreasing brightness). The brightest star in a constellation is alpha, the second-brightest is beta, the third is gamma,

etc.

1/2half

When something is divided into two equal parts, each of these two parts is half of the original object. Half can be written

as 0.5 or 1/2.

half moonA half moon looks like half a

circle.

hectogonA hectogon is a hundred-sided

figure.hemisphere

A hemisphere is half of a sphere.

hendecagonA hendecagon is an eleven-sided figure (undecagon is

another word for this figure). The Canadian one dollar coin (also called the loonie) is a regular hendecagon.

heptagonA heptagon is a

seven-sided figure.

hexaflexagonA hexaflexagon is a folded geometric

figure that can be "flexed" to expose its many sides.

hexagonA hexagon is a six-sided

figure. Beehives have hexagonal cells.

hexagonal prismA hexagonal prism is a geometric solid (but not a Platonic

solid) that has eight faces; each end is a hexagon, and the six other faces are rectangles.

hieroglyphicsThe ancient Egyptians wrote

using hieroglyphics.

histogramA histogram is a block-style graph

that presents frequency data in statistics. hour

There are 24 hours in a day.

hour handAn hour hand on a

clock tells you what hour it is.

100hundred

One hundred is the number between 99 and 101. A hundred-sided figure is called

a hectogon.

HypatiaHypatia of Alexandria (AD 370(?)-415) was a Greek mathematician, astronomer, teacher, and head of the

Platonist school at Alexandria about AD 400. Hypatia wrote commentaries on the astronomical canon of

Ptolemy and did work on conic sections . Her works are lost, but are referred to in the Suda lexicon. She was the daughter of the mathematician and philosopher Theon of Alexandria (he was also the last head of the Museum at

Alexandria). A pagan, she was murdered in 415 by Christian monks in a religious/political struggle. The

lunar Crater Hypatia and Rimae Hypatia were named for her.

hyperbolaA hyperbola is a conic section (the

intersection of a cone with a plane) that has two mirror-image branches. Hyperbolas have

an eccentricity greater than 1.

hypotenuseThe hypotenuse is the longest side of a right triangle, the side opposite the right angle.

ii is an imaginary number, defined

as the square root of negative one.

II equals 1 in Roman

numerals.

icosahedronAn icosahedron is a twenty-

0

identity for additionThe additive identity is the number zero because zero plus any number is equal to the original number. For example, 2

+ 0 = 0 + 2 = 2.

sided geometric solid.

1

identity for multiplicationThe identity for multiplication (also called the multiplicative identity) is one, because a times 1 = 1 times a = a. For example, 2

times 1 = 1 times 2 = 2.

illusionAn illusion is

something that tricks your eyes.

i

imaginary numberAn imaginary number is a

number of the form bi, where i is the square root of negative one and b is a real number.

Improper FractionAn improper fraction is one whose numerator is larger than the denominator (like 5/4). Improper

fractions can be written as a mixed number, a number plus a fraction (5/4 = 1 1/4).

inchAn inch is a unit of measurement that is

equal to one-twelfth of a foot. The symbol for inch is ".

infinityInfinity is a concept of

endlessness. The symbol above represents infinity.

integerThe integers are the

numbers ..., -3, -2, -1, 0, 1, 2, ....

= Equal 1 = 1> Greater Than 2 > 1

< Less Than 1 < 3

inequalityAn inequality is a mathematical expression

that contains an inequality symbol. The inequality symbols are :

< less than (1<2) > greater than (2>1)

≤ less than or equal to ≥ greater than or equal to

≠ not equal to (1≠2).

intersectionAn intersection is where two or more things,

like roads or sets, meet or overlap. The intersection of two sets is the set of objects

that belong to both of the original sets.

inverse property of addition

The inverse property of addition states that for

every number a, a + (-a) = 0 (zero).

inverse property of multiplication

The inverse property of multiplication states that for every non-zero number a, a

times (1/a) = 1.

irrational numberAn irrational number is a number that

cannot be written as a fraction (like a/b, where a and b are whole numbers and b is ≠ 0). For example, the square root of 2 is an

irrational number.

isosceles triangleAn isosceles triangle has two sides that are the same length and two angles that are the same.

KILOGRAMA kilogram (kg) is a unit of mass defined as the weight of one liter of water. One kilogram is equivalent to 1,000 grams or 2.2 pounds. kite

A kite is a four-sided figure (a quadrilateral) in which the two pairs of adjacent sides have the same length.

KMKm is short for

kilometer or kilometers.

LL equals 50 in

Roman numerals.

latitudeLatitude is the angular distance north or south from the equator to a particular location. The

equator has a latitude of zero degrees. The North Pole has a latitude of 90 degrees North; the

South Pole has a latitude of 90 degrees South.

LCDLCD stands for Least Common

Denominator. LCD is the smallest common denominator of two or more fractions. For example, the LCD for

1/7 and 3/5 is 35

LCMThe Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 6 and 8 is 24 or LCM(6,8)=24.

Least Common DenominatorThe Least Common Denominator

(LCD) is the smallest common denominator of two or more fractions.

For example, the LCD for 1/7 and 3/5 is 35.

Least Common MultipleThe Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 6 and 8 is 24 or LCM(6,8)=24.

lessThe opposite of

less is more.

<less than

The mathematical symbol < means "less than." When one number is less than a second

number, the first one is smaller than the second. For example, 1 is less than 2, which is

written 1 < 2.

lineA line is a set of points that form

an infinitly long straight path. The equation y=mx+b or

ax+by+c=0 graph a line (these are linear equations).

linear equationA linear equation is a first degree

equation (the variable are raised to the first power). For example, y=mx+b and

ax+by+cz=0 are examples of linear equations - when graphed, they plot a

line.

line segment

A line segment is a portion of a

line.

logarithmLogarithms are the inverse of exponentiation. For

example, if you want to compute the log to the base 10 of 100, also written log10(100), you must determine the

power you have to raise 10 to in order to get 100. Since 102=100, log(100)=2. Similarly, since 101=10, log(10)=1. Logarithms to the base 10 are called common logarithms

and written log or log10. Logarithms to the base e are called natural logarithms and written ln or loge [note:

ln(e) = 1].

logicLogic is the

study of reasoning and

proof.

longWhen

something is long, it is not

short.

long divisionIn long division, the dividend is divided by the

divisor, resulting in a quotient plus a remainder.

longitudeLongitude is the angular distance east or west from the north-

south line that passes through Greenwich, England, to a particular location. Greenwich, England, has a longitude of zero degrees. The farther east or west of Greenwich you are, the greater your

longitude. Midway Islands (in the Pacific Ocean) have a longitude of 180 degrees (they are on the opposite side of the

globe from Greenwich).

MM equals 1000 in Roman numerals.

5 4 66 5 44 6 5

magic squaremap

A map (also called a cartograph) shows the features of an area. You can find your way around by using a map.

In a magic square, the rows, columns, and diagonals all add up

to the same number.

mathematicianA mathematician is a person who studies

mathematics.mathematics

Mathematics is the study of numbers, shapes, patterns, and

logical reasoning.

mazeGetting through the passages of a maze

is tricky.

mean, arithmeticThe arithmetic mean of a set of numbers (also called the average)

is equal to the sum of the numbers divided by the number of numbers. For example, for the data set {1, 2, 3, 6}, the mean =

(1+2+3+6)/4 = 12/4 = 3.

measuring cup

A measuring cup is useful in

baking and cooking.

{1, 2, 5, 8, 10}

medianThe median of a set of numbers is the middle

number (when the numbers are in order). When the number of numbers is odd, the median is the middle number; when the number of numbers is

even, the median is the average of the two middle numbers. For example, the median of the

set {1,2,5,8,10} is 5. The median of the set {1,2,5,6,9,10} is 5.5..

medianThe median of a triangle is a line segment from a vertex to

the midpoint of the opposite side. The median of a trapezoid is a line segment that connects the midpoints of the non-

parallel sides.

mental mathMental math is

math that is done in your head, without writing or using a calculator or other

device.

milliMilli is a prefix that means one-

thousandth. For example, a millimeter is one thousandth of a meter.

millionA million is 1,000,000

or one thousand thousand or 106.

minuendThe minuend is the number from which

another number is subtracted in a subtraction problem.

-minus sign

The mathematical symbol - means "minus." Four minus three

is written, 4 - 3.

minuteA minute is a measure of

angle that is equal to 1/60th of a degree.

minuteA minute is a measure of time that is

1/60th of an hour. A minute is composed of 60 seconds.

minute handA minute hand on a clock tells you how

many minutes past the hour it is.

1 2/3

mixed numberA mixed number is a number that is

written as a whole number plus a fraction, like 1 2/3.

Möbius stripA Möbius strip is a piece of paper with

only one side!

modeThe mode of a group of numbers

is the number that occurs the most in that set. For example, in the set {1, 2, 3, 3, 3, 8} the mode

is 3.

modular arithmeticModular arithmetic is arithmetic done with a limited set of numbers. For example, clock

arithmetic is an example of modular arithmetic; when adding hours, 11+2=1 (and

not 13).

moneyMoney is used as a basis for trade. Most money is decimal (based on the number 10). Only a few

countries have money with another base (like Madagascar and Mauritania, which have base 5

money).

monomialA monomial is a polynomial

expression with only one term. For example, 3xy is a monomial; the

number 6 is also a monomial.

monthThere are 12 months in a year: January, February, March, April, May, June, July, August, September, October, November, and

December.

MULLER, JOHANNJohann Müller, also known as Johann

Regiomontanus (1436-1476) was a German astronomer and mathematician. He studied

trigonometry, translating Ptolemy's Almagest, from the original Greek. Ironically, his

translation helped overthrow the Ptolemaic view of the universe (in which the Earth was thought to be at the center of the universe). He also did

work on plane and spherical trigonometry. Muller also observed the motion of the moon, planets, and comets. A 108 km diameter lunar crater, called Regiomontanus (Latitude: -28.3

degrees, Longitude: 1.0 degrees), was named for Muller.

Multiples of 2:

2,4,6,8,10,12,...

multipleA multiple of a number is the product of the original number

and another number. For example, the multiples of the 2

are 2, 4, 6, 8, 10, 12, 14, 16, and so on.

multiplicandThe multiplicand is the number that is multiplied by the multiplier in a

multiplication problem.

1 x 2 = 2

2 x 3 = 6

multiplicationMultiplication is a

mathematical operation used to compute areas, volumes,

and many other calculations.

1multiplicative identity

The multiplicative identity (also called the identity for multiplication) is one, because a * 1

= 1 * a = a. For example, 2*1=1*2=2.

multiplicative inverseThe multiplicative inverse of a is 1/a (where a is not equal to

zero), since for every number a, a * (1/a) = 1.

multiplierThe multiplier is the number by which the multiplicand is multiplied.

nanometerA nanometer is unit of measure equal to 10 angstroms, which is one billionth (1 x 10-9)

of a meter.

natural numberThe natural numbers (also called counting numbers) are the positive whole numbers, 1, 2, 3, 4, 5... . Mathematicians usually include the

number zero with the natural numbers.

negative numberA negative number is a a

number less than zero, like -1, -2, -3/4, etc.

Newton, IsaacIsaac Newton (1642-1727) was an English mathematician and

physicist who invented calculus (simultaneously, but independently of Leibniz), formulated the laws of gravitation, investigated the nature of light (he discovered that sunlight is made of light of different colors),

and the laws of motion: 1. An object in uniform motion tends to remain in that state of motion unless an external force is applied to it

(the Law of Inertia). 2. A force causes a change in the velocity (acceleration) of an object (F=ma). 3. For every action there is an

equal and opposite reaction. Newton also improved the design of the refracting telescope (using an objective mirror, instead of a lens), and

it is now called a Newtonian telescope.

nineNine is the number between eight and ten. There are nine planets in our Solar System. A nine-sided figure is called

a nonagon.

19nineteen

Nineteen is the number between eighteen and twenty. A nineteen-sided polygon is

called an enneadecagon.

nonagonA nonagon is a nine-sided

polygon.

normalIn mathematics, a normal line is perpendicular (at

right angles) to the tangent of a curve.

{ }null set

The null set is the empty set, a set

with no members.

number lineA number line is a line in which real numbers can be placed, according to their value. Each point on a number line corresponds to a real number, and each real number has a unique point that corresponds to it. For example, the number 1.5 (1 1/2) corresponds to the point on a number line that is

halfway between one and two.

numberNumbers tell you "how many" or "how much."

Some numbers are -12, 0, 5, 1/2, 1.33333, π, 1600.

numeralA numeral is a symbol for a number. For example, the symbol 2 is the

numeral we use to represent the number two. In our base ten numbers, there are 10 numerals, o, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

numeratorThe numerator is the top number in a

fraction.

1, 2, 3, 4, 5

numerical orderWhen numbers are in

numerical order, they are in order from lowest to highest.

obeliskAn obelisk is a tall,

four-sided tower topped with a

pyramid.

obliqueLines or planes are oblique when

they are neither parallel nor perpendicular to each other.

obtuse angleAn obtuse angle is

an angle greater than ninety degrees.

obtuse triangleOne of the interior angles of an obtuse triangle is obtuse ( an obtuse angle is

over 90 degrees).

octadecagonAn octadecagon is an eighteen-

sided figure.octagon

An octagon is an eight-sided figure. Stop signs are octagons. octahedron

An octahedron is an eight-sided geometric solid (a 3-D object).

1, 3, 5, 7, 9, 11, ...

odd numberAn odd number is not divisible

evenly by two.

oneOne is the number between zero

and two. One is the multiplicative identity, since one times any

number is equal to that number.

1/2one half

When something is divided into two equal parts, each of these two parts is one half of the

original object.

operationAn operation is a rule for taking one or two numbers as inputs and producing a number as an output. Some arithmetic operations are multiplication, division, addition, and

subtraction.

oppositesOpposites are things that are very, very

different from each other. Some examples of opposites are: positive and

negative, add and subtract, left and right, big and small, up and down.

orbAn orb is a ball-shaped

object.

order of operationsIn mathematical operations, the standard

order of operations is: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Within a

category, operations are done from left to right.

ordinal numberOrdinal numbers show order. Some

ordinals are first (1st), second (2nd), third (3rd), fourth (4th), fifth (5th), sixth (6th), seventh (7th), eighth (8th), ninth (9th), tenth (10th), eleventh (11th), twelfth

(12th), etc. originThe origin is the point (0,0) -- where the x and y

axes meet. In a 3-d coordinate system, the origin is the point (0,0,0) -- where the x, y and z axes meet.

ordinateOrdinate is another name for the y-axis (the vertical axis). The ordinate is the

second number in a point (x,y).

ounceAn ounce is a unit of measure. Eight ounces are in one cup.

ovalAn oval

is an egg-shaped figure.

MOM2002

palindromeA palindrome is a word, phrase or number

that reads the same forwards or backwards. A palindromic number is a number that reads the same forwards or

backwards, like 2002. Some other palindromes are: the name Bob, the

number 101, and the phrase, "Madam, I'm Adam."

parabolaA parabola (a type of conic section) is a curve that is a set of points (P) such that the distance from a line (the directrix) to P is equal to the

distance from P to the focus F. Parabolas have an eccentricity of 1.

parallelParallel lines extend

in the same direction, are

always the same distance apart, and

never intersect (meet).

parallelogramA parallelogram is a four-sided figure (a quadrilateral) whose

opposite sides are parallel.

Pascal's trianglePascal's triangle is a triangular pattern of numbers devised in 1653 by the

French mathematician, physicist, and philosopher Blaise Pascal (June 19, 1623 - Aug. 19, 1662). The numbers in each row are derived by adding pairs of

patternA pattern is something that is repeated, like a design or a series of

numbers. pennyA penny is a coin worth one cent.

pentadecagonA fifteen-sided

polygon is called a pentadecagon.

numbers in the row above it. The number one is tacked onto the beginning and end of each row. The first few rows of Pascal's triangle are shown above. The rows represent the binomial coefficients in a triangular format. Note that the row with the numbers [1 2 1] represent the coefficients of (x+y)2 The nth row

represents the coefficients of (x+y)n.

pentagonA pentagon is a five-sided

polygon.

%percent

Percent mean "per hundred." The sign for percent is %. 100% means all, 50% means half or 50 out of 100, 25% means one quarter or 25 out of 100, 10% means one tenth or 10 out of 100, and 0% means none or 0 out of 100. To

convert a percentage to decimal notation, divide the percentage by 100; for example, 50% = 0.5

and 10% = 0.1. To convert a decimal to a percent, multiply the number by 100; for

example, .25 = 25%.

perfect numberA perfect number is a number (an

integer) for which the sum of its proper factors (divisors) is equal to the number

itself. For example, 6 is a perfect number because the proper divisors of 6

are 1, 2, and 3 which add up to 6. Compare with abundant number,

deficient number.

perimeterPerimeter is the distance around the edges of a figure. The perimeter of a square with side length a is P = a+a+a+a = 4 times a. The perimeter of a circle is P = 2πr. The perimeter of a regular polygon is P = ns (where n is the number of sides and s is

the side length).

perpendicularWhen two lines are

perpendicular, they are at right angles (90 degrees). A

line can also be perpendicular to a plane (if the line goes through the

plane at a 90 degree angle).

piPi is the ratio of the circumference of

a circle to the diameter of a circle. For any circle, you can divide the

circle's circumference (the distance around the circle) by the diameter

(the distance across the circle through the center) and you will

always get exactly the same number (pi), no matter how big or how small the circle is. Pi is a number roughly equal to 3.14159265... - the digits of pi never end or repeat. The value of

pi has been calculated up to the millions of digits. Pi is a transcendental number.

pie chartA pie chart (also called a circle

graph) is a diagram that is useful for displaying information about the

percentages or parts of a whole. Pie charts were invented in 1801 by

William Playfair (Sept 22, 1759 - Feb 11, 1823).

place valuePlace value is a positional system of

notation in which the position of a number with respect to a point determines its

value. In the decimal (base ten) system, the value of the digits is based on the

number ten.

planeA plane is a flat (2-dimensional) surface that

extends to infinity in all directions. A plane has no thickness.

plotA plot is a graph done in a coordinate system. Each point on the graph is plotted (marked on the graph in the coordinate

system).

+plus sign

A plus sign (+) means addition or indicates that a number is

positive.

.

pointA point is an exact location, a

spot with no width or thickness.

polygonA polygon is a many-sided figure with straight edges. A regular polygon is a polygon whose sides are all the same length and whose interior angles are all the same (like an

equilateral triangle and a square).polyhedron

Polyhedra are solids whose faces are polygons.

5x 2 - 2x - 8

polynomial

A polynomial is a sum or difference of terms; each term is: a constant (like 5) a constant times a variable (like 3x)

a constant times the variable to a positive integer power (like 2x2)

a constant times the product of variables to positive integer powers (like 2x3y).

A monomial is a polynomial with only one term. A binomial is a polynomial that has two terms. A trinomial is a polynomial with three terms.

Degree of a Polynomial: The degree of a term within a polynomial is the sum of the exponents of variables that occur in that term (if there is no exponent written on a variable, such as in 3x, the exponent is one). The degree of a polynomial is the greatest degree of any term in the polynomial (for instance, for the polynomial 4x2 + 7xyz, the degree is 3 because of the last term).

If a polynomial isn't just a constant and if each term has at most a variable to the first power (like 4x - 2 or 3y), then it is a first-degree polynomial (also called a linear polynomial).

If a polynomial's highest degree is two, it is a quadratic (or second-degree) polynomial (example: 4x2 + 3x + 7).

If a polynomial has more than one variable, then its degree is the sum of the exponents of the highest-degree term. For example, the polynomial 2xy2 -3xy + 6x - 2 has degree 3 (the sum of the xy2 exponents, 1 + 2).

Polynomials are often written in descending order, in which the terms with the largest powers are written first (like 9x2 - 3x + 6). If they are written with the smallest terms appearing first, this is ascending order (like 6 - 3x + 9x2).

polynomial equationA polynomial equation is an equation

involving a polynomial.

positive integerA positive integer

is an integer (a whole number)

greater than zero, like 1, 2, 3, 4, ...

positive numberA positive number is a number greater than

zero. Numbers written without a sign are

assumed to be positive. For example, 3 = +3.

xn

powerThe power is the same as an exponent. For example, x to the second power is the same as x squared (x2). A number

to the third power is the same as that number cubed (x3).

2,3,5,7,11,13,17...prime number

A prime number is a positive number that has exactly two factors, 1 and itself. Alternatively, you can think of a prime number as a number

greater than one that is not the product of smaller numbers. For example, 13 is a prime number because it can only be divided evenly by 1 and 13. For another example, 14 is not a prime number because it can

be divided evenly by 1, 2, 7, and 14. The number one is not a prime number because it has only one factor, 1 itself.

prismA prism is a solid figure that

has two parallel and congruent bases, and its faces

are rectangles or parallelograms.

probabilityProbability is the chance that a certain event will occur. A

probability of 0 (or 0%) means that the event will not occur. A probability of 1 (or 100%) means that the event will

definitely occur. For example, the probability that a coin toss will result in heads has a probability of 1/2 (or 50%). The probability that a die throw will result in a six has a

probability of 1/6 (or about 17%).

productThe product is the answer in

a multiplication problem.

proofA proof is a logical

mathematical argument that persuades the reader that a statement is true.

protractorA protractor is a

device that measures angles.

PtolemyClaudius Ptolemaeus or Ptolemy (about 87-150) was a Greek astronomer and mathematician who

wrote about his belief that all celestial bodies revolved around the Earth. His writings

influenced people's ideas about the universe for over a thousand years, until the Copernican

System (with a heliocentric solar system) was accepted.

pyramidA pyramid is a shape that has a flat polygonal base and triangular sides that

meet at a point on the top. The pyramids in Egypt are

huge buildings build by ancient Egyptians.

PythagorasPythagoras of Samos (569-475 BC) was a Greek philosopher, mathematician, and astronomer who founded a philosophical and religious school, the Pythagorean school in Croton, Italy. Pythagoras believed that the Earth was a sphere at the center

of the Universe. He correctly realized that the morning star and the evening star were the same

object, the planet Venus. Pythagoras (or the Pythagoreans) made a number of fundamental

mathematical discoveries: that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (known as the Pythagorean theorem); that the sum of the

angles of a triangle is equal to two right angles; and that irrational numbers exist. A 142 km wide lunar crater was named for Pythagoras (Latitude

63.5°, Longitude 63.0°).

Pythagorean theoremThe Pythagorean theorem states that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse: a2 +

b2 = h2.

Q.E.D.Q.E.D. is an

abbreviation of the Latin phrase "quod erat demonstrandum"

(meaning "that which was to be

demonstrated"). Q.E.D. can be written at the end of a mathematical proof to show that the proof is

complete.

quadrantA quadrant is a quarter of a plane.

The x-axis and y-axis divide the x-y plane into four quadrants. The axes

themselves are not part of the quadrants.

quadratic equationA quadratic equation is an equation that has a second-degree term and no higher terms. A second-degree

term is a variable raised to the second power, like x2, or the

product of exactly two variables, like x and y.

When you graph a quadratic equation in one variable like ax2 + bx + c, you get a parabola, and the solutions to the quadratic equation

represent the points where the parabola crosses the x-axis.

quadratic formulaThe quadratic formula is a formula ax2 + bx + c

= 0 that gives you a solution to the quadratic equation. The quadratic formula is obtained by

solving the general quadratic equation.

quadrilateralA quadrilateral is a four-sided figure. The square, rectangle, rhombus, trapezoid, kite, and

parallelogram are quadrilaterals.

quartA quart is one-

fourth of a gallon. Four quarts make

one gallon.

quarterA quarter is a coin that

is worth 25 cents. Four quarters make

one dollar.

quartileA quartile for a data set is one of three data points that divide the set of

data into four parts, each containing a quarter of the data. The first point marks the lower quartile boundary at the 25th percentile. The second marks the middle quartile (or midpoint of the data set), the median or the 50th percentile. The last marks the upper quartile (or

75th percentile) of a frequency distribution.

quotientThe quotient is the answer in long division. The dividend divided by the divisor is the quotient (plus a remainder).

radianA radian is a unit of angular measure that is

equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. A radian is about 57.2957° (1 degree = 0.0174532 radians). There are 2*pi radians

in 360°.

radiusThe radius is the

distance from the center of a

circle (or a sphere) to the

edge.

1/2ratio

A ratio is the relationship between two numbers,

denoted by division. For example, if the ratio of boys to girls at a school is 4 to 5, this can be written as 4/5 or 4:5.

rational numberA rational number is a number that can be

expressed in the form a/b, where a and b are integers and b≠0. For example, 0, 1/2, and -41 are

rational numbers. Each rational number corresponds to a unique point on the number line

(but most points on the number line do not correspond to a rational number -- they correspond

to an irrational number).

rayA ray (also called a half line) is a straight line that extends infinitely far in one direction from a point.

real numberReal numbers are all rational and irrational

numbers (but not the imaginary numbers). The real numbers represent all the points on the number

line.

rectangleA rectangle is a four-sided figure (a quadrilateral) whose

sides are at right angles to each other. A square is a type of rectangle whose four sides are all the same length.

regular polygonA regular polygon is a polygon (a polygon is a many-sided figure with straight edges) whose

sides are all the same length and whose interior angles are all the same (like an equilateral

triangle or a square).

remainderThe remainder is the part part of the answer in long division that does not go evenly into the divisor. The dividend divided by the divisor is

the quotient plus the remainder.

rhomboidA rhomboid is a

parallelogram with oblique angles and adjacent sides

have different lengths.

rhombusA rhombus is a

parallelogram with equal-length sides.

right angleA right angle looks like the corner

of a square; it extends ninety degrees. Each of the interior

angles of a square is a right angle.

right triangleA right triangle has one

angle that is a right angle (extending 90

degrees).

Roman numeralsThousands of years ago, in ancient Rome, the Romans used a system of numbers that we call Roman numerals. In this system, I=1, V=5, X=10, L=50, C=100, D=500, and

M=1,000.Roman numerals express numbers as sums and differences. For example, 6 is VI (five +

one), but nine is IX (ten - one). In general, when a smaller Roman numeral follows a larger numeral, you add the numbers (for example, XII is ten +one+one=twelve). When

a larger numeral follows a smaller one, you subtract the numbers (for example, IV is five-one=four, and XL is 50-10=40).

roundRound things are curved. A

circle is round.

Number Nearest ten Nearest hundred Nearest thousand368 370 400 0

1,234 1,230 1,200 1,00089,355 89,360 89,400 89,000

roundingWhen a number is rounded (or rounded off), it is approximated by eliminating the least

significant digits. Whole numbers can be rounded to the tens place, hundreds place, thousands place, and so on. Decimals can also be rounded, estimating the number to the

nearest tenth, hundredth, thousandth, and so on. Rounding is used to make a number easier to work with. For example, if you know that there are 496 students in your school, you can

say that there are approximately 500 students in your school.

rulerA ruler is a long,

straight object that is used for measuring

distances or drawing straight lines

scalarA scalar is a number (a

magnitude) without a direction (compare with vector). For

example, speed is a scalar; it tells you how fast something is traveling but not the direction.

scalene triangleThe sides of a

scalene triangle are all different lengths.

scienceScientists study science to learn

about the physical world.

scientific notationScientific notation is a mathematical format used to

write very large and very small numbers; this system avoids using a lot of zeros by using powers

(exponents). In scientific notation, there is a number between 1 and 10 multiplied by a power of

ten. For example, the number 250 written in scientific notation is 2.5 x 102. For another

example, the number 0.000052 written in scientific notation is 5.2 x 10-5.

secantSecant (abbreviated sec) is a trigonometric ratio,

corresponding to the length of the hypotenuse divided by the length of the adjacent side of the right triangle.

Secant is equal to 1/cosine.

secant lineA secant line is a line that intersects a circle or curve in two places.

secondThe second item comes after the

first item and before the third

secondA second is a measure of angle

that is equal to 1/60th of a minute (a minute is 1/60th of a

degree).

item. Second is abbreviated 2nd.

secondA second is a measure of time that is equal to

1/60th of a minute.

semicircleA semicircle is

half a circle.semi-major axis

The semi-major axis of an ellipse (a flattened circle) is half the length of the line segment across the

longest part of the ellipse.

semi-minor axisThe semi-minor axis of an ellipse (a flattened circle)

is half the length of the line segment across the shortest part of the ellipse.

1+1/2+1/3+1/4+1/5+...

seriesA series is a sum of a sequence of

numbers.

setA set is a collection of numbers or objects. The items in a set are called the elements or members of that set. The empty set

{} is also called the null set.

sevenSeven is the number between six and eight.

There are seven days in the week. A heptagon is a seven-sided figure.

sineSine (abbreviated sin) is a trigonometric ratio,

corresponding to the length of the opposite side divided by the length of the hypotenuse of the

right triangle.

sixSix is the number between five and seven. A six-sided figure is called a hexagon. Insects have

six legs.

skewTwo lines are skew if they do not lie on the same plane and are not parallel. Skew lines do not ever

intersect.

skip countingSkip counting is counting

while skipping some numbers, like 2, 4, 6, 8,...

slopeThe slope of a line (also called the rise over the run) is the steepness of a line. To find the slope of a line, look at any two points on the line, (x1, y1)

and (x2, y2) and determine the rise/run, or (y2-y1)/(x2-x1). When a linear equation is in the form: y=mx+b, m is the slope of the line (and b is the y-

intercept).

solveWhen you solve an

equation or a problem, you find

solutions for it.

sphereA sphere is a ball-shaped object. The volume of a sphere is 4πr3/3 (where

r=radius of sphere).

spiralA spiral is a curve

that winds in on itself. Snail shells have a

spiral pattern.

squareA square is a four-sided figure (a

quadrilateral) that has four, equally long sides which are at right angles to

each other.

square numbersSquare numbers are numbers that are the

square of an integer, like 1 (which is 12), 4 (which is 22), 9 (which is 32), 16 (which is

42), 25 (which is 52), etc.

square rootThe square roots of a number n are the

numbers s such that s2=n. For example, the square roots of 4 are 2 and -2; the square

roots of 9 are 3 and -3.

starA star is a shape that has many

points.

subtendTo subtend is to be opposite to and to delimit. For example, in

the triangle above, the side labeled b subtends the angle B.

1-1=0

5-3=2

subtractionSubtraction is an operation in which one number is

taken away from another number. For example, 4 - 1 = 3 (four minus one equals three). A number minus

itself is equal to zero (for example, 3 - 3 = 0). Subtraction is the inverse operation of addition. That

is, a + b - b = a. Subtraction is considered to be a binary operation because it is performed on two

numbers.

subtrahendThe subtrahend is the number that is subtracted from another

number in a subtraction problem.

sumThe sum is the answer to an addition problem.

xsuperscript

superscriptA superscript is a raised text, usually

in a smaller font. A superscript in mathematics often means a power or exponent. For example, x2 means x

squared (or x to the second power or x times x). x0.5 means the square root

of x.

supplementary angleA supplementary angle is an angle that, when added to another angle, equals

180 degrees.

! /,< +-=÷¢

symbolA symbol is a mark or sign that stands for something else. For example, the symbol ÷ means

divide.symmetry

A figure exhibits symmetry when part of the figure is the mirror image of another part of the figure. For example, an

object has line (or reflection) symmetry when one side of the figure is a mirror image of the other across the line of

symmetry (for example, a heart has linear symmetry). An object has plane symmetry when two halves of the object are

mirror reflections of each other across a plane of symmetry (for example, a cylinder has plane symmetry). An object has radial (or point) symmetry when it is symmetric around a point (for example, a circle has point symmetry since every point on the

circle has a mirror image of itself across the central point).

tally marksTally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers;

the fifth number is represented by a diagonal line across the previous four.

tangentTangent (abbreviated tan) is a

trigonometric ratio, corresponding to the length of the oppsite side

divided by the length of the adjacent side of the right triangle.

tangramA tangram is a

traditional Chinese puzzle that can be made into many

shapes.

tape measureA tape measure is a simple device used to measure

things.

temperatureTemperature is a measure of the heat. Temperature is measured

using a thermometer.

tenTen is the number between nine and eleven. People have ten fingers and ten toes. Our number system is base 10. A ten-sided polygon is called a decagon.

tetrahedronA tetrahedron is a

pyramid formed by four triangles.

thermometerA thermometer is used for measuring the temperature.

thirdThe third person or item comes after the first and

second. Third is abbreviated 3rd.

13*************

thirteenThirteen is the number after twelve (12)

and before fourteen (14). A thirteen-sided polygon is called a tridecagon.

30******************************

thirtyThirty is the number after twenty nine (29) and before thirty one (31). A thirty-sided polygon is

called an triacontagon.

1,000thousand

One thousand is a whole number that is equal to

100 times 10.

threeThree is the number between two and four. A tricycle has three wheels. A triangle has three sides. A Triceratops is a dinosaur that

had three horns. Tri means three!

timeTime is measured in

seconds, minutes, hours, days, weeks, months, and years.

timelineA timeline is a graphic display that shows a series of events that happen in a time period.

time zoneThe Earth is divided into 24 time zones so that

everyone in the world can be on roughly similar schedules (like having noon when the

sun is highest in the sky).

torusA torus is a

doughnut-shaped solid object.

transcendental numberA transcendental number is a number that is not the root of a polynomial equation with integer coefficients. Examples of

transcendental numbers include e and pi .

transversalA transversal is a line that intersects at least two other

lines.

trapezoidA trapezoid is a four-sided figure (a quadrilateral) with exactly two

parallel sides.

triangleA triangle is a geometric figure (a polygon) that has three sides. The sum of the

interior angles of a triangle is 180 degrees. The perimeter of a triangle is the sum of the lengths of the three sides. The area of a triangle is (1/2)base*height. A triangle with three equal sides (and three equal angles) is called an equilateral triangle. A

triangle with two equal sides (and two equal angles) is called an isosceles triangle. A triangle with no equal sides (and no equal angles) is called an scalene triangle. A

triangle with one right angle is called a right triangle. The Pythagorean theorem states that for a right triangle, the sum of the squares of the two shorter sides is equal to the

square of the hypotenuse: a2 + b2 = h2. A triangle with one obtuse angle is called a obtuse triangle. A triangle with all acute angles is called a acute triangle.

2x + 3y

trinomialA trinomial is a

polynomial expression that has three terms, like

3x2 + 4yz - 5.

trisectTo trisect is to divide into three

equal parts. For example, if a 90-degree angle is trisected, the result

is three 30-degree angles.

12************

twelveTwelve (12) is the number between eleven (11) and thirteen (13). Dozen is another word for twelve. A

dodecagon is a twelve-sided figure. A dodecahedron is a twelve-sided geometric solid whose faces are

pentagons.

twentyTwenty is the number between nineteen and twenty-one. There are

twenty (20) apples above. A twenty-sided polygon is called an icosagon.

twoTwo is the number between one and

three. We have two eyes, two ears, two arms, and two legs.

undecagonAn undecagon is an eleven-sided figure

(hendecagon is another word for this figure). The Canadian one dollar coin (also called the

loonie) is an undecagon.

unionA union of two sets A and B (written A U B) is the set consisting of all the

elements that are in either or both of those two sets. For example if A={1, 2, 3} and B={3, 4, 5}, A U B= {1, 2, 3, 4,

unitA unit means one.

5}.

unit fractionA unit fraction is a fraction that has a one in the

numerator, like 1/2, 1/3, 1/4, etc.

unknownAn unknown is a number whose value is not known. For example,

in the equation 2x2 - 3x = 6, x is the unknown.

unlike fractionUnlike fractions are two or

more fractions whose denominators are not the same,

like 1/2, 1/3, and 1/5.

VV equals 5 in

Roman numerals.

variableA variable is an unknown or placeholder in an algebraic expression. For example, in 2x+y, x and y are variables.

vectorA vector is a number (a magnitude) together with a direction

(compare with scalar). A vector can be represented by an arrow whose length represents the magnitude and the direction

represents the direction. For example, velocity is a vector; velocity tells you how fast something is traveling, and its direction.

Venn diagramA Venn diagram is a diagram

that uses overlapping circles to show relationships among sets

of things.

vertexA vertex of an angle is a point at which two sides of the angle meet. A vertex of a polygon is

a point at which two of the sides meet. A vertex of a polyhedron is a point at which 3 or more faces meet.

volumeVolume is a measure of 3-dimensional space expressed

in cubic units.

wavelengthA wavelength is the distance

between two wave crests.

wedgeA wedge is a tapered block that is used for holding things in place, splitting things or tightening things.

weekThere are 7 days in a week; Sunday, Monday,

Tuesday, Wednesday, Thursday, Friday, and Saturday. There are 52 weeks in a year.

whole numberThe whole numbers are an infinite set of

numbers: {0, 1, 2, 3, 4, 5...}. wideWhen something is wide, it takes up a lot

space from side to side.

word problemA word problem is a mathematical question phrased in

terms of words, not equations.

XX equals 10 in

Roman numerals. x-axisThe x-axis is usually the horizontal axis.

x-coordinateThe x-coordinate (also called the abscissa) is

the horizontal distance of a point from the origin. It is the first number in the ordered

pair representing a point (x,y).x-intercept

An x-intercept is a point (x,0) at which a graph goes through (intersects) the x-axis. The x-intercepts are the

points on the graph at which y=0.

yardstickA yardstick is three feet long (a yard);

it is used for measuring things. y-axisThe y-axis is usually the

vertical axis.

y-coordinateThe y-coordinate (also called the ordinate) is the vertical distance of a point from the origin. It is the second number in the ordered pair representing a point (x,y).

yearA year consists of 12 months, 52 weeks, or

about 365 days.y-intercept

An y-intercept is a point (0,y) at which a graph goes through (intersects) the y-axis. The y-intercepts are the points on the graph at which x=0.

z-axisThe z-axis

represents the third dimension in a

graph.

0zero

Zero is a number that stands for the absence of size or quantity. One is the additive identity, since one plus any number is equal to that number. Any number times zero

is zero. You cannot divide a number by zero.

f(x) = 0

zeros of a functionThe zeros of a function are the points at which the

value of the function is zero. Graphically, these are the points at which the plot touches or crosses

the x-axis (i.e., y=0).

zigzagA zigzag is a line that sharply turns back and forth.