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|-3|=3 abundant number absolute value An abundant number (also called a redundant The absolute value of a number) is number (an integer) for which the number is the distance from sum of its proper factors (divisors) is greater abacus the origin on a number line. abscissa than the number itself. For example, 12 is an An abacus is an ancient The abscissa is the x-axis of a coordinate For example, the absolute abundant number because the proper divisors of device that is used for system. The numerical value of the value of 2 is 2 (written |2|=2). 12 are 1, 2, 3, 4, 6, which add up to 16, which is arithmetic calculations. The absolute value of -2 is abscissa tells you the distance from the greater than 12. Compare with perfect number, origin along the x-axis. The abscissa is also 2 (written |-2|=2). deficient number. the first number, x, in the coordinates of a point (x,y). 1+1=2 2+3=5 acute angle An acute angle is less than 90 degrees. 0 acute triangle addition addend All three interior angles of an acute triangle are acute (less than 90 degrees). algebra Addition is the summing of The addend is one of the numbers that is being numbers to determine their total. added in order to find a sum. algorithm Algebra is the study of generalized arithmetic. In additive identity An algorithm is series of steps alpha The additive identity is the algebra, unknown numbers can be represented by letters or rules used for solving a Alpha is the first letter in the in order to solve equations. For example, 4 + x = 10 is number zero because zero problem. For example, the Greek alphabet. Alpha often true for x=6. Algebra (originally called al-jabr) was plus any number is equal to standard method for doing denotes the first term in a invented in the Middle East by Abu Ja'far Muhammad the original number. For long division problems is an series or the brightest star in ibn Musa Al-Khwarizmi (born in Baghdad about AD example, 2+0=0+2=2. algorithm. a constellation. 825) during the Middle Ages. angular distance Angstrom An Angstrom is equal to one angle ten billionth (1 x 10-10) of a An angle is the amount of rotation it would take meter. This unit of measure is named for the Swedish to put one intersecting physicist Anders J. Ångström. line on top of another. Angular distance is the measure of an arc (a segment of the circumference of a circle). Angular distance measures the arc proportion of a circle that the arc in question consists of. An arc is a segment along Angular distance is expressed in degrees, radians, arc minutes the circumference of a (one-sixtieth of a degree), or arc seconds (one-sixtieth of a circle, or the part of any minute). For example, latitude is the angular distance north or curve between two points. 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. arithmetic sequence (or arithmetic progression) 1+1=2 area 7-4=3 The 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 Arithmetic is the study of addition, subtraction, multiplication, and division. arithmetic An arithmetic sequence, also called an arithmetic progression, is an The arithmetic mean of a set of ordered list of numbers where each numbers (also called the average) term is obtained by adding (or is equal to the sum of the numbers subtracting) a constant amount to the divided by the number of previous term. For example, the numbers. For example, for the data arithmetic sequence set {1, 2, 3, 6}, the mean is 0, 2, 4, 6, 8, 10, ... (1+2+3+6)/4 = 12/4 = 3. is the sequence of numbers starting with 0 where the terms increase by 2 in turn. arithmetic mean (a + b) + c =a+ (b + c) (a x b) x c =a x (b x c) average associative property The 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. Also called the arithmetic mean, the average of of a set of numbers asymmetrical is the sum of the numbers divided Something that is by the number of numbers. For asymptote asymmetrical is not example, the average of 1,4,6,9 is symmetrical - it does not An asymptote is a straight line that defines (1+4+6+9)/4=5. the limits of a curve (such as a hyperbola). have symmetry. For example, the figure above In the picture above, the dashed lines are asymptotes of the hyperbola. is asymmetrical. axiom axis of symmetry An axiom is a statement that is assumed or accepted to be true as a starting point for proving other things. axis An 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. An axis of symmetry is a line about which something is symmetrical. For example, the diameter of a circle is an axis of symmetry. base bar code Bar 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 base bar graph A bar graph is a type of graph that The base is the bottom of a geometric figure, like the bottom In 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 items that need to be tracked (like visually displays information using train cars). a series of bars or rectangles. of a cone. The base is defined as the side opposite a vertex. power of 8 (and only the numbers 0 through 7 are used). 2x + 3y 1,000,000,000 binary number system bisect binomial The binary number system is a way of expressing billion To bisect is to divide into two A binomial is a A billion is a thousand million or ten numbers in base two. Each place value is a power of 2 (in equal (congruent) parts. For polynomial our ordinary base ten system, each place value is a power to the ninth power. The Earth is expression that has example, if you bisect a 90 billions of years old and there are of 10). Only the numbers 0 and 1 are used in this system. degree angle, you divide it two terms, like 3x2 For example, in the binary number system, 11 represents billions of stars in the sky. into two 45 degree angles. + 4yz. the number 3, and 101 represents the number 5. bisector A bisector is is a line or ray that divides something (an angle, line segment or arc) into two equal (congruent) parts. calculus C C equals 100 in Roman numerals. calculator A calculator is a machine that solves math problems. Calculus is a branch of mathematics that was developed separately by calendar Gottfried Wilhelm Leibniz and Isaac Newton in the 1600s. Calculus is used to A calendar divides the calculate motion and areas (and many other things). Differentiation and year into periods and lets integrations are two major areas of calculus. you know what day it is. ≤5 ≥5 Even 0,2,4 6,8,10 Odd 1,3 5,7,9 cardinal number A cardinal Carroll diagram carry number is a A Carroll diagram (named for the When you carry in whole number mathematician/author Lewis Carroll) is addition, the sum of the Cartesian coordinates that tells you a rectangular chart that is used to sort numbers is ten or more, A Cartesian coordinate system is a rectangular coordinate system "How many?". items with respect to one, two or three with two axes (x is the horizontal axis and y is the vertical axis). and the ten's place is binary (yes/no) categories. Every point on the plane can be located by an ordered pair (x,y), "carried" to the next place. 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. center of mass cent Cent is another word for penny. centi The center of mass is the location at which the entire Centi is a prefix that mass of an object (or set of objects) may be means one-hundredth. For considered for purposes of calculations. It is the example, a centimeter is point of the average weighted position in space of an one hundredth of a meter. object (or a collection of objects). centroid The centroid is the point at which a geometric figure balances. The centroid of a triangle is the point at which the three medians intersect. circumference circle chord A chord is a line segment that connects two points on a circle. The longest chord on a circle is the diameter of the circle. All 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 graph A circle graph (also called a pie chart) is a diagram that is useful for displaying information about the percentages or parts of a whole. The circumference is the distance around an object. The circumference of a circle of radius r is 2πr . axb=bxa collinear Points that are collinear are on the same line. clock A clock tells you what time it is. coin commutative property The 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. A coin is a piece of metal money. complementary angle compatible numbers compass Two compatible numbers form a A compass is a device that division fact. For example, since 72 divided by 9 is 8, 72 and 9 are always points north. A compatible numbers (so are 72 and 8). compass is also a device that draws circles. compass rose A compass rose is a design on a map that shows direction. It points which way is north, south, east, west, and some intermediate directions on the map. A complementary angle is an angle that, when added to another angle, equals 90 degrees. complex fraction complex number A complex fraction is a A complex number is a number that can fraction that has a fraction in be written in the form a + bi, where a and the numerator, denominator, b are real numbers and i is the square root or both. of -1 (an imaginary number ). concentric circles conditional composite number A 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. computer You are using a computer right now. congruent A conditional (also called an if-then Congruent means having the same statement or an implication) is a shape and size. For example, two cone Concentric circles statement of the form, "if p then q" - p is triangles are congruent if they have A cone is a shape that has a point at the center are circles that called the antecedent, p is called the the same interior angles and same side and a circular cross-section throughout (it have the same consequent. The conditional "if p then q" length. Two line segments are looks like two infinitely-long ice cream cones center point. is false only when p is true and q is false. congruent if they are the same length. 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). conic section conjecture connect-the-dots A conic section is set of points that A conjecture is When you do a connect- results from the intersection of a cone an educated and a plane. Some conic sections the-dots puzzle, you draw guess. include a point, ellipse, circle, a line from number to parabola, and hyperbola. number to make a picture. consecutive cosecant 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. cosine cotangent Cosecant (abbreviated csc) is a Cotangent (abbreviated cot) is a Consecutive means in order. Cosine (abbreviated cos) is a trigonometric ratio, corresponding to trigonometric ratio, corresponding to the For example, 1 and 2 are trigonometric ratio, corresponding the length of the hypotenuse divided by length of the adjacent side divided by consecutive whole numbers; to the length of the adjacent side the length of the opposite side of the the length of the opposite side of the 6 and 8 are consecutive even divided by the length of the right triangle. Cosecant is equal to right triangle. Cotangent is equal to numbers. hypotenuse of the right triangle. 1/sine. 1/tangent. counting number cube cubed Cubed means raised to the The counting numbers are crescent A cube is a solid geometric figure with six square faces. third power, like x3 . For the positive whole A crescent is the shape of the The volume of a cube is s3 (where s=length of a side of the example, 2 cubed = 2 x 2 x 2 numbers, 1, 2, 3, 4, 5... . moon shortly before and after cube). The surface area of a cube is 6s2 (where s=length of = 8. the time of the new moon. a side of the cube). cubic equation cube root The 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. cylinder A cubic equation is an A cylinder is a 3-dimensional figure with a long tube-like body and equation whose highest congruent, parallel bases. A right-circular cylinder has a base that is curve degree term is 3. For 3 2 A curve is perpendicular to the axis of the cylinder (it is like a can of food). The example, 5x - 8x + volume of a right-circular cylinder is πr2L (where L=length of cylinder, a wavy 2xy = 4 is a cubic r=radius of cylinder). The surface area of a cylinder is 2πrL (where line. equation. L=length of cylinder, r=radius of cylinder). 1.33 decagon deci decimal Deci is a prefix that A decimal is a base 10 A decagon is a means one-tenth. For number that is written ten-sided decimal point example, a decimeter with a decimal point in geometric A decimal point is a dot that separates the a number into it. For example, 1.1, is one tenth of a figure. the whole number part (on the left of the decimal point) 10.43, and 0.01 are meter. and the fraction (to the right of the decimal point). For decimals. example in 21.46, 21 is the whole number and .46 (fortysix hundredths) is the fraction. deficient number A 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. degree Descartes A degree is a measure of René Descartes ( March 31, 1596 temperature or angle. There are February 11, 1650) was a French denominator 360 degrees in a circle. Each mathematician and philosopher. The denominator is degree is divided into 60 minutes, Descartes invented the Cartesian the bottom number represented by the apostrophe coordinate system and many principles in a fraction. symbol, '. 1°=60'. of philosophy. diagonal diameter A diagonal is a line that joins The diameter is the longest two non-consecutive vertices distance from one side of a circle of a polygon. (or a sphere) to the other. diamond dice A diamond is a four-sided figure (a quadrilateral) whose sides are all the same length. People play baseball on a diamondshaped field. Dice are cubes with numbers on each side that are used in games. A single one is called a die. digit A digit is a single numeral within a number. For difference dime example, the number 153 is The difference is the answer in A dime is a coin a 3-digit number. a subtraction problem. worth ten cents. dividend The dividend is the number that is divided (in long division). The dividend divided by the divisor is the quotient (plus a remainder). directrix The 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. division Division 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. divisor The 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). dodecagon A dodecagon is a twelve-sided polygon (figure). dot dollar A dollar is worth 100 cents. dodecahedron A dodecahedron is a twelve-sided geometric solid whose faces are pentagons. A dot is a tiny speck or point. dominoes Dominoes is a game played with tiles that have dots on them. **** **** **** 12 dozen Dozen is another word for twelve. 18 e e e is a transcendental number that is equal to approximately 2.71828182845904523536028747135266249... e is an irrational, nonrepeating decimal and is the base of the natural logarithm. The symbol e honors the Swiss mathematician Euler (e is sometimes called Euler's number). eight eighteen Eight is the number Eighteen is the number between seven and nine. between seventeen and Spiders have eight legs. nineteen. An eighteenStop signs have eight sided polygon is called an sides. An eight-sided octadecagon. figure is called an octagon. 80 eighty Eighty is the number between seventy-nine and eightyone. 11 {} ***** ****** empty set ellipse enneadecagon The empty set (also An enneadecagon is a eleven An ellipse looks like a flattened circle. It consists of all the points in a called the null set) nineteen-sided Eleven is the number between plane that satisfy the following: a+b=(twice the length of the semiis the set that has polygon. ten and twelve. Eleven is ten no elements. major axis), where a is the distance from one focus to the point on the plus one. An eleven-sided figure ellipse, and b is the distance from the other focus to the same point on is called a hendecagon or an the ellipse. undecagon. = equal When two things are equal they are exactly the same in number, quality, or amount. 1+1=2 3-x=2 equator equation An equation is a mathematical statement that contains an equal sign, like ax + b = c. 0, 2, 4, 6, 8, 10, ... 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. even number An even number is divisible by two. The equator is an imaginary circle around the Earth or any orb, halfway between the North and South Poles. ! exclamation point equilateral triangle The sides of an equilateral triangle are all the same length and all the interior angles are 60 degrees. x n exponent An exponent is a power that In mathematics, the exclamation point means factorial. a number is raised to. For The factorial of a number is equal to the number times example, in 23, the exponent all the positive whole numbers less than it. For is 3. example, 5!= 5x4x3x2x1=120 exponential notation expression Exponential notation (also called scientific notation) is a short-hand way of expressing very small or An algebraic expression consists of one or very large numbers; this system avoids using a lot of zeros by using powers (exponents). In scientific more variables, constants, and operations, like notation, there is a number between 1 and 10 multiplied by a power of ten. For example, the number 3x-4. Each part of an expression that is added 250 written in scientific notation is 2.5 x 10 2. For another example, the number 0.000052 written in or subtracted is called a term For example, the scientific notation is 5.2 x 10 -5. expression 4x2 -2x+7 has three terms. factor ! The factor of a number is factor tree factorial Fahrenheit a number that divides that A factor tree is a graphical In math, the exclamation point means Fahrenheit is a measure of temperature that is number exactly. For representation in tree form factorial! The factorial of a number is equal abbreviated F. Water freezes at 32°F and boils example, the factors of 6 that shows the factors of a to the number times all the positive whole at 212°F. are 1, 2, 3 and 6. specific number. numbers less than it. For example, 5!= 5x4x3x2x1=120. 1, 1, 2, 3, 5, 8, 13... Fibonacci numbers The 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 ********** ********** ********** ********** ********** fifty Fifty is the number after forty nine (49) and before fifty one (51). A fifty-sided figure is called a pentacontagon. first The first person or thing comes before the others. First is abbreviated 1st. (ax + b)( cx + d) FOIL FOIL is an acronym that stands for First, Outer, Inner, foot Last. It refers to a method of multiplying two binomials, A foot is a unit of like (ax + b)( cx + d). To multiply, you must multiply each measurement that is term out, including the first terms (ax times cx), the inner equal to twelve inches or terms (b times cx), the outer terms (ax times d), and the one third of a yard. 2 last terms (b times d). For example, (2x + 3)( 4x + 5) = 8x + 10x + 12x + 15 = 8x2 + 22x + 15. five Five is the number between four and six. We have five fingers on each hand. A pentagon is a five-sided figure. focus A focus (plural foci) is one of the central points of a conic section, such as an ellipse, hyperbola, or parabola. F=ma formula A formula shows a mathematical relationship between expressions. 40 ********** ********** ********** ********** forty Forty is the number after thirty nine (39) and before forty one (41). 14 ******* ******* fourteen four Four is the number after three (3) and before five (5). A quadrilateral is a geometric figure that has four sides. 1/2 fraction fractal Fractals are patterns Fourteen is the number after thirteen (13) and within patterns within before fifteen (15). A fourteen-sided polygon patterns. is called a tetradecagon. 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. GCF GCD Johann Carl Friedrich Gauss (April 30, 1777-Feb. 23, 1855) was The Greatest Common Factor (GCF) [also called the Greatest Common Divisor a great German mathematician, physicist, and astronomer. Gauss Greatest Common Divisor or GCD] is the largest (GCD) means the same did important work in number theory, analysis, differential positive integer that is a factor of two or more numbers. thing as Greatest Common geometry, statistics, magnetism, and the motion of planetoids. For example, the GCF of 14 and 21 is 7. It can be Factor (GCF). written GCF(14, 21) = 7. geometry Geometry is the mathematical study of points, lines, angles, and solids. Goldbach's Conjecture globe Goldbach's Conjecture states that every even integer greater than 2 can be expressed as the A globe is a small, sum of two prime numbers. It was first noticed by the mathematician Christian Goldbach spherical model of the in 1742. It has yet to be proven or disproven. Earth. googol 100 A googol is the number 10 (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. googolplex A 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 ratio The 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. > graph A graph is a diagram that shows relationships between things. GCF great circle A great circle is an imaginary circle greater than on the surface of a sphere whose The mathematical symbol > means "greater than." plane passes through the center of When one number is greater than a second number, the the sphere. first one is bigger than the second. For example, 4 is greater than 2, or 4 > 2. Greatest 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 Greek Alphabet Greatest Common Divisor The Greatest Common Divisor (GCD) is another was of writing the Greatest Common Factor (GCF). The 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. 1/2 half 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. hectogon half moon A half moon looks like half a circle. A hectogon is a hundred-sided figure. hemisphere A hemisphere is half of a sphere. hendecagon A 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. hexagon heptagon A heptagon is a seven-sided figure. hexaflexagon A hexaflexagon is a folded geometric figure that can be "flexed" to expose its many sides. A hexagon is a six-sided figure. Beehives have hexagonal cells. histogram hexagonal prism A 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. hieroglyphics The ancient Egyptians wrote using hieroglyphics. A histogram is a block-style graph that presents frequency data in statistics. hour There are 24 hours in a day. Hypatia 100 hundred hour hand An hour hand on a clock tells you what hour it is. One hundred is the number between 99 and 101. A hundredsided figure is called a hectogon. Hypatia 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 hyperbola Alexandria). A pagan, she was murdered in 415 by A hyperbola is a conic section (the Christian monks in a religious/political struggle. The intersection of a cone with a plane) that has lunar Crater Hypatia and Rimae Hypatia were named for two mirror-image branches. Hyperbolas her. have an eccentricity greater than 1. hypotenuse The hypotenuse is the longest side of a right triangle, the side opposite the right angle. 0 i i is an imaginary number, defined I as the square root of negative I equals 1 in Roman one. numerals. identity for addition icosahedron An icosahedron is a twentysided geometric solid. 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. 1 i identity for multiplication imaginary number The 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. An imaginary number is a number of the form bi, where i is the square root of negative one and b is a real number. illusion An illusion is something that tricks your eyes. Improper Fraction An 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). = Equal > Greater Than < Less Than 1=1 2>1 1<3 inequality inch An inch is a unit of measurement that is equal to one-twelfth of a foot. The symbol for inch is ". Infinity is a concept of endlessness. The symbol above represents infinity. inverse property of addition The inverse property of An intersection is where two or more things, addition states that for every number a, a + (-a) like roads or sets, meet or overlap. The = 0 (zero). intersection of two sets is the set of objects that belong to both of the original sets. intersection integer infinity The integers are the numbers ..., -3, -2, -1, 0, 1, 2, .... An 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). inverse property of multiplication The inverse property of multiplication states that for every non-zero number a, a times (1/a) = 1. irrational number An 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 triangle An isosceles triangle has two sides that are the same length and two angles that are the same. KM KILOGRAM A 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. Km is short for kilometer or kilometers. kite A kite is a four-sided figure (a quadrilateral) in which the two pairs of adjacent sides have the same length. LCD latitude L L equals 50 in Roman numerals. LCM LCD stands for Least Common The Least Common Multiple (LCM) is Latitude is the angular distance north or south Denominator. LCD is the smallest the smallest number that is a multiple of from the equator to a particular location. The common denominator of two or more two or more numbers. For example, the equator has a latitude of zero degrees. The North fractions. For example, the LCD for LCM of 6 and 8 is 24 or LCM(6,8)=24. Pole has a latitude of 90 degrees North; the 1/7 and 3/5 is 35 South Pole has a latitude of 90 degrees South. < Least Common Denominator Least Common Multiple The Least Common Denominator The Least Common Multiple (LCM) is (LCD) is the smallest common the smallest number that is a multiple of denominator of two or more fractions. two or more numbers. For example, the For example, the LCD for 1/7 and 3/5 is LCM of 6 and 8 is 24 or LCM(6,8)=24. 35. less than less The mathematical symbol < means "less The opposite of than." When one number is less than a second less is more. number, the first one is smaller than the second. For example, 1 is less than 2, which is written 1 < 2. logarithm linear equation line A 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). line segment A line segment is a portion of a line. long When something is long, it is not short. Longitude is the angular distance east or west from the northsouth line that passes through Greenwich, England, to a particular long division location. Greenwich, England, has a longitude of zero degrees. In long division, the dividend is divided by the The farther east or west of Greenwich you are, the greater your divisor, resulting in a quotient plus a remainder. longitude. Midway Islands (in the Pacific Ocean) have a longitude of 180 degrees (they are on the opposite side of the globe from Greenwich). 5 4 6 6 5 4 4 6 5 M 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]. longitude logic Logic is the study of reasoning and proof. A 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. Logarithms 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 10 1=10, log(10)=1. map M equals 1000 in Roman numerals. magic square In a magic square, the rows, columns, and diagonals all add up to the same number. A map (also called a cartograph) shows the features of an area. You can find your way around by using a map. mathematician maze mean, arithmetic A mathematician is a person who studies mathematics. Getting through the passages of a maze is tricky. The 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. mathematics Mathematics is the study of numbers, shapes, patterns, and logical reasoning. {1, 2, 5, 8, 10} median The 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 A measuring middle number; when the number of numbers is median cup is useful in even, the median is the average of the two The median of a triangle is a line segment from a vertex to baking and middle numbers. For example, the median of the the midpoint of the opposite side. The median of a trapezoid cooking. set {1,2,5,8,10} is 5. The median of the set is a line segment that connects the midpoints of the non{1,2,5,6,9,10} is 5.5.. parallel sides. measuring cup mental math Mental math is math that is done in your head, without writing or using a calculator or other device. milli million Milli is a prefix that means onethousandth. For example, a millimeter is one thousandth of a meter. A million is 1,000,000 or one thousand thousand or 106. minus sign minuend The minuend is the number from which another number is subtracted in a subtraction problem. The mathematical symbol means "minus." Four minus three is written, 4 - 3. 1 2/3 minute minute A minute is a measure of angle that is equal to 1/60th of a degree. A minute is a measure of time that is 1/60th of an hour. A minute is composed of 60 seconds. mixed number A mixed number is a number that is written as a whole number plus a fraction, like 1 2/3. minute hand A minute hand on a clock tells you how many minutes past the hour it is. mode modular arithmetic The mode of a group of numbers Modular arithmetic is arithmetic done with a Möbius strip is the number that occurs the limited set of numbers. For example, clock money A Möbius strip is a most in that set. For example, in arithmetic is an example of modular Money is used as a basis for trade. Most money piece of paper with the set {1, 2, 3, 3, 3, 8} the mode arithmetic; when adding hours, 11+2=1 (and is decimal (based on the number 10). Only a few only one side! is 3. not 13). countries have money with another base (like Madagascar and Mauritania, which have base 5 money). MULLER, JOHANN monomial month A monomial is a polynomial expression with only one term. For example, 3xy is a monomial; the number 6 is also a monomial. There are 12 months in a year: January, February, March, April, May, June, July, August, September, October, November, and December. Johann Müller, also known as Johann Multiples of 2: Regiomontanus (1436-1476) was a German astronomer and mathematician. He studied 2,4,6,8,10,12,... trigonometry, translating Ptolemy's Almagest, from the original Greek. Ironically, his multiple translation helped overthrow the Ptolemaic view of the universe (in which the Earth was thought A multiple of a number is the to be at the center of the universe). He also did product of the original number and another number. For work on plane and spherical trigonometry. example, the multiples of the 2 Muller also observed the motion of the moon, are 2, 4, 6, 8, 10, 12, 14, 16, planets, and comets. A 108 km diameter lunar and so on. crater, called Regiomontanus (Latitude: -28.3 degrees, Longitude: 1.0 degrees), was named for Muller. 1x2=2 2x3=6 1 multiplicative identity multiplicative inverse The multiplicative inverse of a The multiplicative identity (also called the is 1/a (where a is not equal to multiplication multiplicand identity for multiplication) is one, because a * 1 zero), since for every number a, Multiplication is a The multiplicand is the number that = 1 * a = a. For example, 2*1=1*2=2. a * (1/a) = 1. is multiplied by the multiplier in a mathematical operation used to compute areas, volumes, multiplication problem. and many other calculations. multiplier The multiplier is the number by which the multiplicand is multiplied. nanometer A nanometer is unit of measure equal to 10 angstroms, which is one billionth (1 x 10 -9) of a meter. natural number negative number The 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. A negative number is a a number less than zero, like -1, -2, -3/4, etc. Newton, Isaac Isaac 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. 19 nine nineteen nonagon Nineteen is the number Nine is the number between A nonagon is eight and ten. There are nine between eighteen and twenty. a nine-sided polygon. planets in our Solar System. A nineteen-sided polygon is called an enneadecagon. A nine-sided figure is called a nonagon. {} normal null set number line A number line is a line in which real numbers can be placed, according to number In mathematics, a normal The null set is the their value. Each point on a number line corresponds to a real number, and Numbers tell you "how line is perpendicular (at empty set, a set each real number has a unique point that corresponds to it. For example, many" or "how much." right angles) to the tangent with no the number 1.5 (1 1/2) corresponds to the point on a number line that is Some numbers are -12, 0, of a curve. members. halfway between one and two. 5, 1/2, 1.33333, π, 1600. 1, 2, 3, 4, 5 numerical order numeral A 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. oblique obelisk An obelisk is a tall, four-sided tower topped with a pyramid. obtuse angle numerator The numerator is the top number in a fraction. When numbers are in numerical order, they are in order from lowest to highest. obtuse triangle Lines or planes are oblique when An obtuse angle is One of the interior angles of an obtuse they are neither parallel nor an angle greater triangle is obtuse ( an obtuse angle is perpendicular to each other. than ninety degrees. over 90 degrees). 1, 3, 5, 7, 9, 11, ... octadecagon An octadecagon is an eighteensided figure. odd number 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). An odd number is not divisible evenly by two. 1/2 one half one One is the number between zero and two. One is the multiplicative identity, since one times any number is equal to that number. orb An orb is a ball-shaped object. operation When something is divided into two equal parts, each of these two parts is one half of the original object. opposites An operation is a rule for taking one or two Opposites are things that are very, very numbers as inputs and producing a number different from each other. Some as an output. Some arithmetic operations examples of opposites are: positive and are multiplication, division, addition, and negative, add and subtract, left and right, subtraction. big and small, up and down. order of operations ordinal number In 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 numbers show order. Some ordinals are first (1st), second (2 nd), third (3rd), fourth (4th), fifth (5th), sixth (6th), seventh (7th), eighth (8th), ninth (9th), tenth (10th), eleventh (11th), twelfth (12th), etc. origin The 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. oval ounce An ounce is a unit of measure. Eight ounces are in one cup. ordinate Ordinate is another name for the y-axis (the vertical axis). The ordinate is the second number in a point (x,y). An oval is an eggshaped figure. MOM 2002 parallel palindrome A palindrome is a word, phrase or number that reads the same forwards or backwards. A palindromic number is a parabola number that reads the same forwards or A parabola (a type of conic section) is a curve backwards, like 2002. Some other that is a set of points (P) such that the distance palindromes are: the name Bob, the from a line (the directrix) to P is equal to the number 101, and the phrase, "Madam, I'm distance from P to the focus F. Parabolas have Adam." an eccentricity of 1. Parallel lines extend in the same direction, are always the same distance apart, and never intersect (meet). parallelogram A parallelogram is a four-sided figure (a quadrilateral) whose opposite sides are parallel. pattern Pascal's triangle Pascal'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 A pattern is something that is repeated, like a design or a series of numbers. pentadecagon penny A penny is a coin worth one cent. A 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. % percent perfect number Percent mean "per hundred." The sign for A perfect number is a number (an percent is %. 100% means all, 50% means half integer) for which the sum of its proper perimeter or 50 out of 100, 25% means one quarter or 25 pentagon out of 100, 10% means one tenth or 10 out of factors (divisors) is equal to the number Perimeter is the distance around the edges of a figure. The perimeter of a square with itself. For example, 6 is a perfect A pentagon is 100, and 0% means none or 0 out of 100. To a five-sided convert a percentage to decimal notation, divide number because the proper divisors of 6 side length a is P = a+a+a+a = 4 times a. The perimeter of a circle is P = 2πr. The are 1, 2, and 3 which add up to 6. polygon. the percentage by 100; for example, 50% = 0.5 perimeter of a regular polygon is P = ns Compare with abundant number, and 10% = 0.1. To convert a decimal to a (where n is the number of sides and s is deficient number. percent, multiply the number by 100; for the side length). example, .25 = 25%. pi Pi is the ratio of the circumference of a circle to the diameter of a circle. perpendicular For any circle, you can divide the When two lines are circle's circumference (the distance perpendicular, they are at around the circle) by the diameter place value pie chart right angles (90 degrees). A (the distance across the circle Place value is a positional system of A pie chart (also called a circle line can also be through the center) and you will perpendicular to a plane (if always get exactly the same number graph) is a diagram that is useful for notation in which the position of a number with respect to a point determines its displaying information about the the line goes through the (pi), no matter how big or how small value. In the decimal (base ten) system, plane at a 90 degree angle). the circle is. Pi is a number roughly percentages or parts of a whole. Pie charts were invented in 1801 by the value of the digits is based on the equal to 3.14159265... - the digits of number ten. William Playfair (Sept 22, 1759 pi never end or repeat. The value of Feb 11, 1823). pi has been calculated up to the millions of digits. Pi is a transcendental number. + plane A plane is a flat (2-dimensional) surface that extends to infinity in all directions. A plane has no thickness. plus sign A plus sign (+) means addition or plot indicates that a number is A plot is a graph done in a coordinate system. Each point on positive. the graph is plotted (marked on the graph in the coordinate system). . point A point is an exact location, a spot with no width or thickness. polygon A 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. 5x2 - 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 2x 3 y). 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: 4x 2 + 3x + 7). If a polynomial has more than one variable, then its degree is the sum of the exponents of the highestdegree 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 equation A polynomial equation is an equation involving a polynomial. positive integer positive number xn 2,3,5,7,11,13,17... power prime number A prime number is a positive number that has exactly two factors, 1 and A positive number is a The power is the same as an A positive integer itself. Alternatively, you can think of a prime number as a number number greater than exponent. For example, x to is an integer (a greater than one that is not the product of smaller numbers. For zero. Numbers written the second power is the same whole number) example, 13 is a prime number because it can only be divided evenly by without a sign are as x squared (x2). A number greater than zero, 1 and 13. For another example, 14 is not a prime number because it can assumed to be positive. to the third power is the same like 1, 2, 3, 4, ... be divided evenly by 1, 2, 7, and 14. The number one is not a prime For example, 3 = +3. as that number cubed (x3). number because it has only one factor, 1 itself. probability prism Probability is the chance that a certain event will occur. A A prism is a solid figure that probability of 0 (or 0%) means that the event will not occur. has two parallel and A probability of 1 (or 100%) means that the event will congruent bases, and its faces definitely occur. For example, the probability that a coin are rectangles or toss will result in heads has a probability of 1/2 (or 50%). parallelograms. The probability that a die throw will result in a six has a probability of 1/6 (or about 17%). proof A proof is a logical mathematical argument product The product is the answer in that persuades the reader that a statement is true. a multiplication problem. Pythagoras protractor A protractor is a device that measures angles. Pythagoras of Samos (569-475 BC) was a Greek philosopher, mathematician, and astronomer who founded a philosophical and religious school, the pyramid Pythagorean school in Croton, Italy. Pythagoras A pyramid is a shape that believed that the Earth was a sphere at the center Ptolemy Claudius Ptolemaeus or Ptolemy (about 87-150) has a flat polygonal base of the Universe. He correctly realized that the was a Greek astronomer and mathematician who and triangular sides that morning star and the evening star were the same meet at a point on the top. wrote about his belief that all celestial bodies object, the planet Venus. Pythagoras (or the The pyramids in Egypt are revolved around the Earth. His writings Pythagoreans) made a number of fundamental huge buildings build by mathematical discoveries: that for a right triangle, influenced people's ideas about the universe for ancient Egyptians. over a thousand years, until the Copernican the sum of the squares of the two shorter sides is System (with a heliocentric solar system) was equal to the square of the hypotenuse (known as accepted. 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 theorem 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: a 2 + 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. quadratic equation A 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, quadratic formula like x and y. The quadratic formula is a formula ax2 + bx + c = 0 that gives you a solution to the quadratic quadrant When you graph a quadratic equation. The quadratic formula is obtained by A quadrant is a quarter of a plane. 2 equation in one variable like ax + solving the general quadratic equation. The x-axis and y-axis divide the x-y bx + c, you get a parabola, and the plane into four quadrants. The axes solutions to the quadratic equation themselves are not part of the represent the points where the quadrants. parabola crosses the x-axis. quartile quadrilateral A quadrilateral is a four-sided figure. The square, rectangle, rhombus, trapezoid, kite, and parallelogram are quadrilaterals. A 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 quarter quart point marks the lower quartile boundary at the 25th percentile. The A quarter is a coin A quart is onesecond marks the middle quartile (or midpoint of the data set), the that is worth 25 cents. fourth of a gallon. Four quarters make median or the 50th percentile. The last marks the upper quartile (or Four quarts make 75th percentile) of a frequency distribution. one dollar. one gallon. quotient The quotient is the answer in long division. The dividend divided by the divisor is the quotient (plus a remainder). 1/2 rational number A rational number is a number that can be ratio radius expressed in the form a/b, where a and b are A ratio is the relationship The radius is the integers and b≠0. For example, 0, 1/2, and -41 are between two numbers, radian distance from rational numbers. Each rational number denoted by division. For A radian is a unit of angular measure that is the center of a corresponds to a unique point on the number line example, if the ratio of boys to equal to the angle subtended at the center of a circle (or a (but most points on the number line do not circle by an arc equal in length to the radius of sphere) to the girls at a school is 4 to 5, this correspond to a rational number -- they correspond can be written as 4/5 or 4:5. the circle. A radian is about 57.2957° (1 edge. to an irrational number). degree = 0.0174532 radians). There are 2*pi radians in 360°. ray real number rectangle Real numbers are all rational and irrational A ray (also called a half line) is a numbers (but not the imaginary numbers). The real A rectangle is a four-sided figure (a quadrilateral) whose straight line that extends infinitely numbers represent all the points on the number sides are at right angles to each other. A square is a type of far in one direction from a point. rectangle whose four sides are all the same length. line. rhomboid regular polygon A regular polygon is a polygon (a polygon is a remainder many-sided figure with straight edges) whose The remainder is the part part of the answer in sides are all the same length and whose interior long division that does not go evenly into the angles are all the same (like an equilateral divisor. The dividend divided by the divisor is triangle or a square). the quotient plus the remainder. A rhomboid is a parallelogram with oblique angles and adjacent sides have different lengths. rhombus A rhombus is a parallelogram with equal-length sides. Roman numerals right angle right triangle Thousands 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. A right angle looks like the corner A right triangle has one of a square; it extends ninety angle that is a right degrees. Each of the interior Roman numerals express numbers as sums and differences. For example, 6 is VI (five + angle (extending 90 angles of a square is a right angle. degrees). 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). Number 368 1,234 89,355 Nearest ten 370 1,230 89,360 Nearest hundred Nearest thousand 400 1,200 89,400 0 1,000 89,000 ruler round rounding Round things are curved. A circle is round. When 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. A ruler is a long, straight object that is used for measuring distances or drawing straight lines scientific notation Scientific notation is a mathematical format used to scalar write very large and very small numbers; this A scalar is a number (a system avoids using a lot of zeros by using powers magnitude) without a direction (exponents). In scientific notation, there is a (compare with vector). For science scalene triangle number between 1 and 10 multiplied by a power of example, speed is a scalar; it Scientists study The sides of a ten. For example, the number 250 written in tells you how fast something is scalene triangle are science to learn scientific notation is 2.5 x 10 2. For another traveling but not the direction. all different lengths. about the example, the number 0.000052 written in scientific physical world. notation is 5.2 x 10-5. secant secant line Secant (abbreviated sec) is a trigonometric ratio, A secant line is a line corresponding to the length of the hypotenuse divided by that intersects a circle the length of the adjacent side of the right triangle. Secant or curve in two places. is equal to 1/cosine. second A second is a measure of angle that is equal to 1/60th of a second minute (a minute is 1/60th of a The second item comes after the degree). first item and before the third item. Second is abbreviated 2nd. second A second is a measure of time that is equal to 1/60th of a minute. semicircle A semicircle is semi-major axis semi-minor axis half a circle. The semi-major axis of an ellipse (a flattened circle) The semi-minor axis of an ellipse (a flattened circle) is half the length of the line segment across the is half the length of the line segment across the longest part of the ellipse. shortest part of the ellipse. 1+1/2+1/3+1/4+1/5+... set series A series is a sum of a sequence of numbers. A 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. sine Sine (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. seven Seven is the number between six and eight. There are seven days in the week. A heptagon is a seven-sided figure. skew six Six is the number between five and seven. A six-sided figure is called a hexagon. Insects have six legs. Two lines are skew if they do not lie on the same plane and are not parallel. Skew lines do not ever intersect. skip counting Skip counting is counting while skipping some numbers, like 2, 4, 6, 8,... slope The 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, (x 1 , 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 yintercept). solve When you solve an equation or a problem, you find solutions for it. square numbers square A square is a four-sided figure (a quadrilateral) that has four, equally long sides which are at right angles to each other. Square 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. spiral sphere A spiral is a curve A sphere is a ball-shaped that winds in on itself. object. The volume of a Snail shells have a sphere is 4πr3/3 (where spiral pattern. r=radius of sphere). square root The square roots of a number n are the star numbers s such that s2=n. For example, the A star is a shape square roots of 4 are 2 and -2; the square that has many roots of 9 are 3 and -3. points. 1-1=0 5-3=2 subtraction subtend To subtend is to be opposite to and to delimit. For example, in the triangle above, the side labeled b subtends the angle B. Subtraction is an operation in which one number is taken away from another number. For example, 4 - 1 subtrahend = 3 (four minus one equals three). A number minus sum The subtrahend is the number itself is equal to zero (for example, 3 - 3 = 0). The sum is the answer that is subtracted from another Subtraction is the inverse operation of addition. That to an addition problem. number in a subtraction problem. is, a + b - b = a. Subtraction is considered to be a binary operation because it is performed on two numbers. ! /,< +-=÷¢ x superscript superscript supplementary angle symbol A supplementary angle is A symbol is a mark A superscript is a raised text, usually an angle that, when or sign that stands in a smaller font. A superscript in added to another angle, for something else. mathematics often means a power or equals 180 degrees. For example, the exponent. For example, x2 means x symbol ÷ means squared (or x to the second power or divide. x times x). x0.5 means the square root of x. 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). tangent tally marks Tally 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. Tangent (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. tape measure tangram A tangram is a traditional Chinese puzzle that can be made into many shapes. temperature Temperature is a measure of the heat. Temperature is measured using a thermometer. ten Ten 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. A tape measure is a simple device used to measure things. thermometer tetrahedron A tetrahedron is a pyramid formed by four triangles. A thermometer is used for measuring the temperature. third The third person or item comes after the first and second. Third is abbreviated 3rd. thirteen time Three 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! Time is measured in seconds, minutes, hours, days, weeks, months, and years. A torus is a doughnut-shaped solid object. 1,000 thousand Thirteen is the number after twelve (12) thirty and before fourteen (14). A thirteen-sided Thirty is the number after twenty nine (29) and polygon is called a tridecagon. before thirty one (31). A thirty-sided polygon is called an triacontagon. three torus 30 ********** ********** ********** 13 ****** ******* One thousand is a whole number that is equal to 100 times 10. time zone timeline The Earth is divided into 24 time zones so that A timeline is a graphic display everyone in the world can be on roughly that shows a series of events similar schedules (like having noon when the that happen in a time period. sun is highest in the sky). transcendental number transversal trapezoid A 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 . A transversal is a line that intersects at least two other lines. A trapezoid is a four-sided figure (a quadrilateral) with exactly two parallel sides. triangle 2x + 3y A 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 trisect the lengths of the three sides. The area of a triangle is (1/2)base*height. A triangle trinomial To trisect is to divide into three with three equal sides (and three equal angles) is called an equilateral triangle. A A trinomial is a equal parts. For example, if a 90triangle with two equal sides (and two equal angles) is called an isosceles triangle. A polynomial expression degree angle is trisected, the result triangle with no equal sides (and no equal angles) is called an scalene triangle. A that has three terms, like 2 is three 30-degree angles. triangle with one right angle is called a right triangle. The Pythagorean theorem states 3x + 4yz - 5. 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. 12 ****** ****** two twelve twenty Twelve (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. Twenty is the number between nineteen and twenty-one. There are twenty (20) apples above. A twenty-sided polygon is called an icosagon. undecagon An undecagon is an eleven-sided figure (hendecagon is another word for this figure). The Canadian one dollar coin (also called the union A 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 unit A unit means one. Two is the number between one and three. We have two eyes, two ears, two arms, and two legs. loonie) is an undecagon. those two sets. For example if A={1, 2, 3} and B={3, 4, 5}, A U B= {1, 2, 3, 4, 5}. unlike fraction unit fraction unknown Unlike fractions are two or A unit fraction is a fraction that has a one in the An unknown is a number whose value is not known. For example, more fractions whose numerator, like 1/2, 1/3, 1/4, etc. in the equation 2x2 - 3x = 6, x is the unknown. denominators are not the same, like 1/2, 1/3, and 1/5. vector A vector is a number (a magnitude) together with a direction (compare with scalar). A vector can be represented by an arrow A variable is an unknown or whose length represents the magnitude and the direction placeholder in an algebraic represents the direction. For example, velocity is a vector; velocity Venn diagram expression. For example, in A Venn diagram is a diagram tells you how fast something is traveling, and its direction. 2x+y, x and y are variables. that uses overlapping circles to show relationships among sets of things. variable V V equals 5 in Roman numerals. vertex volume A vertex of an angle is a point at which two sides of the angle meet. A vertex of a polygon is Volume is a measure of 3-dimensional space expressed a point at which two of the sides meet. A vertex of a polyhedron is a point at which 3 or in cubic units. more faces meet. wavelength A wavelength is the distance between two wave crests. wedge week A wedge is a tapered block that is used for holding things in place, splitting things or tightening things. There are 7 days in a week; Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday. There are 52 weeks in a year. whole number word problem The whole numbers are an infinite set of numbers: {0, 1, 2, 3, 4, 5...}. A word problem is a mathematical question phrased in terms of words, not equations. wide When something is wide, it takes up a lot space from side to side. x-coordinate X X equals 10 in Roman numerals. x-axis The x-axis is usually the horizontal axis. The 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. yardstick y-coordinate A yardstick is three feet long (a yard); it is used for measuring things. The 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). y-axis The y-axis is usually the vertical axis. year A 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-axis The z-axis represents the third dimension in a graph. 0 f(x) = 0 zeros of a function zigzag The zeros of a function are the points at which the A zigzag is a line Zero is a number that stands for the absence of size or value of the function is zero. Graphically, these quantity. One is the additive identity, since one plus any are the points at which the plot touches or crosses that sharply turns back and forth. number is equal to that number. Any number times zero the x-axis (i.e., y=0). is zero. You cannot divide a number by zero. zero