Math Glossary

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z #

 

A

Acute
    
     A positive angle measuring less than 90 degrees.  

                                          acuteangle      

Adjacent
    
    
Two angles that share both a side and a vertex.

adjacent angles                       adjacent angles

Angles

     The union of two rays with a common endpoint, called the vertex.

     acute angle  acuteangle       right anglerightangle    

     obtuse angle  obtuseangle 

     Two angles that share both a side and a vertex.

Arc

     A portion (part) of the circumference of a circle.

arc                  arc 2                       arc 3

Area

     Area is the inside of a figure and you either count up the squares or multiply the
     length and width. 

areaIf the length is 5 and the width is 2.  A = 10 sq

Associative Property of Addition
     (a + b) + c = a + (b + c)

     Example: 3 + 4 + 5 can be done either of the following two ways

     a)  (3 + 4) + 5
     b)  3 + (4 + 5)

Associative Property of Multiplication
     (a x b) x c = a x (b x c)

     Example: 3 x 4 x 5 can be done either of the following two ways

     a)  (3 x 4) x 5
     b)  3 x (4 x 5)

Average
     A number that represents the characteristics of a data set.

     Example: A data set of the numbers 12, 17, 23, 29, and 34
     1) Add all the numbers in the data set together
         12
         17                   2) Take the sum of all the numbers and divide it by how many 
         23                        numbers there are in the data set - for this example 
         29                        there are five numbers
       +34                        115 ÷ 5 = 23  
      _____                                
       115                                     3) Thus the average for this data set is 23

                                                                 4) Remember that the average will always be 
                                                                     a number between the smallest number (in
                                                                     this case the number 12 is smallest) and
                                                                     the largest number (in this case the 
                                                                     number 34) - notice that our average 23
                                                                     is between these two numbers.
 

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B

Base

     The bottom of a plane figure or three-dimensional figure.

 base

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C

Chord

     A line segment that connects two points on a curve (not through the center).

chord

Circumference

     The distance around a circle.

diameter and circumference

Common Multiple

     A multiple of two or more numbers.

Commutative Property of Addition

     a + b = b + a

     Example: 3 + 4 = 4 + 3

Commutative Property of Multiplication

     a x b = b x a

     Example: 3 x 4 = 4 x 3

Complementary Angles

     Two angles whose sum is 90 degrees.
      = angle, thus  ABC is an angle that has points A, B, and C on it.

     Example:   FAB or  FAD (same angle) is 45° and  CAB is 90° then  CAF is 
     also 45° which makes  FAB and  CAF complimentary angles since they add
     to 90°

complimentary angles

Composite Number

      A natural number that is not prime. Which is any number that has factors of more than one
     and itself. Such as 4 which has factors of (1, 2, 4) - 1x4 and 2x2.

Cone

     A three-dimensional figure with one vertex and a circular base.

cone               cone 2                cone 3

Congruent

     Figures or angles that have the same size and shape.

congruent

Coordinate Plane

     The plane determined by a horizontal number line, called the x-axis, and a
     vertical number line, called the y-axis, intersecting at a point called the origin. 
     Each point in the coordinate plane can be specified by an ordered pair of 
     numbers.

Coordinate Plane

Cross Product

     A product found by multiplying the numerator of one fraction by the denominator of another
     fraction and the denominator of the first fraction by the numerator of the second.

Cube

     A solid figure with six square faces.

cube

Cylinder

     A three-dimensional figure having two parallel bases that are congruent circles.

cylinder

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D

Data

      Information that is gathered.

Decimal Number

     The numbers in the base 10 number system, having one or more places to the
     right of a decimal point.  

     Example: 12.38

Decimals: Compare or Order - (make sure the decimals are in the same place by
                                                      making equivalencies)

     .9      .09  will become  .90 >   .09 as you make the decimals into the same place

     3.80      3.8   will become   3.80  = 3.80

     12.09       12.9  will become    12.09< 12.90

     1.2 , 1.02,  11.2 , 12,  12.1  will become  1.20, 1.02, 11.20, 12.00, 12.10
     When ordered least to greatest it will be 1.02, 1.20,  11.20, 12.00, 12.10

Decimals: Converting to a Fraction and Percent - (the denominator must be 100
                  and you do this by making an equivalent fraction)

     .4  = 4/10  = 40/100  = 40%

     .25 = 25/100 = 25%

Decimals: Counting - (make sure you are in the same place as requested)


     count by tenths

     .8, .9 ,1.0. 1.1 etc....

     count by hundredths

     .98, .99, 1.00, 1.01 etc....
     .9 would need to be changed to .90 before you could count by hundredths 

Decimals: Equivalent (zeros to the right of decimal)

     0.7 = 0.70

     1.9 = 1.90

     13.503 = 13.503 (can't remove zero when trapped by digit to right)

Decimals: Place Value

     1,234.56789

     1 = thousands
     2 = hundreds
     3 = tens
     4 = ones
     5 = tenths
     6 = hundredths
     7 = thousandths
     8 = ten thousandths
     9 = hundred thousandths

Decimals: Rounding - (is usually to the nearest whole number unless indicated
                                       otherwise)

     1.25 = 1      3.09  = 3      1.9 = 2

Degree

     A unit of measure of an angle.

degreedegree 2degree 3

Denominator

     The bottom part of a fraction.

denominator    denominator 3               denominator 2                     

Diameter

     The line segment joining two points on a circle and passing through the center of the circle.

diameter                           diameter and circumference

Difference

     The result of subtracting two numbers.  

difference

Digit

     The ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number 215 has three
     digits: 2, 1, and 5.

Distributive Property of Multiplication

     Example:  34  x  56

     1) way 1:( 30 + 4 ) x ( 50 + 6 )
         (30 x 50) + (30 x 6) + (4 x 50) + (4 x 6)

     2) way 2: (30 + 4) x 56
         (30 x 56) + (4 x 56)

     3) way 3: 34 x (50 + 6)
         (34 x 50) + (34 x 6)

     4) way 4: (40-6 ) x 56
         (40 x 56) - (6 x 56)

Dividend

     In a ÷ b = c, a is the dividend. In the problem division the 56 is the dividend.

Division

     DMSB or dad, mother, sister, brother, is an acronym we use to help us divide. 
     It  stands for divide, multiply, subtract and bring down.

     Does McDonalds Serve Cheese Burgers Daily in another acronym. Does =
     Divide, McDonalds = Multiply, Serve = Subtract, Cheese = Check (check to make
    
sure subtraction answer is lower than number dividing by), Burgers Daily = Bring
    
Down.

Divisor

     In a ÷ b = c, b is the divisor. In the problem division the 8 is the divisor.

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E

Equation

     A mathematical statement that says that two expressions have the same value;
     any number sentence with an =. Examples: 3 + 4 = 7, 5 x 8 = 40, a - b = c

Evaluate

     To substitute number values into an expression. If a = 4, b = 2, substitute the
     numbers for the letters in the expression. a + b = c, 4 + 2 = 6 so c = 6

Even Number

     A natural number that is divisible by 2.

Exponent (see also power)

     A number that indicates the operation of repeated multiplication.

exponent  exponent 3    exponent 2

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F

Face

     A flat surface of a three-dimensional figure.

face

Factor

     One of two or more expressions that are multiplied together to get a product.

factor

Factoring

     To break a number into its factors.

factor tree

Formula

     A equation that states a rule or a fact.

formula

formula 2                   formula 3

Fraction

     A number used to name a part of a group or a whole. The number below the bar is
     the denominator, and the number above the bar is the numerator.

fractions

Fractions: Addition & Subtraction of Fractions with Like Denominators
     - Add the numerators and keep the denominators the same. 

     4/5 + 1/5 = 5/5 = 1                  1  2/5 + 2/5 = 1 4/5            3 2/4 - 1/4 = 31/4

Fractions: Adding & Subtraction of Fractions with Unlike Denominators
     - Must first find common denominator before adding or subtracting 
     - The following is an example - the numbers would change depending on the
        problem.
Step OneStep Two
Step Three
Step Four
Step Six

Fractions: Close to 0, 1/2, 1 or more than 1

     - close to zero if numerator and denominator are far apart  2/20
     - close to one if numerator and denominator are close to together  19/20
     - exactly one if numerator and denominator are the same  7/7
     - over one if the numerator is biggier than the denominator  5/4

Fractions: Comparing & Ordering

     unit fractions have same numerator 1/20     1/5        1/25         1/8
        In this case the bigger the denominator the smaller the piece
        1/25    1/20     1/8   1/5 = least to greatest

     same denominator fractions 3/6   2/6  1/6   5/6
        In this case the bigger the numerator the bigger the piece
         1/6   2/6    3/6     5/6

     when comparing fractions use cross multiplication

         4             8
         12    <     9

       multiply 4 x 9 = 36  and 12 x 8 = 96 so 8/9 is bigger

Fractions: Equivalent

     Fractions that reduce to the same number.  10/15 = 2/3
Fractions: Numerator = number above the fraction bar (division bar)  (the 3 in
                                          this fraction)

Fractions: Fraction of a Whole

     whole number times numerator divided by denominator

     4/5  of 20 =                   4 x 20 = 80        80 divided by 5 = 16

 hundredths                   tenths

     1.2 = 1  2/10 = one and two tenths            
     13.09 =  13  9/100 = 13 and 9 hundredths
     0.54 = 53/100 = fifty three hundredths

Fractions: Whole Set and in Word Problems

      fraction1

     - (a b a)  what fraction is vowels? = 2/3

     - If I have 6 cookies and 9 people, how much will each person get of the cookies? =
       6/9

Frequency

     The number of times a particular item appears in a data set.

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G

Graph

     A type of drawing used to represent data.

verticle bar graphhorizontal bar graphline graphcircle or pie graphpictograph

Verticle Bar    Horizontal Bar        Line               Circle or Pie               Pictograph
     Graph              Graph              Graph                 Graph

Greatest Common Factor (GCF)

     The largest number that divides two or more numbers evenly.
    
     Example: The GCF of 12 and 15 is 3 because it is the largest number that both
     can be divided by

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H

Horizontal

     A line with zero slope.

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I

Improper Fraction
 
     A fraction with a numerator that is greater than the denominator.

improper fraction       improper fraction 2       improper fraction 3

Inequality

     A mathematical expression which shows that two quantities are not equal.

Integers

     The set of numbers containing zero, the natural numbers, and all the negatives of the natural numbers.

Intersecting Lines

     Lines that have one and only one point in common.

intersecting linesintersecting lines 2

Inverse

     Opposite. -5 is the additive inverse of 5, because their sum is zero. 1/3 is the
     multiplicative inverse of 3, because their product is 1.

Inverse operations

     Two operations that have the opposite effect, such as addition and subtraction.

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J

 

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K

 

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L

Least Common Denominator (LCD)

     The smallest multiple of the denominators of two or more fractions.

LCD

Least Common Multiple (LCM)

     The smallest nonzero number that is a multiple of two or more numbers

LCM

Like Fractions (common denominator)

     Fractions that have the same denominator. 

common denominator

 

Line

     A straight set of points that extends into infinity in both directions.

                                        lines
Line of Symmetry

     Line that divides a geometric figure into two congruent portions.
 lines of symmetry

Lines

     parallel linesparallel

     perpendicular linesperpendicular

     intersecting linesintersecting

     line segment has two pointsline segment

     line has two arrowsline

     ray has one arrowray 

Logic

     The study of sound reasoning.

Lowest Terms

     Simplest form; when the GCF of the numerator and the denominator of a
     fraction is 1.

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M

Mean (see Average)

Median

     Example: Data Set: 1,4,7,2,8,2,7,9,7

     1) place in order from least to greatest  1,2,2,4,7,7,7,8,9

     2) Median = the number in the middle (when there is an equal number of 
                          numbers in the data set the two middle numbers are averaged
                          to find the median (see average)

Minuend

     The number to be subtracted from.  

difference

Mixed Number

     A number written as a whole number and a fraction.

mixed number

Mode

     Example: Data Set: 1,4,7,2,8,2,7,9,7

     1) place in order from least to greatest  1,2,2,4,7,7,7,8,9

     2) Mode= the number that is written down the most often (there can be
                      more than one mode in a data set)

Multiple

     A multiple of a number is the product of that number and any other whole number.
     Zero is a multiple of every number.

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N

Natural Numbers

     The counting numbers.

Negative Number

     A real number that is less than zero.

Number Line

     A line on which every point represents a real number.

number line

Numerator

     The top part of a fraction.

numerator

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O

Obtuse Angle 

     An angle that is greater than 90 degrees

                                          obtuseangle

Obtuse Triangle

     A triangle with an obtuse angle.

obtuse triangle

Octagon

     A polygon with 8 sides.

octagon

Odd Number

     A whole number that is not divisible by 2
.

Operation

     Addition, subtraction, multiplication, and division are the basic arithmetic operations.

Opposites

     Two numbers that lie the same distance from 0 on the number line but in opposite
      directions.

     Example: 8 and -8   also   -3/4 and 3/4

Order of Operations

     PEMDAS is an acronym that shows what to do first in an equation:  p stands for 
     parenthesis, m for multiplication, d for division, a for addition, and s for subtraction. 
     You solve a problem using this order.

     The multiplication and division are reversable
     - do whichever comes first, also the addition and subtraction are also reversable - 
     do whichever comes first.

     example:  32 ÷ (4 + 4) x 2   You would do addition first to get 8 because it is in the
     parenthesis, then the division to get 4, and then finally the multiplication to get 8.

Ordered Pair

     Set of two numbers in which the order has an agreed-upon meaning, such as the
     Cartesian coordinates (x, y), where the first coordinate represents the horizontal
     position, and the second coordinate represents the vertical position.

Outcome

     In probability, a possible result of an experiment.

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P

Parallel

     Two lines are parallel if they are in the same plane and never intersect.

parallel

Parallelogram 

     A quadrilateral with opposite sides parallel.

parallelogram

Pentagon

     A five-sided polygon.

pentagon

Percent

     A fraction, or ratio, in which the denominator is assumed to be 100. The symbol %
     is used for percent.

     Example: 34% = 34 parts of 100

Perimeter

     The perimeter is the outside of a figure and you add up all the sides.

     areaIf the length is 5 and the width is 2.  P = 14

Perpendicular

     Two lines are perpendicular if the angle between them is 90 degrees.

perpendicular

Pi

     The ratio of the circumference of a circle to its diameter.

pi

Place Value

     expanded form = 300,000 + 20,000 + 3,000 + 400 + 60 + 9
     written form = three hundred  twenty three thousand four hundred sixty nine

     3,456,789
     value of 3 = 3,000,000
     place value of 3 = million 

Plane

     A flat surface that stretches into infinity.

Point

     A location in a plane or in space, having no dimensions.

Polygons
     - are many sided figures

regular polygons

     *triangle is a three sided figure                      *quadrilaterial is a four sided figure
     *pentagon is a five sided figure                      *hexagon is a six sided figure
     *heptagon is a seven sided figure                  *octagon is a eight sided figure
     *nonagon is a nine sided figure                      *decagon is a ten sided figure

     CLICK HERE for more about regular polygons

Polyhedron

     A three-dimensional solid that is bounded by plane polygons.

regular polyhedron

Positive Number

     A real number greater than zero.

Power (also see exponent)

     A number that indicates the operation of repeated multiplication.

exponent

Prime Number

     A number whose only factors are itself and 1. Such as 3 - 1x3, 5 - 1x5, 7 - 1x7,
     11 - 1x11, and 13 1x13, ect.

Probability

     For an experiment, the total number of successful events divided by the total
     number of possible events.

     a,4,a,b,3,4,6,7

     Probability of pulling out an "a" from above list is 2/8 and unlikely
     Probability of pulling out a "number" from the above list is 5/8 and likely

     The words we use are impossible, unlikely, maybe, likely, and certain.

Product

     The result of two numbers being multiplied together.

product

Proper Fraction

     A fraction whose numerator is less than its denominator.

proper fraction

Pyramid

     A three-dimensional figure that has a polygon for its base and whose faces are
     triangles having a common vertex.

pyramid

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Q

 Quadrant

     One of the quarters of the plane of the Cartesian coordinate system (coordinate
     grid)

quadrantquadrant 2quadrant 3quadrant 4

Quadrilaterals
     - are four sided figures

     trapezoid has one set of parallel linestrapezoid

     parallelogram has two sets of parallel sidesparallelogram

     rectangle has two sets of parallel and equal sides with right angles

     rhombus has all sides equalrhombus

Quotient

     The answer to a division problem.

quotient

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R

Radius

     The distance from the center to a point on a circle; the line segment from the
     center to a 
point on a circle.

radiusradiusradius 3radius 4

 

Range

     Example: Data Set: 1,4,7,2,8,2,7,9,7

     1) place in order from least to greatest  1,2,2,4,7,7,7,8,9

     2) Range = highest number minus lowest number  9-1 = 8 

Rate

     A ratio that compares different kinds of units.

     Example: 10 km per 2 hours or 5 km per hour - comparing km to hours

Ratios

     girls 13  boys  15 (written 3 ways for each)

     ratio of girls to boys is 13 to 15 or 13/15 or 13:15

     ratio of girls to total is 13 to 28 or 13/28 or 13:28

Ray

     part of a line, with one endpoint, and extending to infinity in one direction.

ray

Reciprocal

     The number which, when multiplied times a particular fraction, gives a result of 1.

     Example: 3/4 x 4/3 = 12/12 which equals 1

Rectangle

     A quadrilateral with four 90-degree angles.

rectanglesquare

                                     regular rectangle              square which is a
                                                                               special rectangle

Reflection

     A transformation resulting from a flip.

reflection / flip

Right angle

     An angle that is exactly 90 degrees

                                   rightangle    

Rhombus

     A parallelogram with four equal sides.

rhombusrhombus 2square

Right Angle

     An angle whose measure is 90 degrees.

right angle

Right Triangle

     A triangle that contains a right angle.

right triangle

Rotation

     A transformation in which a figure is rotated through a given angle, about a point.

rotation / turn

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S

Scale Drawing

     A drawing that is a reduction or an enlargement of the original.

Scalene Triangle

     A triangle with three unequal sides.

scalene triangle

Scientific Notation

     A method for writing extremely large or small numbers compactly in which the number is
     shown as the product of two factors.

Scientific Notation

Shapes: Analyzing

     Students will need to be able to analyzse a figure to see if it has certain 
     characteristics.  For example:trapezoid2a trapezoid has parallel lines and in this
     case obtuse and acute angles.

     Students will need to be able to analyse a figure to see what other shapes can be
     found in the figure.  For example:  trap3a trapezoid could be made up of
     three triangles or a rectangle with two triangle.

Shapes: Congruency & Similarity

     Congruent is the same size and shape
     Similar is the same shape

Shapes: Nets

     There may be more than one net for each figure.

     cube   cubenet

     cone                     cylinder

 

     cyclindercone

     CLICK HERE for many more nets that can be printed and made

Shapes: Plotting

     Students will ned to be able to plot a geometry figure or line on a coordinate grid.
     The trapezoid is at points (2,1) and (4,1) and (5, 4) and (1, 4).  
     coordinategrid

Similar

     Two polygons are similar if their corresponding sides are proportional.

Similar ShapesSimilar Shapes 2Similar Shapes

Simplifying

     Reducing to lowest terms.

Simplifying Fractions

Solution

     The value of a variable that makes an equation true.

     Example: 4a - 3 = 21  solving for the variable a gets the solution a = 6

Square Root

     The square root of x is the number that, when multiplied by itself, gives the
     number, x.

square root                   square root 2

Statistics

     The science of collecting, organizing, and analyzing data.

Stem and Leaf Plot

     A technique for organizing data for comparison.

stem and leaf plot                 stem and leaf plot 2

Straight Angle

     An angle that measures 180 degrees.

straight angle

 

Subtrahend

     The number to number to be subtracted.  

difference

Supplementary Angles

     Two angles are supplementary if their sum is 180 degrees.

supplementary angles            supplementary angles 2

Surface Area

     For a three-dimensional figure, the sum of the areas of all the faces.

surface area

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T

Transformation

     A change in the position, shape, or size of a geometric figure.

transformations

Translation

     A transformation, or change in position, resulting from a slide with no turn.

translation                     translation 2

Trapezoid

     A quadrilateral that has exactly two sides parallel.

trapezoid

Tree Diagrams

 

     I have three flavors of ice cream: vanilla, chocolate, and praline.  I have two types
     of cones: sugar and plain.  I have two toppings: nuts and fruit.  How many
     combinations can I make?    3  x  2  x  2 =  12 combinations

     1)   vanilla: sugar: nuts
     2)   vanilla: sugar: fruit
     3)   vanilla: plain: nuts
     4)   vanilla: plain: fruit
     5)   chocolate: sugar: nuts
     6)   chocolate: sugar: fruit
     7)   chocolate: plain: nuts
     8)   chocolate: plain: fruit
     9)   praline: sugar: nuts
     10) praline: sugar: fruit
     11) praline: plain: nuts
     12) praline: plain: fruit

tree diagram          tree diagram 2

Triangles
      three sided figures

     1) Triangles based on their angles:
         -acute triangle has all acute angles       acute triangle
         -obtuse triangle has one obtuse angle  obtuse triangle 2
         -right triangle has one right angle          right triangle 2

     2) Triangles based on their sides:
         
-isosceles triangle has two sides the same length    isosoles triangle
          -equalateral triangle has all sides the same length    equalateral triangle
          -scalene triangle has no sides the same length         scalene triangle

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U

Unit Price

     Price per unit of measure.
 

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V

Variable

     A letter used to represent a number value in an expression or an equation.

     Examples: r - 3 = 12, 4b = 16, 8 + s = 24, 40 ÷ y = 5,  3r + 4 = 22

Vertex

     The point on an angle where the two sides intersect.

vertex

Vertex Edge Graphing

     graphvertex =  a point on a graph ( blue )

     edge = a line segment or curve connecting two vertices ( black lines )

 

     pathpath = a connected sequence of edges that starts at a vertex
                                    and ends at a vertex

     circuit = a path that begins and ends at the same vertex 

 

     numbering
     graph coloring = assigning colors to the vertices of a graph so that adjacent
     vertices are assigned different colorsdegree of vertex = the number of edges that
     come off of a vertex. 
        
     Example:   If 1 is green then 5 and 2 can not be green, but 4 should be green.  If
                           5  is yellow than 6 and three should be yellow. 2 must be a new
                           color. In other words you want to try to color with the fewest colors
                           without having the same color next to each other.This is called
                           chromatic coloring.

     cycle

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

     disconnected graph = a graph that contains two or more vertices that are not
     connected

     The following are some applied problems using the concept of wieghted vertex
     edge graphs.

     a)

shortestpath 

 

     b)

2

     CLICK HERE for more information on Vertex Edge Graphing

Vertical Angles

     A pair of opposite angles that is formed by intersecting lines.

vertical angles

Volume

     A measurement of space, or capacity.

volume

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W

Whole Numbers

     The set of numbers that includes zero and all of the natural numbers.

Word Problems: Key words that signal x, ÷ , + and -

     product x                              increase or decrease by -
     quotient /                              how many more -
     area x                                   difference -
     total x or +                            er word like taller or smaller -
     times x                                  sum +                       
     split evenly /                         perimeter +
     share evenly /

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X

X-Axis

     The horizontal axis in a Cartesian coordinate plane.

x-axisarrow X-Axis

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Y

Y-Axis

     The vertical axis in a Cartesian coordinate system.

Y-Axis

arrow 2

x-axis

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Z

 Zero Property of Multiplication

     The product of zero and any number is zero.

     Example:  3,458 x 0 = 0

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