MATH TIPSfor

PARENTS

NUMBER PROPERTIESTHE OPERATION CALLED ADDITION

Associative Property of Addition:

• Changing the grouping of the terms (addends) will not change the sum (answer in addition).

In Arithmetic: (5 + 3) + 2 = 5 + (3 + 2)

In Algebra: (a + b) + c = a + (b + c)

• Changing the order of the numbers (addends) will not change the sum (answer in addition).

In Arithmetic: 8 + 4 = 4 + 8

In Algebra: a + b = b + a

Commutative Property of Addition

Identity Property of Addition

• Zero added to any given number (given addend), the sum will equal the given number (given addend).

In Arithmetic: 6 + 0 = 6

In Algebra: a + 0 = a

• Subtraction undoes the operation called addition.

In Arithmetic: If 7 + 4 = 11, then11 - 7 = 4 and 11 - 4 = 7

In Algebra: a + b = c, thenc - a = b and c - b = a

Inverse Operation of Addition

THE OPERATION CALLED SUBTRACTION

• Addition undoes the operation called subtraction.

In Arithmetic: If 16 - 9 = 7, then9 + 7 = 16 and 7 + 9 = 16

In Algebra: c - b = a, thenb + a = c and a + b = c

Inverse Operation of Subtraction

THE OPERATION CALLED DIVISION

• Multiplication undoes the operation called division.

In Arithmetic: If 48 / 8 = 6, then8 x 6 = 48 and 6 x 8 = 48

In Algebra: c / b = a, thenb x a = c and a x b = c

Inverse Operation of Division

THE OPERATION CALLED MULTIPLICATION

• Changing the grouping of the factors will not change the product (answer in multiplication).

In Arithmetic: (5 x 4) x 2 = 5 x (4 x 2)

In Algebra: (a x b) x c = a x (b x c) or (ab) c = a (bc)

Associative Property of Multiplication

• Changing the order of the factors (multiplicand and multiplier) will not change the product (answer in multiplication).

In Arithmetic: 6 x 9 = 9 x 6

In Algebra: a x b = b x a or ab = ba

Commutative Property of Multiplication

• The product (answer in multiplication) and 1 is the original number.

In Arithmetic: 7 x 1 = 7

In Algebra: a x 1 = a or a • 1 = a

Identity Property of MultiplicationIdentity Property of Multiplication

• The product (answer in multiplication) of any number and zero is zero.

In Arithmetic: 9 x 0 = 0

In Algebra: a x 0 = 0 or a • 0 = 0

Multiplication is repeated addition. 8 x 4 = 8 + 8 + 8 + 8

Multiplication Property of Zero

• Multiplication by the same factor may be distributed over two or more addends. This property allows you to multiply each term inside a set of parentheses by a term inside the parentheses. *In many cases this is an excellent vehicle for mental math.

In Arithmetic: OVER ADDITION5(90 + 10) = (5 x 90) + (5 x 10)OVER SUBTRACTION5(90 - 10) = (5 x 90) - (5 x 10)

In Algebra: OVER ADDITIONa(b + c) = (a x b) + (a x c) or

a(b + c) = ab + ac OVER SUBTRACTION

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

Distributive Property of Multiplicationover Addition or Subtraction

Distributive Property of Multiplicationover Addition or Subtraction

GLOSSARY ofMATHEMATICAL TERMS

ADDTo put one thing, set or group with another thing, set or group.

ADDENDNumbers to be added.

Example: 12 + 23 = 25 a + b + c = abc

ADDITIONThe operation of putting together two or more numbers, things, groups or sets.

Example: 8 + 2 + 4 = 14 is an addition problem

ARRAYAn orderly arrangement of persons or things, rows and columns. The number of elements in an array can be found by multiplying the number of rows by the number of columns.

Example: * * * * * ** * * * * ** * * * * * 3 x 6 = 18

Add/Addend/Addition/Array

ASSOCIATIVE PROPERTY OF ADDITIONThe way in which three numbers to be added are grouped two at a time does not affect the sum.

Example: 3 + (5 + 6) = (3 + 5) + 6 3 + 11 = 8 + 6

14 = 14

ASSOCIATIVE PROPERTY OF MULTIPLICATIONThe way in which three numbers to be multiplied are grouped two at a time does not affect the product.

Example: 3 x (2 x 6) = (3 x 2) x 6 3 x 12 = 6 x 6

36 = 36

ATTRIBUTEA quality that is thought of as belonging to a person of thing. Characteristics; such as, size, shape, color and/or thickness.

Associative Property of Addition-Multiplication/Attribute

AVERAGEA number found by dividing the sum (total) of two or the sum (total) of two or more quantities by the number of quantities.

The average of 86, 54, 9 and 93 is 68.STEP 1 STEP 2

86 68 is the average

54 How many addends? 4) 272 39 Quantity is 4 - 24+ 93 32 272 sum or total - 32

0

AXIS (axes)Horizontal and vertical number lines in a number plane.

Average/Axis

BAR GRAPHA picture in which number informationis shown by means of bars of different lengths.

BRACESBraces are symbols { }. They are used to list names of numbers (elements) of a set.

Example: { Pauline, April, Joni, Jackie} is a setof secretaries.

{Sunday, Monday, Tuesday, Wednesday,Thursday, Friday, Saturday} is a set ofthe days of the week.

{1, 2, 3, 4, 5, 6, 7, 8, 9} is a set of counting numbers from 1 to 9.

Colors the Class Likes

25

20

15

10

0

Bar Graph/Braces

CAPACITYThe amount that can be held in a space.

CARDINAL NUMBERA number that tells how many there are.

Example: There are five squares

CENTIGRADEDivided into one hundred degrees (100%). On the centigrade temperature scale, freezing point is at zero degrees (0%). The boiling point water is at one hundred degrees (100º)

* Celsius scale is the official name of the temperature

CENTA coin of the United States and Canada. One hundred cents make a dollar.

CENTIMETERA unit of length in the metric system. A centimeter is equal to one hundredths of a meter or .39 of an inch.

Capacity/Cardinal Number/Centigrade/Cent/Centimeter

CENTURYA period of one hundred years.

CLOSED FIGUREA geometric figure that entirely encloses part of the plane.

CLOSUREA property of a set of numbers such that the operation with two or more numbers of that set results in a number of the set.

Example: In addition and multiplication with counting numbers, the results is a counting numbers. 2 + 4 = 6; 2 x 4 = 8

Thus, the counting numbers are closed under these two operations.

In subtraction, if 4 is subtracted from 2, the result (-2) is not a counting number. Also in dividing a 2 by 4, the results (1/2) is not a counting number. Thus, the counting numbers are not closed with respect to subtraction and division.

Century/Closed Figure/Closure

COMBINETo put (join) together.

COMMONBelonging equally to all.

COMMON FACTORA common factor of two or more numbers is a number which is a factor of each of the numbers.Example: 8 = {1, 2, 4, 8}

32 = {1, 2, 4, 8, 16, 32} 1, 2, 4 and 8 are the common factors of 8 and 32

COMMON MULTIPLEA common multiple of two or more numbers is a number which is a multiple of each of the numbers.Example: 12 = {12, 24, 36, 48, 72, 84, 96, 108, 120}

15 = {15, 30, 45, 60, 75, 90, 105, 120, 135, 150} 60 and 120 are the common multiples

Combine/Common/Common Factor/Common Multiple

COMMUTATIVE PROPERTY OF ADDITIONThe order of two numbers (addends) may be switched around and the answer (total, sum) is the same.

Example: 7 + 4 = 11 and 4 + 7 = 11; therefore, 7 + 4 = 4 + 7

COMMUTATIVE PROPERTY OF MULTIPLICATIONThe order of two numbers (factors) may be switched around and the answer (total product) is the same.

Example: 8 x 6 = 48 and 8 x 6 = 48; therefore, 8 x 6 = 6 x 8

COMPARETo study, discover and/or find out how persons or things are alike or different.

COMPOSITE NUMBERA number which has factors other than itself and one.Since 16 = 1 x 16, 2 x 8 and 4 x 4, it is a composite number.

Commutative Property of (Addition)(Multiplication)/Compare/Composite Number

CONDITIONAL SENTENCE (In logically thinking)A sentence of the form “if. . ., then. . .?

Example: If 6 x 7 = 42 and 7 x 6 = 42, Then 42 - 6 = 7 and 42 - 6 = 7

CONGRUENT FIGUREGeometric shapes consisting of the same shape and size.

Example: 8 x 6 = 48 and 8 x 6 = 48; therefore, 8 x 6 = 6 x 8

CONJECTUREA guess resulting from an experiment.

Example: 2, 4, 6, 8, 10 are even numbers; therefore,even numbers must have 0, 2, 4, 5, or 8in the ones’ place.

CONJUNCTION (In logically thinking)A two-part sentence joined by “and” to form true parts.

Example: 1/4 + 1/4 = 2/4 = 1/2

Conditional Sentence/Congruent Figure/Conjecture/Conjunction

COORDINATESTo numbers, an ordered pair, used to plot a point in a number plane.

COUNTING NUMBER (Natural Numbers)To numbers, an ordered pair, used to plot a point in a number plane.

Example: 1, 2, 3, 4, 5. . .*There is no longest number.Counting numbers are infinite.

DECADEA period of ten years.

DECIMALNames the same number as a fraction when the denominator is 10, 100, 1000. . . It is written with a decimal point.

Example: .75

Coordinates/Counting Number/Decade/Decimal

DECIMAL SYSTEMA plan for naming numbers that is based on ten is called a decimal system of numeration. The Hindu-Arabic system is a decimal system.

DIAGONALA straight line that connects the opposite corners of a rectangle.

Example:

DEGREEA unit of angle measurement.

DENOMINATORIn 3/5 the denominator is 5. It tells the number of equal parts, groups or sets the whole was divided.

Decimal System/Diagonal/Degree/Denominator

DIFFERENCEThe number which results when one number is subtracted from another is called the difference. It is a missing addend in addition.

Example: 7 - 4 = 3 the difference is 3

DIGITAny one of the basic numerals, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, is a digit.The numeral 12 is a two-digit numeral and the numeral 354 is a three digit numeral.

DISJOINT SETSSets that have no members in common are disjoint sets.

Example: Set A = {a, b}, Set B {1, 2, 3}.Sets A and B are disjoint

Difference/Digit/Disjoint Sets

DISTRIBUTIVE PROPERTY OFMULTIPLICATION OVER ADDITIONMultiplication by the same factor may be distributed over two or more addends.

Example: 3 x (6 + 4) = (3 x 6) + (3 x 4) = 18 + 12

= 30

DIVIDETo separate into equal parts, pieces, groups or sets..

Example: x x x x x x x x x x10 2 = 5

DIVIDENDA number that shows the total amount to be separated into equal parts, groups of sets by another number.

Example: 100 25 = 4, the dividend is 100

Distributive Property of Multiplication over Addition/Divide/Dividend

DIVISIBLECapability of being separated equally without a remainder.

Example: 18 is divisible by 1, 2, 3, 6, 9 and 18

DIVISORA number that tells what kind of equal parts, groups or sets the dividend is to be separated.

ELEMENTA member of a set.

ELEMENT OF A SETA member of a set.

EMPTY SETThe set which has no members. The number of the empty set is zero. A symbol for the empty set is { }.

Divisible/Divisor/Element/Element of a Set/Empty Set

EQUALA relationship between two expressions denoting exactly the same or equivalent quantities.

Example: The two expressions 2 + 6 and 3 + 5 aresaid to be equal because they both denote exactly the same quantity.

ENDPOINTA point at the end of a line segment or ray.

EQUAL SETSTwo sets with exactly the same things, elements or members.

Example: A = {1, 2, 3} and B = {3, 2, 1}

EQUAL SIGNThe equal sign shows that two numerals or expressions name the same number.

Example: 10 + 9 = 19In a true sentence, the equal sign shows that the numerals on each side of the sign name the same number.

Equal/Endpoint/Equal Sets/Equal Sign

EQUATIONA number sentence in which the equal sign = is used in an equation.

Example: 6 + = 10 and 8 - 3 =are equations

EQUIVALENT SETSIf the members of two sets can be matched one to one, the sets are equivalent. Equivalent sets have the same number of members/elements.

ESTIMATEAn estimate is an approximate answer found by rounding numbers.

Example: 22 + 39 = , 22 may be rounded to 20,39 may be rounded to 40.The estimated sum is 20 + 40 or 60

Equation/Equivalent Sets/Estimate

EVEN NUMBERAn integer that is divisible by 2 without a remainder.

Example: 0, 2, 4, 6. . . Are even numbers

EXPANDED NUMERALAn expanded numeral is a name for a number which shows the value of the digits.

Example: An expanded number for 35 is 30 + 5 or ( 3 x 10) + (5 x 1)

EXPONENTA number which tells how many times a base number issued as a factor. In the example below the base numbers are 10, 3, and 9.

Example: 10 = 10 x 10 3 = 3 x 3 x 310 = 10 x 10 x 10 x 10 x 10 x 10 9 = 9 x 9 x 9 x 9

Even Number/Expanded Numeral/Exponent

FACTORSNumbers to be multiplied. In 2 x 4 = 8, the factor are 2 and 4.

FACTOR TREE A diagram used to show the prime factors of a number.

Example: 24

6 x 4

2 x 3 2 x 2

24 = 2 x 3 x 2 x 2 or 2 x 3

FAHRENHEITOf or according to the temperature scale of which 32 degrees (32º) is the freezing point of water and 212 degrees is the boiling point of water.

Factors/Factor Tree/Fahrenheit

FRACTION FRACTIONAL NUMBEREqual parts of a whole thing, group or set. A number named by a numeral such as 1/2, 2/3, 6/2, 8/4.

GREATER THANLarger than or bigger than something else. In greater than the symbol >, means that the number named at the left is greater than the number named at the right.

Example: 8 > 3 is a true sentence

GREATEST COMMON FACTORThe greatest common factor (GCF) of two or more counting numbers is the largest counting which is a factor of each of the counting numbers.

Example: 10 = {1, 2, 5}12 = {1, 2, 3, 4, 6, 12}2 is the G.C.F. for 10 and 12

Fraction-Fractional Numbers/Greater Than/Greatest Common Factor

GRAPHA graph shows two sets of related information by the use of pictures, bars, lines or a circle. Graphs may be constructed using horizontal or vertical positions.

BOYS’ PERFECT ATTENDANCE TEMPERATURE RECORD

Month Girls Present 20

April 10

May

June 0

Each symbol represents 3 girls 10 11 12 1 2 3

Graphs continued on next page

Graph

GRAPHS (continued)

10,000 9,000 8,000

7,000 6,000

5,000 4,000

3,000 2,000 1,000 0

Caribbean Red North Japan

HINDU ARABIC NUMERATION SYSTEM(Base Ten Decimal Numeration System)There are 10 digits; namely, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. All whole numbers may be represented by using the digits and Base Ten place value (one, tens, hundreds. . .)

Example: 96,5200 = (9 x 10,000) + (6 x 1,000) + (5 x 100) + (2 x 10) + (0 x 1)

or (9 x 10) + (6 x 10) +

(5 x 10) + (2 x 10) + (0 x 1)

Graph/Hindu Arabic Numeration System

HORIZONTALStraight across. Travels from west to east and east to west.

Example: 965 x 4 = 3,860

IDENTITY ELEMENT OF ADDITIONThe sum of any number and zero is the other number.

Example: 6 + 0 = 6

IDENTITY ELEMENT OF MULTIPLICATIONThe sum of any number and one is that number.

Example: 6 x 1 = 6

INEQUALITYA mathematical sentence which states that two expressions de not name the same number. The signs < and > are usually used.

INTEGERThe integers consist of the counting numbers, zero and the negatives of the counting numbers.

Example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. . .

Horizontal/Identity Element of (Addition)(Multiplication)/Inequality/Integer

INTERSECTION OF SETSThe set consisting of all members which are common to two or more sets.

Example: 12 14 3 1 7 4 2 612 14

JOINING SETSForming one set which contains all the members of two or more sets.

Example: If Set A = {a, b} and Set B = {3, 4},Sets A and B may be joined to form the set C = {a, b, 3, 4}

KILOMETERA unit of length in the metric system. A kilometer (KM) is equal to 1000 meters, or about .62 of a mile.

Intersection of Sets/Joining Sets/Kilometer

LEAST COMMON MULTIPLEThe least common multiple of two or more counting numbers is the smallest counting numbers which is a multiple of each of the counting numbers.Example: What are some multiples of both 4 and 6?

Set of multiples of 4 = {4, 8, 12, 16, 20, 24, 28, 32,. . .} Set of multiples of 6 = {6, 12, 18, 24, 30, 36,. . .}

12 is multiple of both 4 and 6. Another multiple of both 4 and 6 is 24. Therefore, 12 and 24 are called common multiples of 4 and 6. 12 is the Least Common Multiple (LCM).

LENGTHThe distance from one end to the other end. Long represents how long something is from the beginning to the end. Endpoint to endpoint.

Least Common Multiple/Length

LESS THANSmaller than something else. In less than the symbol “<“ means that the number to the left of the symbol is smaller than the number to the right of the symbol.

Example: 104 < 140; 5 + 6 < 6 + 6; 1/6 < 1/4

LOWEST TERMSA fraction is in the lowest or simplest form if the numerator and denominator have no other common factors besides 1.

Example: The lowest terms of 8/32 is 1/4

MEASURETo find or show the size, weight or amount of something.

MEASURE OF A SETEach thing belonging to a set is a member of the set. It is also called an element of the set.

Example: In a set, A = {R, S, T}, R, S, and Tare members/elements of set A.

Less Than/Lowest Terms/Measure/Measure of a Set

METERThe basic unit of measure is the metric system. The meter is about 39 inches long.

METRIC SYSTEMA decimal system used for practically all scientific measurement. The standard unit of length is the meter.

MINUENDThe number of things, members or elements in all (whole set) before subtracting.

Example: 904 is the minuend of 904 - 756 = 148The number from which another numberis taken away (subtracted).

MINUSDecreased by. Lower or less than.

Example: 12 - 5 = 7The numeral 12 is decreased by 5or minus 5.

Meter/Metric System/Minuend/Minus

MIXED NUMERALA numeral which consists of numerals for a whole number and a fractional number.

Example: 3

MULTIPLE A number that is multiplied a certain number of times.

Example: Multiples of 10 are 10, 20, 30, 40, 50. . .Multiples of 3 are 6, 9, 12, 15, 18. . .

MULTIPLICAND A number that is to be multiplied by another number.

Example: 36 x 14, 36 is the multiplicand

MULTIPLICATIONThe operation of taking a number and adding it to itself a certain number of times.

Example: 4 x 3 = 4 + 4 +425 x 6 = 25 + 25 + 25 + 25 + 25 + 25

Mixed Numeral/Multiple/Multiplicand/Multiplication

MULTIPLIERA number that tells how many times to multiply another

Example: 7 x 4 means that 7 will be multiplied 4 times.

MULTIPLYTo add a number to itself a certain number of times. Shortcut to addition.

NATURAL NUMBERSCounting numbers.

NEGATIVE NUMBERSNumbers less than 0.

Example: -5, -6, -7, -4, -3, -2. . .

NUMBER SENTENCEA sentence of numerical relationship.

Example: 2 + 5 = 1 + 63 + 8 > 61 x 3 < 9 - 2

Multiplier/Multiply/Natural Numbers/Negative Numbers/Number Sentence

NUMERALA symbol for a number.

Example: The number word six may be denoted by the symbol 6; thus, 6 is a numeral.

NOTE: The fundamental operations(addition, subtraction,multiplication, division) are performed with numbers,not with numerals.

The word “numeral” is used only when referring to the whether to use the word “number” or “numeral,” use the word

NUMERATION A system to name numbers in various ways.

NUMERATOR In 3/5, the numerator is 3. The numerator tells the number of equal parts, groups or sets that is being used.

Numeral/Numeration/Numerator

ODD NUMBERAn integer which is divisible by 2 with a remainder.

Example: ///

ONE-TO-ONE CORRESPONDENCE A one -to-one matching relationship. If to every member in one set there corresponds one and only one member in a second set, and to every member in the second set there corresponds one and only member in the first set, the sets are said to be in one-to-one correspondence.

Example: If every seat in a room is occupied by aperson, and no person is standing, thereis a one-to-one correspondence betweenthe number of persons and the numberof seats.

Odd Number/One-to-One Correspondence

OPEN SENTENCEA mathematical sentence which contains a variable such as n, x, , or .

Example: 3 + = 8An open sentence cannot be judged true or false. When the variable is replaced by a numeral, the open sentence becomes a statement.

OPERATION A specific process for combining quantities.

Example: Addition, subtraction, multiplication, division

ORDER The way in which something is arranged.

Example: 1, 2, 3, 4. . .A, B, C, D. . .9, 8, 7, 6. . .3, 6, 9, 12. . .Z, Y, X, W. . .First, Second, Third, Fourth. . .

Open Sentence/Operation/Order

ORDINAL NUMBERA number which indicates the order place of a member of a set in relation to other members of the same set.

Example: 1st, 2nd, 3rd. . .

PAIR Two persons, animals, or things that are alike/ that go together.

Example: A pair of gloves

PER For each. Similar and are matched to go together.

Example: eggs per dozen

PERCENTRatio with 100 as its second number. Percent means per hundred.

Example: % = /100

Ordinal Number/Pair/Per/Percent

PICTURE GRAPHA graph which uses picture symbols to show number information.

Example: The pictograph shows how much money4 children earned last week. Each means 10 cent.Cierra Alex Paul Calin

PLACE VALUE Place value is the value of each place in a plan for naming numbers. The value of the first place on the right, in our system of naming whole numbers is one. The value of the place to the left of ones place is then. . . [Tens/Ones]

PRIME NUMBER A number greater than one which has factors of only itself and one. 2, 3, 5, 7, 11 and 13 are just a few of the prime numbers.

Picture Graph/Place Value/Prime Number

PRODUCTThe number that results when two or more numbers are multiplied. The answer in a multiplication problem. Example: 2 x 3 = 6, the product is 6

PRODUCT SET The set of all couples formed by pairing every member of one set with every member of a second set.

QUOTIENT In 6 - 2 = 3, 3 is the quotient. For 13 2, 13 = 2 x 6 + 1;6 is the quotient and 1 is the remainder.

RELATED SENTENCES OR EQUATIONSRelated sentences give the same number relation in different ways.

Example: 4 + 3 = 7, 3 + 4 = 7, 7 - 4 = 3, 7 - 3 = 4are all related sentences

Product/Product Set/Quotient/Related Sentences or Equations

REMAINDERThe difference of the dividend and the greatest multiple of the divisor which is less than the dividend.

Example: 17 = (3 x 5) + 2, 3 ) 17 The remainder is 2

The part that’s left over.(xxx) (xxx) (xxx) xx remainder

3 Remainder 23 )11 - 9 2

SCALE DRAWING A drawing the same shape as an object, but which may be larger, the same size, or smaller than the object.

Remainder/Scale Drawing

SCOREA period of twenty years.

SET A set is a collection or group of objects which may be physical things, points, numbers, and so on.

SIMPLEST FORMS OF A FRACTIONAL NUMERAL In simplest form, the greatest common factor of the numerator and the denominator is one.

STANDARDAnything used to set an example or serve as something to be copied.

STATISTICSCollection data expressed through numerical facts.

Score/Set/Simplest Forms of a Fractional Numeral/Standard/Statistics

SUBTRACTTo take away from the whole group or set.

Example: Take Away 5 subtract 2 = 3

SUBTRACTION The act of taking away some things, members or elements in the whole group or set.

Example: 202 - 197 =problem

SUBTRAHEND The number of things, members or elements in the whole group or set.

SUMThe number that results when two or more numbers are added is the sum.

Example: 3 + 2 = 5, the sum is 5

Subtract/Subtraction/Subtrahend/Sum

SYMBOLA letter, numeral or mark which represents quantities, number, operations, or relations.

Example: +, -, x, are symbols for operations=, <, > are symbols for relationsThe symbol (numeral), 67, may be used

to represent the number word, sixty-seven.

TOTAL The whole amount.

VARIABLE A letter or symbol that represents a number. The unknown.

Example: N x 20 = 100 - 8 = 5

Symbol/Total/Variable

VERTICALStraight up and down.

Example: 567493+48

WEIGH To measure the heaviness of a person or thing.

WEIGHT The amount of heaviness of a person or thing.

WHOLE NUMBERSThe numbers which tell “how many” are whole numbers. The set of whole numbers contains the counting numbers and zero.

Set of Whole Numbers = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9. . .} They are infinite.

WIDTH The distance from one side of something to the other side. How wide something is from one side to the other side.

Vertical/Weigh/Weight/Whole Numbers/Width

GEOMETRY

Our environment contains many physical objects for which mathematicians have developed geometric ideas. These objects then serve as models of the geometric ideas.

TO NAME A LINE. Illustration: AB MEANS LINE AB.

TO NAME A LINE SEGMENT Illustration: AB MEANS LINE SEGMENT AB

TO NAME A RAY Illustration: AB MEANS RAY AB.

FOR ANGLE Illustration: ABC

FOR CONGRUENT Illustration: A B C D

AB CD

FOR TRIANGLE Illustration: ABC

FOR PARALLEL Illustration: A B C D

AB CD

Common Geometric Symbols

Glossary of Geometric Terms

ADJACENTNear or close to something; adjoining.

ALPHABETLetters to name geometric ideas.

ANGLEA model to indicate that a line extends indefinitely in both directions.Illustration:

ACUTE RIGHTOBTUSE

Adjacent/Alphabet/Angle

AREA• The amount of space enclosed by a plane figure (simple closed figure).• The measure of the interior (region) of a simple closed figure.

NOTE: The measure of the interior of a simple closed figure is called its area-measure. • The measure of a region is expressed by such terms as: square inches, square centimeters, square feet, square yard, square meter, etc. • The area of a square one inch long and one inch wide is a square inch. • The area of a square one foot long and one foot wide is a square foot. • The area of a square one yard long and one yard wide is a square yard. • The area of a square one meter long and one meter wide is a square meter.

AREA OF A RECTANGLE:• The number of square inches in a rectangle equals the number of rows one inch wide times the number of square inches in a row.Illustration:

• The number of square centimeters or square feet in a rectangle is its area.

Area/Area of a Rectangle

TO FIND THE AREA OF A SQUARE:

Area = Side Squared or A = S x S or A = S

TO FIND THE AREA OF A RECTANGLE:

Area = Length times width (formula)or

A = L x W or A = LW

TO FIND THE AREA OF A TRIANGLE:

Area = One-half the base times the height or

A = bh or A =

TO FIND THE AREA OF A PARALLELOGRAM:

Area = Base times height over two plus base times height over two or

A = + or A = 2 or A = bh

bh2

bh2

bh2

(bh)2

Finding the area of (square)(rectangle)(triangle)(parallelogram)

ARROWA model to indicate that a line extends indefinitely in both directions.

BISECTSeparate into two congruent parts.

COMMONThe same.

CONGRUENTFigures, in geometry, that have the same size and shape.

CONSTRUCTIONSGeometric drawings made with only a compass and a straight edge.

CURVESA line having no straight part; bend having no angular part.

Arrow/Bisect/Common/Congruent/Constructions/Curves

DEGREEA standard unit of measure used in the measurement of angles.

DIAGONALIn a polygon, a line segment that joins two non-adjacent vertices; extending slantingly between opposite corners.

Illustration:

DIMENSIONThe measurement of the length and width.

EDGEA line segment formed by the intersection of two faces of a solid figure such as a prism.

ENCLOSEShut in all around; surrounded.

Degree/Diagonal/Dimension/Edge/Enclose

ENDPOINTIn a line segment, the two points at the end of the segment used to name it.

FACEA plane surface of a space figure.

GEOMETRIC FIGUREEvery set of points in space.

GEOMETRYThe study of space and figures in space.

INTERSECTIONA set that contains all the members common to two other sets no other members. The intersection of the model.Illustration:

A D

C BY

•

•

•

•

•The intersection of angles AYD and CYD is “Y.”

Endpoint/Face/Geometric Figure/Geometry/Intersection

LINEA set of points.

Illustration:

• The word “line” means straight line.• Extends indefinitely in each of its two directions.• A geometric line is the property these models of lines have in common; it has length but no thickness and no width; it is an idea.• The edge of a ruler, a taut string or wire or an edge of this page is a model of a line.

LINE SEGMENT or SEGMENT:• A part of a straight line consisting of two points, called endpoints, and all the points that are between these points on the line.• Has definite length.

Illustration:

••P Q

Line/Line Segment or Segment

LINE OF SYMMETRY:A line which divides a figure into two congruent parts. When a figure is folded along a line symmetry, the parts fit exactly onone another. Illustration:

MIDPOINT ON A LINE:The point on a line segment which is the same distance fromthe endpoints; midway between the endpoints of a line segment.Illustration:

A BQ•R

P

• ••

•

Line of Symmetry/Midpoint of a Line

POINT SYMMETRY:Can be fitted onto itself by making 1/2 turn about a point. Illustration:

PARALLEL LINES:Two lines in the same plane that do not intersect.Illustration:

C

•D

B A

O

B

D C

A

••pointsymmetry

BA

DC

YS

XR

ZY

XW

Point Symmetry/Parallel Lines

PERPENDICULAR BISECTOR:A line which bisects a segment and is perpendicular to it. Illustration:

PARALLELTravel the same direction apart of every point, so as never to meet, as lines, planes, etc.

C D

E

G

R

Perpendicular/Parallel

PERIMETER• The distance around a figure (polygon).• The perimeter of any polygon can be found by adding the measures of the sides of the polygon, if they are given in the same unit.• When you find the perimeter of a figure, the length and the width must be in the same units. 1. If the dimensions of a figure are in inches, the perimeter will be in inches. 2. If the dimensions of a figure are in centimeters, the perimeter will be in centimeters. 3. If the dimensions of a figure are in feet, the perimeter will be in feet.

• Finding the perimeter of any polygon is based on addition of measures.• The perimeter of some polygons can be expressed by a formula.

1. PERIMETER OF A RECTANGLE:Perimeter = 2 x Length + 2 x Width

or P = 2 x L + 2 x W or P = 2 x (L + W)

2. PERIMETER OF A SQUARE:Perimeter = 4 x length of one side

or P = S + S + S + S or P = 4S3. PERIMETER OF A TRIANGLE:Perimeter = Side + Side + Side or P = S + S + S

Perimeter

PLANETravel the same direction apart of every point, so as never to meet, as lines, planes, etc.Illustration:

PLANE FIGUREAll the points of a figure lying on the same plane.Illustration:

a b c d e

POINTAn idea about an exact location; it has no dimensions whatsoever but is represented by a dot (•) There is an unlimited number of lines through a point.

Z

Y

X

RQ

Plane/Plane Figure/Point

POLYGONA simple closed figure that consists only of line segments.

REGULAR POLYGON:A polygon with congruent sides and congruent angles.

FIGURE:In Geometry, any sets of points.

PLANE FIGURES:Rectangle, square and circle are the most common.

SIMPLE CLOSED FIGURE:A Simple Closed Figure is one that does not intersect (cross)itself. If it is made up of line segments it is called a polygon. Illustration:

Polygon(Regular Polygon/Figure/Plane Figures/Simple Closed Figure)

PARALLELOGRAM:A quadrilateral in which opposite sides are parallel.

PENTAGON:A polygon with five sides.

OCTAGON:An eight-sided polygon.

QUADRILATERAL:A polygon (simple closed figure) formed by four line segments.

RECTANGLE:A quadrilateral (polygon) with two pairs of parallel sides and four right angles (4 sides and 4 square corners). Illustration:

P O

M N

Polygon (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)

SQUARE:A quadrilateral (polygon) with congruent sides the same length and four right angles. Also, the product when a number is multiplied by itself.Example: 3 x 3 = 9, The square of 3 or 3

Illustration:

TRAPEZOID:A quadrilateral (polygon) with only one pair of parallel sides. Illustration:

8"

22"

12"

W

Z

X

Y

Polygon (Square/Trapezoid)

TRIANGLE:A figure (polygon) with three sides.KINDS:1. EQUILATERAL TRIANGLE: A triangle all of whose sides are congruent.

2. ISOSCELES TRIANGLE: A triangle with at least two sides congruent.

3. RIGHT TRIANGLE: A triangle with one right angle.

4. SCALENE TRIANGLE: A triangle with no congruent sides.

• LEGS (of a right triangle): The two sides in a right triangle that

are also sides of the right angles.

Illustration:

• HYPOTENUSE: The side opposite the right angle in a right triangle.

RIGHT

ISOSCELES

EQUILATERAL

A C

B

SCALENE

G

H

K

Hypotenusec b

a leg

leg

Polygon (Triangle)

PROTRACTORAn instrument for measuring angles just as a ruler is an instrument for measuring line segments.

PRISMA closed space figure. The bases are congruent polygons in parallel planes.

RAY• A point on a line and all the points in one direction from the point.• Has infinite length and only one endpoint (vertex).• The sides of the angle.

Illustration:

FIGURE 1:RS and SQ are used to form the Acute Angle RSQ

E

D

GQS

R

FIGURE 2:DE and EG are used to form the Obtuse Angle DEG

NOTE:

FIGURE 1: FIGURE 2:

Protractor/Prism/Ray

REGIONA closed curve and all the points inside it.

SIZERefers to the amount of opening between the side (rays) of the angle.

SPACE FIGUREA figure encloses a part of space.

STRAIGHT EDGEHas no marks on it with which measurements can be made; by tracing along its edge one can construct a line segment.

VERTEXA common endpoint of two rays, two segments, or three or more edges of a space figure.Illustration:

FIGURE 1:Point B is the Vertexof angle CBA.

R

S

QFIGURE 2:Point R is the Vertex of Angles QRS, SRT and TRQ.

NOTE:

A

B

C

FIGURE 1: FIGURE 2:T

Region/Size/Space Figure/Straight Edge/Vertex

UNITS OF MEASURE

LENGTHENGLISH METRIC

12 inches (in.) = 1 foot (ft.) 1000 milliliters (mm) = 1 meter 3 feet (ft.) = 1 yard (yd.) 100 centiliters (cm) = 1 meter 36 inches = 1 yard (yd.) 10 deciliters (dm) = 1 meter 5280 feet = 1 mile (MI.) 1000 liters = 1 kilometer

LIQUIDENGLISH METRIC

2 cups (c.) = 1 pint (pt.) 1000 milliliters (ml) = 1 liter (l) 2 pints = 1 quart (qt.) 100 centiliters (cl) = 1 liter (l) 4 quarts = 1 gallon (gal.) 10 deciliters (dl) = 1 liter (l)

1000 liters (l) = 1 kiloliter (kl)

WEIGHTENGLISH METRIC

16 ounces (oz.) = 1 pound (lb.) 1000 milligrams (mg) = 1 gram (g)2000 pounds = 1 ton (T.) 100 centigrams (cg) = 1 gram

10 decigrams (dg) = 1 gram 1000 grams = 1 kilogram

Length/Liquid/Weight

EQUIVALENT UNITSLENGTH LIQUID WEIGHT

2.5 centimeters is about 1 inch. .95 liter is about 1 quart. 28.35 grams is about 1 ounce. .9 meter is about 1 yard. 3.79 liters is about 1 gallon. .45 kilogram is about 1 pound. 1.6 kilometers is about 1 mile.

TIME 60 seconds (sec.) = 1 minute 60 minutes (min.) = 1 hour 24 hours (hr.) = 1 day 7 days = 1 week (wk.) 365 days = 1 year (yr.) 366 days = 1 leap year 10 years = 1 decade 20 years = 1 score 100 years = 1 century

Equivalent Units/Time