MATH TIPS
for
PARENTS
NUMBER PROPERTIES
THE 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)
Commutative Property of Addition
• 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
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
Inverse Operation of Addition
• Subtraction undoes the operation called addition.
In Arithmetic: If 7 + 4 = 11, then
11 - 7 = 4 and 11 - 4 = 7
In Algebra:
a + b = c, then
c - a = b and c - b = a
THE OPERATION CALLED SUBTRACTION
Inverse Operation of Subtraction
• Addition undoes the operation called subtraction.
In Arithmetic: If 16 - 9 = 7, then
9 + 7 = 16 and 7 + 9 = 16
In Algebra:
c - b = a, then
b + a = c and a + b = c
THE OPERATION CALLED DIVISION
Inverse Operation of Division
• Multiplication undoes the operation called division.
In Arithmetic: If 48 / 8 = 6, then
8 x 6 = 48 and 6 x 8 = 48
In Algebra:
c / b = a, then
b x a = c and a x b = c
THE OPERATION CALLED MULTIPLICATION
Associative Property of 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)
Commutative 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
Identity 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
Multiplication Property of Zero
• 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.
8x4=8+8+8+8
Distributive Property of Multiplication
over Addition or Subtraction
• 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 ADDITION
5(90 + 10) = (5 x 90) + (5 x 10)
OVER SUBTRACTION
5(90 - 10) = (5 x 90) - (5 x 10)
In Algebra:
OVER ADDITION
a(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)
GLOSSARY of
MATHEMATICAL TERMS
Add/Addend/Addition/Array
ADD
To put one thing, set or group with another thing, set or group.
ADDEND
Numbers to be added.
Example:
12 + 23 = 25
a + b + c = abc
ADDITION
The operation of putting together two or more numbers, things,
groups or sets.
Example:
8 + 2 + 4 = 14 is an addition problem
ARRAY
An 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
Associative Property of Addition-Multiplication/Attribute
ASSOCIATIVE PROPERTY OF ADDITION
The 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 MULTIPLICATION
The 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
ATTRIBUTE
A quality that is thought of as belonging to a person of thing.
Characteristics; such as, size, shape, color and/or thickness.
Average/Axis
AVERAGE
A 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
54
39
+ 93
272
68
4) 272
- 24
32
- 32
0
How many addends?
Quantity is 4
sum or total
is the average
AXIS (axes)
Horizontal and vertical number lines in a number plane.
Bar Graph/Braces
Colors the Class Likes
BAR GRAPH
A picture in which number information
is shown by means of bars of
different lengths.
25
20
15
10
0
BRACES
Braces are symbols { }. They are used to list names of numbers
(elements) of a set.
Example:
{ Pauline, April, Joni, Jackie} is a set
of secretaries.
{Sunday, Monday, Tuesday, Wednesday,
Thursday, Friday, Saturday} is a set of
the days of the week.
{1, 2, 3, 4, 5, 6, 7, 8, 9} is a set of counting
numbers from 1 to 9.
Capacity/Cardinal Number/Centigrade/Cent/Centimeter
CAPACITY
The amount that can be held in a space.
CARDINAL NUMBER
A number that tells how many there are.
Example:
There are five squares
CENTIGRADE
Divided 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
CENT
A coin of the United States and Canada. One hundred cents make
a dollar.
CENTIMETER
A unit of length in the metric system. A centimeter is equal to one
hundredths of a meter or .39 of an inch.
Century/Closed Figure/Closure
CENTURY
A period of one hundred years.
CLOSED FIGURE
A geometric figure that entirely encloses part of the plane.
CLOSURE
A 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.
Combine/Common/Common Factor/Common Multiple
COMBINE
To put (join) together.
COMMON
Belonging equally to all.
COMMON FACTOR
A 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 MULTIPLE
A 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
Commutative Property of (Addition)(Multiplication)/
Compare/Composite Number
COMMUTATIVE PROPERTY OF ADDITION
The 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 MULTIPLICATION
The 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
COMPARE
To study, discover and/or find out how persons or things are alike
or different.
COMPOSITE NUMBER
A 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.
Conditional Sentence/Congruent Figure/Conjecture/Conjunction
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 FIGURE
Geometric 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
CONJECTURE
A guess resulting from an experiment.
Example:
2, 4, 6, 8, 10 are even numbers; therefore,
even numbers must have 0, 2, 4, 5, or 8
in 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
Coordinates/Counting Number/Decade/Decimal
COORDINATES
To 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.
DECADE
A period of ten years.
DECIMAL
Names the same number as a fraction when the denominator is
10, 100, 1000. . . It is written with a decimal point.
Example:
.75
Decimal System/Diagonal/Degree/Denominator
DECIMAL SYSTEM
A plan for naming numbers that is based on ten is called a decimal
system of numeration. The Hindu-Arabic system is a decimal
system.
DIAGONAL
A straight line that connects the opposite corners of a rectangle.
Example:
DEGREE
A unit of angle measurement.
DENOMINATOR
In 3/5 the denominator is 5. It tells the number of equal parts,
groups or sets the whole was divided.
Difference/Digit/Disjoint Sets
DIFFERENCE
The 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
DIGIT
Any 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 SETS
Sets 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
Distributive Property of Multiplication over Addition/Divide/Dividend
DISTRIBUTIVE PROPERTY OF
MULTIPLICATION OVER ADDITION
Multiplication 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
DIVIDE
To separate into equal parts, pieces, groups or sets..
Example:
xx xx
xx xx xx
10  2 = 5
DIVIDEND
A 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
Divisible/Divisor/Element/Element of a Set/Empty Set
DIVISIBLE
Capability of being separated equally without a remainder.
Example:
18 is divisible by 1, 2, 3, 6, 9 and 18
DIVISOR
A number that tells what kind of equal parts, groups or sets the
dividend is to be separated.
ELEMENT
A member of a set.
ELEMENT OF A SET
A member of a set.
EMPTY SET
The set which has no members. The number of the empty set is
zero. A symbol for the empty set is { }.
Equal/Endpoint/Equal Sets/Equal Sign
EQUAL
A relationship between two expressions denoting exactly the same
or equivalent quantities.
Example:
The two expressions 2 + 6 and 3 + 5 are
said to be equal because they both
denote exactly the same quantity.
ENDPOINT
A point at the end of a line segment or ray.
EQUAL SETS
Two sets with exactly the same things, elements or members.
Example:
A = {1, 2, 3} and B = {3, 2, 1}
EQUAL SIGN
The equal sign shows that two numerals or expressions name the
same number.
Example:
10 + 9 = 19
In a true sentence, the equal sign shows that the numerals on
each side of the sign name the same number.
Equation/Equivalent Sets/Estimate
EQUATION
A number sentence in which the equal sign = is used in an
equation.
Example:
6+
= 10 and 8 - 3 =
are equations
EQUIVALENT SETS
If the members of two sets can be matched one to one, the sets
are equivalent. Equivalent sets have the same number of
members/elements.
ESTIMATE
An 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
Even Number/Expanded Numeral/Exponent
EVEN NUMBER
An integer that is divisible by 2 without a remainder.
Example:
0, 2, 4, 6. . . Are even numbers
EXPANDED NUMERAL
An 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)
EXPONENT
A 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 3
10 = 10 x 10 x 10 x 10 x 10 x 10
9 = 9 x 9 x 9 x 9
Factors/Factor Tree/Fahrenheit
FACTORS
Numbers 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
2
x
x
3 2
4
x
2
24 = 2 x 3 x 2 x 2 or 2 x 3
FAHRENHEIT
Of 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.
Fraction-Fractional Numbers/Greater Than/
Greatest Common Factor
FRACTION FRACTIONAL NUMBER
Equal 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 THAN
Larger 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 FACTOR
The 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
Graph
GRAPH
A 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
Month
April
Girls Present


 
TEMPERATURE RECORD
20

10
  
 
June
Each symbol
 represents 3 girls
May


0
10
11
12
1
2
3
Graphs continued on next page
Graph/Hindu Arabic Numeration System
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)
Horizontal/Identity Element of
(Addition)(Multiplication)/Inequality/Integer
HORIZONTAL
Straight across. Travels from west to east and east to west.
Example:
965 x 4 = 3,860
IDENTITY ELEMENT OF ADDITION
The sum of any number and zero is the other number.
Example:
6+0=6
IDENTITY ELEMENT OF MULTIPLICATION
The sum of any number and one is that number.
Example:
6x1=6
INEQUALITY
A mathematical sentence which states that two expressions de not
name the same number. The signs < and > are usually used.
INTEGER
The 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. . .
Intersection of Sets/Joining Sets/Kilometer
INTERSECTION OF SETS
The set consisting of all members which are common to two or
more sets.
Example:
12
14
3
1
7
4
2
6
12
14
JOINING SETS
Forming 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}
KILOMETER
A unit of length in the metric system. A kilometer (KM) is equal to
1000 meters, or about .62 of a mile.
Least Common Multiple/Length
LEAST COMMON MULTIPLE
The 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).
LENGTH
The distance from one end to the other end. Long represents how
long something is from the beginning to the end. Endpoint to
endpoint.
Less Than/Lowest Terms/Measure/Measure of a Set
LESS THAN
Smaller 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 TERMS
A 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
MEASURE
To find or show the size, weight or amount of something.
MEASURE OF A SET
Each 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 T
are members/elements of set A.
Meter/Metric System/Minuend/Minus
METER
The basic unit of measure is the metric system. The meter is
about 39 inches long.
METRIC SYSTEM
A decimal system used for practically all scientific measurement.
The standard unit of length is the meter.
MINUEND
The number of things, members or elements in all (whole set)
before subtracting.
Example:
904 is the minuend of 904 - 756 = 148
The number from which another number
is taken away (subtracted).
MINUS
Decreased by. Lower or less than.
Example:
12 - 5 = 7
The numeral 12 is decreased by 5
or minus 5.
Mixed Numeral/Multiple/Multiplicand/Multiplication
MIXED NUMERAL
A 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
MULTIPLICATION
The operation of taking a number and adding it to itself a certain
number of times.
Example:
4 x 3 = 4 + 4 +4
25 x 6 = 25 + 25 + 25 + 25 + 25 + 25
Multiplier/Multiply/Natural Numbers/
Negative Numbers/Number Sentence
MULTIPLIER
A number that tells how many times to multiply another
Example:
7 x 4 means that 7
will be multiplied 4 times.
MULTIPLY
To add a number to itself a certain number of times. Shortcut to
addition.
NATURAL NUMBERS
Counting numbers.
NEGATIVE NUMBERS
Numbers less than 0.
Example:
-5, -6, -7, -4, -3, -2. . .
NUMBER SENTENCE
A sentence of numerical relationship.
Example:
2+5 = 1+6
3+8 > 6
1x3 < 9-2
Numeral/Numeration/Numerator
NUMERAL
A 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.
Odd Number/One-to-One Correspondence
ODD NUMBER
An 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 a
person, and no person is standing, there
is a one-to-one correspondence between
the number of persons and the number
of seats.
Open Sentence/Operation/Order
OPEN SENTENCE
A mathematical sentence which contains a variable such as n, x,
, or .
Example:
3+
=8
An 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. . .
Ordinal Number/Pair/Per/Percent
ORDINAL NUMBER
A 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
PERCENT
Ratio with 100 as its second number. Percent means per hundred.
Example:
% = /100
Picture Graph/Place Value/Prime Number
PICTURE GRAPH
A graph which uses picture symbols to show number information.
Example:
The pictograph shows how much money
4 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.
Product/Product Set/Quotient/Related Sentences or Equations
PRODUCT
The 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 EQUATIONS
Related sentences give the same number relation in different
ways.
Example:
4 + 3 = 7, 3 + 4 = 7,
7 - 4 = 3, 7 - 3 = 4
are all related sentences
Remainder/Scale Drawing
REMAINDER
The 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
3 )11
-9
2
Remainder 2
SCALE DRAWING
A drawing the same shape as an object, but which may be larger,
the same size, or smaller than the object.
Score/Set/Simplest Forms of a Fractional
Numeral/Standard/Statistics
SCORE
A 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.
STANDARD
Anything used to set an example or serve as something to be
copied.
STATISTICS
Collection data expressed through numerical facts.
Subtract/Subtraction/Subtrahend/Sum
SUBTRACT
To 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.
SUM
The number that results when two or more numbers are added is
the sum.
Example:
3 + 2 = 5, the sum is 5
Symbol/Total/Variable
SYMBOL
A letter, numeral or mark which represents quantities, number,
operations, or relations.
Example:
+, -, x,  are symbols for operations
=, <, > are symbols for relations
The 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
Vertical/Weigh/Weight/Whole Numbers/Width
VERTICAL
Straight up and down.
Example:
567
493
+48
WEIGH
To measure the heaviness of a person or thing.
WEIGHT
The amount of heaviness of a person or thing.
WHOLE NUMBERS
The 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.
GEOMETRY
Our environment contains many physical objects
for which mathematicians have developed
geometric ideas. These objects then serve as
models of the geometric ideas.
Common Geometric Symbols


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:
FOR CONGRUENT
Illustration: A

ABC
B
AB

FOR TRIANGLE
Illustration:
 FOR PARALLEL
Illustration:
D
CD
 ABC
A
C
AB


C
CD
B
D
C
FOR INTERSECTION
Illustration:
A
AB  CD
B
D
Glossary of Geometric Terms
Adjacent/Alphabet/Angle
ADJACENT
Near or close to something; adjoining.
ALPHABET
Letters to name geometric ideas.
ANGLE
A model to indicate that a line extends indefinitely in both directions.
Illustration:
ACUTE
OBTUSE
RIGHT
Area/Area of a Rectangle
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.
Finding the area of (square)(rectangle)(triangle)(parallelogram)
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
bh
A =  bh or A =
2
TO FIND THE AREA OF A PARALLELOGRAM:
Area = Base times height over two plus base times height over two
or
bh
bh
A=
+
or A = 2 (bh)
or A = bh
2
2
2
Arrow/Bisect/Common/Congruent/Constructions/Curves
ARROW
A model to indicate that a line extends indefinitely in both directions.
BISECT
Separate into two congruent parts.
COMMON
The same.
CONGRUENT
Figures, in geometry, that have the same size and shape.
CONSTRUCTIONS
Geometric drawings made with only a compass and a straight edge.
CURVES
A line having no straight part; bend having no angular part.
Degree/Diagonal/Dimension/Edge/Enclose
DEGREE
A standard unit of measure used in the measurement of angles.
DIAGONAL
In a polygon, a line segment that joins two non-adjacent vertices;
extending slantingly between opposite corners.
Illustration:
DIMENSION
The measurement of the length and width.
EDGE
A line segment formed by the intersection of two faces of a solid figure
such as a prism.
ENCLOSE
Shut in all around; surrounded.
Endpoint/Face/Geometric Figure/Geometry/Intersection
ENDPOINT
In a line segment, the two points at the end of the segment used to
name it.
FACE
A plane surface of a space figure.
GEOMETRIC FIGURE
Every set of points in space.
GEOMETRY
The study of space and figures in space.
INTERSECTION
A set that contains all the members common to two other sets no other
members. The intersection of the model.
Illustration:
•
•D
A
C
•
•Y
B
•
The intersection of angles AYD
and CYD is “Y.”
Line/Line Segment or Segment
LINE
A 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 of Symmetry/Midpoint of a Line
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 on
one another.
Illustration:
MIDPOINT ON A LINE:
The point on a line segment which is the same distance from
the endpoints; midway between the endpoints of a line segment.
Illustration:
•
•A Q• •B
R•
P
Point Symmetry/Parallel Lines
POINT SYMMETRY:
Can be fitted onto itself by making 1/2 turn about a point.
Illustration:
A
point
symmetry
•
B
•
D
D
C
•O
C
B
A
PARALLEL LINES:
Two lines in the same plane that do not intersect.
Illustration:
R
S
W
X
Y
Z
X
Y
A
B
C
D
Perpendicular/Parallel
PERPENDICULAR BISECTOR:
A line which bisects a segment and is perpendicular to it.
Illustration:
R
E
C
D
G
PARALLEL
Travel the same direction apart of every point, so as never to meet, as
lines, planes, etc.
Perimeter
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=2xL+2xW
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 = 4S
3. PERIMETER OF A TRIANGLE:
Perimeter = Side + Side + Side or
P=S+S+S
Plane/Plane Figure/Point
PLANE
Travel the same direction apart of every point, so as never to meet, as
lines, planes, etc.
Illustration:
PLANE FIGURE
All the points of a figure lying on the same plane.
Illustration:
a
b
c
d
e
Z
X
Q
R
Y
POINT
An 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.
Polygon
(Regular Polygon/Figure/Plane Figures/Simple Closed Figure)
POLYGON
A 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
(Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)
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 (Square/Trapezoid)
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:
Z
Y
W
X
TRAPEZOID:
A quadrilateral (polygon) with only one pair of parallel sides.
Illustration:
12"
8"
22"
Polygon (Triangle)
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.
H
Illustration:
B
leg
Hypotenuse
c
K
G
b
a leg
SCALENE
A
ISOSCELES
C
EQUILATERAL
RIGHT
• HYPOTENUSE: The side opposite the right angle in a right
triangle.
Protractor/Prism/Ray
PROTRACTOR
An instrument for measuring angles just as a ruler is an instrument for
measuring line segments.
PRISM
A 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:
R
D
FIGURE 2:
FIGURE 1:
S
NOTE:
Q
FIGURE 1:
RS and SQ are used to form
the Acute Angle RSQ
E
G
FIGURE 2:
DE and EG are used to form
the Obtuse Angle DEG
Region/Size/Space Figure/Straight Edge/Vertex
REGION
A closed curve and all the points inside it.
SIZE
Refers to the amount of opening between the side (rays) of the angle.
SPACE FIGURE
A figure encloses a part of space.
STRAIGHT EDGE
Has no marks on it with which measurements can be made; by tracing
along its edge one can construct a line segment.
VERTEX
A common endpoint of two rays, two segments, or three or more edges of
a space figure.
C
Illustration:
S
FIGURE 1:
B
R
A
NOTE:
FIGURE 1:
Point B is the Vertex
of angle CBA.
FIGURE 2:
T
Q
FIGURE 2:
Point R is the Vertex of
Angles QRS, SRT and TRQ.
UNITS OF MEASURE
Length/Liquid/Weight
LENGTH
ENGLISH
12 inches (in.)
3 feet (ft.)
36 inches
5280 feet
METRIC
=
=
=
=
1 foot (ft.)
1 yard (yd.)
1 yard (yd.)
1 mile (MI.)
1000 milliliters (mm)
100 centiliters (cm)
10 deciliters (dm)
1000 liters
=
=
=
=
1 meter
1 meter
1 meter
1 kilometer
LIQUID
ENGLISH
2 cups (c.)
2 pints
4 quarts
METRIC
= 1 pint (pt.)
= 1 quart (qt.)
= 1 gallon (gal.)
1000 milliliters (ml)
100 centiliters (cl)
10 deciliters (dl)
1000 liters (l)
= 1 liter (l)
= 1 liter (l)
= 1 liter (l)
= 1 kiloliter (kl)
WEIGHT
ENGLISH
METRIC
16 ounces (oz.) = 1 pound (lb.)
2000 pounds
= 1 ton (T.)
1000 milligrams (mg)
100 centigrams (cg)
10 decigrams (dg)
1000 grams
= 1 gram (g)
= 1 gram
= 1 gram
= 1 kilogram
Equivalent Units/Time
EQUIVALENT UNITS
LENGTH
LIQUID
WEIGHT
2.5 centimeters is about 1 inch.
.9 meter is about 1 yard.
1.6 kilometers is about 1 mile.
.95 liter is about 1 quart.
3.79 liters is about 1 gallon.
28.35 grams is about 1 ounce.
.45 kilogram is about 1 pound.
TIME
60 seconds (sec.)
60 minutes (min.)
24 hours (hr.)
7 days
365 days
366 days
10 years
20 years
100 years
=
=
=
=
=
=
=
=
=
1 minute
1 hour
1 day
1 week (wk.)
1 year (yr.)
1 leap year
1 decade
1 score
1 century