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Word
Definition
rectangular array
a rectangular arrangement of objects in rows and columns
such that each row has the same number of objects and each
column has the same number of objects.
number model
a number sentence that models or fits a situation
Example: Harry is 8 years older than his 5 year old sister can
be modeled by the number sentence 8 + 5 = 13.
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turn-around rule
factor
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one of two numbers that are multiplied to give a product
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factor pair
a rule for solving addition and multiplication problems
based on the commutative property
Example: 6 X 8 =48, the turn around rule is 8 X 6 = 48
Commutative property- the changing of the order of the
numbers being added or multiplied doesn't change the
answer.
two whole-number factors of a number
a number may have more than one factor pair
Example: the factor pairs for 18 are 1 and 18, 2 and 9, and 3
and 6
factor rainbow
a way to show factor pairs in a list of all the factors of a
number
product
the result of multiplying two numbers
divisible by
one whole number is divisible by another whole number if
there is not remainder
divisibility test
a test to find out whether a whole number is divisible by
another whole number without actually doing the division.
quotient
the result of dividing one number by another number
Example: In 35/5 =7, the quotient is 7.
remainder
an amount left over when one number is divided by another
number.
Example: 35 divided by 5 = 7 equal groups with a remainder
of 3
composite number
a whole number that has more than two factors
prime number
a whole number that has exactly two factors, itself and 1.
square array
is a special rectangular array that has the same number of
rows as it has columns
square number
a number that is a product of a whole number multiplied by
itself
exponent
a small raised number in exponential notation that tells how
many times the base is to be multiplied by itself
base
the number that is raised to some power
exponential
notation
a way to show repeated multiplication by the same factor
3
Example: 2
is exponential notation for 2 X 2 X 2
square root
4 is the square root of 16 because 4 X 4 = 16
name-collection
box
a box-like diagram tagged with a given number and used for
collecting equivalent names for that number.
factor string
a number written as a product of at least two whole-number
factors.
Example: a factor string for the number 24 is 2 X 3 X 4. This
factor string has three factors, so its length is 3. The number 1
is never part of a factor string.
factor tree
a way to get the prime factorization of a number. The original
number is written as a product of factors; then each of these
factors is written as a product of factors and so on, until the
factors are all prime numbers.
prime factorization
a whole number expressed as a product of prime factors.
Example: the prime factorization of 24 is 2 X 2 X 2 X 3.
Factors
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are a way to breakdown numbers
help you understand the relationships between numbers
there are different ways to express factors
Prime Factors of the number 12
12 = 2 X 2 X 3 the numbers 2 & 3 are prime numbers
Factors of the number 12
1 & 12, 2 & 6, 3 & 4
Factor Rainbow for the number 12
1, 2, 3, 4, 6, 12
Divisibility Rules
Help you decide if a number will be divisible by another number. If you know these
tests it can help make dividing easier for you.
A number is divisible by 2- if it is an even number
A number is divisible by 3- if the sum of the digits is divisible by 3.
(534 is divisible by 3 because 5 + 3 + 4=12 and 12
is divisible by 3)
A number is divisible by 6-if it is divisible by 2 & 3.
A number is divisible by 9-if the sum of the digits is divisible by 9.
(8,253 is divisible by nine because 8 + 2 + 5 + 3=
18)
A number is divisible by 5- if it ends in a 5 or a 0.
A number is divisible by 10 -if it ends in a zero.
Hints:
1. Underline the last digit of the number you are working with.
2. Determine if the number will be divisible by 2, 5, and 10 first because
they are the easy ones.
3. Next add up the digits in the number and write the sum in a circle next
to your number.
4. After you add the digits you can determine if the number will be
divisible by 3, 6, and 9.