FTCE
FTCE ELEMENTARY EDUCATION
K-6
MATH/ELA/S/SS CORRECT
100%
Major operations on rational numbers - ANSWER
addition subtraction multiplication division
Addition and Subtraction: 4 types of problems -
ANSWER join
part-part-
whole
separat
e
compar
e
Join - ANSWER involve adding or joining elements to a set.
3 quantities involved:
the starting amount__?__
+56=85 the changing amount
29+__?__=85 the resulting
amount 29+56=__?__
variations of the join problem include situations when the result is unknown,
the change is unknown, or the starting amount is unknown.
Separate - ANSWER involves removing elements
3quanities/ variations result
unknown->85-29=__?__
change unknown->85-__?
__=29 start unknown->__?
__-56=29
Part-Part_Whole - ANSWER involve no action or change over time as happens
with join and separate problems.
Focus on the relationship between a set and its two subsets (or a whole and
2 parts)
Variations involve situations the whole
is unknown-> 29+56=__?__ part of the
whole is unknown -> 29+__?__=85
Compare - ANSWER involves no action, but involve comparision between
2 different
FTCE ELEMENTARY EDUCATION K-6 MATH ELA S SS CORRECT 100%
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sets- how much or how much less is one/than
another.
Variatio
n:
Difference unknown: 56+__=85 or 85-
56=__
Larger unknown:
56+29=__
Smaller unknown: 29+__=85 or 85-
29=__
Types of problems for Multiplication/Division - ANSWER Equal groups or
repeated
additio
n
Area and
array
Combinati
on
Multiplicative
Comparison
Equal groups or repeated addition - ANSWER involves making a certain
numbers of
equal sized groups repeated
3x6=6+6+6
3 numbers involved: numbers of groups (factor), size of the group (factor),
total number
of the objects
(product)
ex:3x6 3 groups of 6
objects
Area and Array - ANSWER involve finding the area of a
rectangular area or
arrangeme
nt.
5 rows of 17 apple
trees
ex:Multiplication-
>5x17=__
85 palm
trees/5rows
Division->85 divided by 5=__
Combination - ANSWER Involve different combinations that can be made
from two
sets
FTCE ELEMENTARY EDUCATION K-6 MATH ELA S SS CORRECT 100%
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.
ex: shirts and pants
Multiplication->Oscar 17apples/Tom 5 times as many 5x17=__ apples as
Oscar, how
many does Tim
have?
Division-> Tom has 85 apples, 5 times as many as Oscar. 85 divided by 5=__
Multiplicative Comparison - ANSWER involves the comparison of 2 quantities
manipulatively, involves finding "how many times as much" of 1 quantity is
compared in another quantity, or "stretching" the original by a certain
quantity.
Whole Numbers - ANSWER The whole numbers are the
counting numbers and 0. The whole numbers are
0,1,2,3,4,5... Cannot be negative
Natural Numbers - ANSWER The counting numbers 1,2,3,4,5...
Prime Numbers - ANSWER is a whole number greater than 1 that has
exactly two
factors, 1 and
itself.
2-the only even prime
number,
3,5,7,11,13,17,19,23,31,41,43,47,53,59,61,71,73,79,
83,89,97
1 IS NOT
PRIME
Composite Number - ANSWER is a whole number greater than 1 that
has more than
two
factors
4,6,8,
9
1 IS NOT
COMPOSITE
Factor - ANSWER A factor of a number divides the number evenly.
This means the
quotient is a whole number and the
remainder is 0.
ex: 24-
>2,3,4,6,8,12
Multiples - ANSWER A multiple of a number is the product of that
number and any
FTCE ELEMENTARY EDUCATION K-6 MATH ELA S SS CORRECT 100%
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whole
number.
ex: 3-
>6,9,12,15...
What is the smallest multiple off 12,15 and 20? -
ANSWER 60
Start with the number 20 and go out
by 10s.
Greatest Common Factor (GCF) - ANSWER the greatest factor that
two or more
numbers have in
common.
ex: 6 is the greatest common factor of 18
and 30.
Use the factor tree,
include 1
Least Common Multiple (LCM) - ANSWER The least number that is a
common multiple
of two or more
numbers.
Find the LCM of 30 and
20.
30:
30,60,90,120
20:
20,40,60,80,100,120
Rules of Divisibility - ANSWER A number is divisible by another number
if the quotient
is a counting number and the
remainder is 0.
2: The number is even.
3: The sum of the digits is divisible by 3.
5: The last digit is 0 or 5.
6: The number is even and divisible
by 3. 9: The sum of the digits is
divisible by 9.
Decimals - ANSWER Decimals are a method of writing fractional
numbers without
writing a fraction having a numerator and
denominator.
The fraction 7/10 could be written as the decimal 0.7. The period or
decimal point
indicates that this is a
decimal.
FTCE ELEMENTARY EDUCATION K-6 MATH ELA S SS CORRECT 100%
FTCE ELEMENTARY EDUCATION
K-6
MATH/ELA/S/SS CORRECT
100%
Major operations on rational numbers - ANSWER
addition subtraction multiplication division
Addition and Subtraction: 4 types of problems -
ANSWER join
part-part-
whole
separat
e
compar
e
Join - ANSWER involve adding or joining elements to a set.
3 quantities involved:
the starting amount__?__
+56=85 the changing amount
29+__?__=85 the resulting
amount 29+56=__?__
variations of the join problem include situations when the result is unknown,
the change is unknown, or the starting amount is unknown.
Separate - ANSWER involves removing elements
3quanities/ variations result
unknown->85-29=__?__
change unknown->85-__?
__=29 start unknown->__?
__-56=29
Part-Part_Whole - ANSWER involve no action or change over time as happens
with join and separate problems.
Focus on the relationship between a set and its two subsets (or a whole and
2 parts)
Variations involve situations the whole
is unknown-> 29+56=__?__ part of the
whole is unknown -> 29+__?__=85
Compare - ANSWER involves no action, but involve comparision between
2 different
FTCE ELEMENTARY EDUCATION K-6 MATH ELA S SS CORRECT 100%
,FTCE
sets- how much or how much less is one/than
another.
Variatio
n:
Difference unknown: 56+__=85 or 85-
56=__
Larger unknown:
56+29=__
Smaller unknown: 29+__=85 or 85-
29=__
Types of problems for Multiplication/Division - ANSWER Equal groups or
repeated
additio
n
Area and
array
Combinati
on
Multiplicative
Comparison
Equal groups or repeated addition - ANSWER involves making a certain
numbers of
equal sized groups repeated
3x6=6+6+6
3 numbers involved: numbers of groups (factor), size of the group (factor),
total number
of the objects
(product)
ex:3x6 3 groups of 6
objects
Area and Array - ANSWER involve finding the area of a
rectangular area or
arrangeme
nt.
5 rows of 17 apple
trees
ex:Multiplication-
>5x17=__
85 palm
trees/5rows
Division->85 divided by 5=__
Combination - ANSWER Involve different combinations that can be made
from two
sets
FTCE ELEMENTARY EDUCATION K-6 MATH ELA S SS CORRECT 100%
,FTCE
.
ex: shirts and pants
Multiplication->Oscar 17apples/Tom 5 times as many 5x17=__ apples as
Oscar, how
many does Tim
have?
Division-> Tom has 85 apples, 5 times as many as Oscar. 85 divided by 5=__
Multiplicative Comparison - ANSWER involves the comparison of 2 quantities
manipulatively, involves finding "how many times as much" of 1 quantity is
compared in another quantity, or "stretching" the original by a certain
quantity.
Whole Numbers - ANSWER The whole numbers are the
counting numbers and 0. The whole numbers are
0,1,2,3,4,5... Cannot be negative
Natural Numbers - ANSWER The counting numbers 1,2,3,4,5...
Prime Numbers - ANSWER is a whole number greater than 1 that has
exactly two
factors, 1 and
itself.
2-the only even prime
number,
3,5,7,11,13,17,19,23,31,41,43,47,53,59,61,71,73,79,
83,89,97
1 IS NOT
PRIME
Composite Number - ANSWER is a whole number greater than 1 that
has more than
two
factors
4,6,8,
9
1 IS NOT
COMPOSITE
Factor - ANSWER A factor of a number divides the number evenly.
This means the
quotient is a whole number and the
remainder is 0.
ex: 24-
>2,3,4,6,8,12
Multiples - ANSWER A multiple of a number is the product of that
number and any
FTCE ELEMENTARY EDUCATION K-6 MATH ELA S SS CORRECT 100%
, FTCE
whole
number.
ex: 3-
>6,9,12,15...
What is the smallest multiple off 12,15 and 20? -
ANSWER 60
Start with the number 20 and go out
by 10s.
Greatest Common Factor (GCF) - ANSWER the greatest factor that
two or more
numbers have in
common.
ex: 6 is the greatest common factor of 18
and 30.
Use the factor tree,
include 1
Least Common Multiple (LCM) - ANSWER The least number that is a
common multiple
of two or more
numbers.
Find the LCM of 30 and
20.
30:
30,60,90,120
20:
20,40,60,80,100,120
Rules of Divisibility - ANSWER A number is divisible by another number
if the quotient
is a counting number and the
remainder is 0.
2: The number is even.
3: The sum of the digits is divisible by 3.
5: The last digit is 0 or 5.
6: The number is even and divisible
by 3. 9: The sum of the digits is
divisible by 9.
Decimals - ANSWER Decimals are a method of writing fractional
numbers without
writing a fraction having a numerator and
denominator.
The fraction 7/10 could be written as the decimal 0.7. The period or
decimal point
indicates that this is a
decimal.
FTCE ELEMENTARY EDUCATION K-6 MATH ELA S SS CORRECT 100%
