FTCE Elementary
Education K-6
Math/ELA/Science/Social
Studies 2026 | Study
Guide, Practice Questions,
Answers, Rationales &
Exam Review | Complete
Ethics Study Guide
Updated 2026 Questions and Answers
100% Verified Exam Prep and Comprehensive
Rationales
Included
,Major operations on rational numbers addition
subtraction
multiplication
division
Addition and Subtraction: 4 types of problems join
part-part-whole
separate
compare
Join 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 involves removing elements
3quanities/ variations
result unknown->85-29=__?__
change unknown->85-__?__=29
start unknown->__?__-56=29
Part-Part_Whole 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 involves no action, but involve comparision between 2 different sets- how much or
how much less is one/than another.
Variation:
Difference unknown: 56+__=85 or 85-56=__
Larger unknown: 56+29=__
Smaller unknown: 29+__=85 or 85-29=__
Types of problems for Multiplication/Division Equal groups or repeated addition
Area and array
Combination
Multiplicative Comparison
Equal groups or repeated addition 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 involve finding the area of a rectangular area or arrangement.
5 rows of 17 apple trees
ex:Multiplication->5x17=__
85 palm trees/5rows
Division->85 divided by 5=__
Combination Involve different combinations that can be made from two sets.
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 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 The whole numbers are the
counting numbers and 0. The whole numbers are 0,1,2,3,4,5...
Cannot be negative
Natural Numbers The counting numbers 1,2,3,4,5...
Prime Numbers 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 is a whole number greater than 1 that has more than two factors
4,6,8,9
1 IS NOT COMPOSITE
Factor 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 A multiple of a number is the product of that number and any whole number.
ex: 3->6,9,12,15...
What is the smallest multiple off 12,15 and 20? 60
Start with the number 20 and go out by 10s.
, Greatest Common Factor (GCF) 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) 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 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 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.
Fractions A fraction is part of an entire object.
ex: 1/5,3/7,12/50
1=Numerator
_
5=Denominator
parts of integers and therefore fit between then, when comparing size.
In order to compare fractions, their DENOMINATORS must be equal.
Integers are also called whole numbers negative whole numbers and zero.
ex: 560,-35,2,0,-197744
Percents The best way to compare a percent to other number expression is either to
_convert it to a decimal and leave it as that.
_convert it to a fraction (depending on how the other numbers are expressed)
ex: 76%->move 2 decimal places to the left .76.
ex: .76-> 76/100->can be simplified to 16/25
Exponents how many times a base number is used.
to compare number with exponents it is best to multiply them out or estimate what
they might be.
ex: 22=4, if you had 2-2 the answer would be 1/4 or (1 over 2*2)
ex: when you have a number that is being raised to zero it always equals 1.
(195*0=1)
Education K-6
Math/ELA/Science/Social
Studies 2026 | Study
Guide, Practice Questions,
Answers, Rationales &
Exam Review | Complete
Ethics Study Guide
Updated 2026 Questions and Answers
100% Verified Exam Prep and Comprehensive
Rationales
Included
,Major operations on rational numbers addition
subtraction
multiplication
division
Addition and Subtraction: 4 types of problems join
part-part-whole
separate
compare
Join 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 involves removing elements
3quanities/ variations
result unknown->85-29=__?__
change unknown->85-__?__=29
start unknown->__?__-56=29
Part-Part_Whole 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 involves no action, but involve comparision between 2 different sets- how much or
how much less is one/than another.
Variation:
Difference unknown: 56+__=85 or 85-56=__
Larger unknown: 56+29=__
Smaller unknown: 29+__=85 or 85-29=__
Types of problems for Multiplication/Division Equal groups or repeated addition
Area and array
Combination
Multiplicative Comparison
Equal groups or repeated addition 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 involve finding the area of a rectangular area or arrangement.
5 rows of 17 apple trees
ex:Multiplication->5x17=__
85 palm trees/5rows
Division->85 divided by 5=__
Combination Involve different combinations that can be made from two sets.
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 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 The whole numbers are the
counting numbers and 0. The whole numbers are 0,1,2,3,4,5...
Cannot be negative
Natural Numbers The counting numbers 1,2,3,4,5...
Prime Numbers 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 is a whole number greater than 1 that has more than two factors
4,6,8,9
1 IS NOT COMPOSITE
Factor 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 A multiple of a number is the product of that number and any whole number.
ex: 3->6,9,12,15...
What is the smallest multiple off 12,15 and 20? 60
Start with the number 20 and go out by 10s.
, Greatest Common Factor (GCF) 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) 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 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 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.
Fractions A fraction is part of an entire object.
ex: 1/5,3/7,12/50
1=Numerator
_
5=Denominator
parts of integers and therefore fit between then, when comparing size.
In order to compare fractions, their DENOMINATORS must be equal.
Integers are also called whole numbers negative whole numbers and zero.
ex: 560,-35,2,0,-197744
Percents The best way to compare a percent to other number expression is either to
_convert it to a decimal and leave it as that.
_convert it to a fraction (depending on how the other numbers are expressed)
ex: 76%->move 2 decimal places to the left .76.
ex: .76-> 76/100->can be simplified to 16/25
Exponents how many times a base number is used.
to compare number with exponents it is best to multiply them out or estimate what
they might be.
ex: 22=4, if you had 2-2 the answer would be 1/4 or (1 over 2*2)
ex: when you have a number that is being raised to zero it always equals 1.
(195*0=1)
