FTCE Elementary Education K-6 – Mathematics Study
Guide with Key Concepts and Practice Questions
addition
subtraction
multiplication
division - correct answer ✔✔ Major operations on rational numbers
join
part-part-whole
separate
compare - correct answer ✔✔ Addition and Subtraction: 4 types of problems
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. - correct answer ✔✔ Join
involves removing elements
3quanities/ variations
result unknown->85-29=__?__
change unknown->85-__?__=29
start unknown->__?__-56=29 - correct answer ✔✔ Separate
,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 - correct answer ✔✔ Part-Part_Whole
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=__ - correct answer ✔✔ Compare
Equal groups or repeated addition
Area and array
Combination
Multiplicative Comparison - correct answer ✔✔ Types of problems for Multiplication/Division
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 - correct answer ✔✔ Equal groups or repeated addition
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=__ - correct answer ✔✔ Area and Array
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=__ - correct answer
✔✔ Combination
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. - correct answer ✔✔ Multiplicative Comparison
The whole numbers are the
counting numbers and 0. The whole numbers are 0,1,2,3,4,5...
Cannot be negative - correct answer ✔✔ Whole Numbers
The counting numbers 1,2,3,4,5... - correct answer ✔✔ Natural Numbers
is a whole number greater than 1 that has exactly two factors, 1 and itself.
Guide with Key Concepts and Practice Questions
addition
subtraction
multiplication
division - correct answer ✔✔ Major operations on rational numbers
join
part-part-whole
separate
compare - correct answer ✔✔ Addition and Subtraction: 4 types of problems
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. - correct answer ✔✔ Join
involves removing elements
3quanities/ variations
result unknown->85-29=__?__
change unknown->85-__?__=29
start unknown->__?__-56=29 - correct answer ✔✔ Separate
,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 - correct answer ✔✔ Part-Part_Whole
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=__ - correct answer ✔✔ Compare
Equal groups or repeated addition
Area and array
Combination
Multiplicative Comparison - correct answer ✔✔ Types of problems for Multiplication/Division
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 - correct answer ✔✔ Equal groups or repeated addition
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=__ - correct answer ✔✔ Area and Array
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=__ - correct answer
✔✔ Combination
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. - correct answer ✔✔ Multiplicative Comparison
The whole numbers are the
counting numbers and 0. The whole numbers are 0,1,2,3,4,5...
Cannot be negative - correct answer ✔✔ Whole Numbers
The counting numbers 1,2,3,4,5... - correct answer ✔✔ Natural Numbers
is a whole number greater than 1 that has exactly two factors, 1 and itself.
