Praxis 5025: Mathematics Questions With Complete
Solutions
5 counting principles
stable order, one to one correspondence, cardinality, abstraction, order irrelevance
one-to-one correspondence
counting and quantity principe that refers to the understanding that each object in a
group can be counted once and only once
Subitizing
ability to quickly identify a number of items in a small group without having to count
them, regardless of the arrangement of items. Example dots on a dice
conservation of numbers
a person is able to understand that the number of objects remains the same even when
rearranged
cardinality
understanding that the last number spoken in a counting sequence names the quantity
for that set
stable order
understanding the verbal sequence of counting; being able to say the number names in
sequential order
abstraction
understanding that no matter what the student is counting, how the student counts stays
the same
order irrelevance
knowledge that the order that items are counted in is irrelevant
manipulatives (physical modes)
used to represent counting, patterns, operations, physical attributes of geometric figures
and formulas
, attribute blocks
can be used for sorting, patterns and attributes of figures
base-10 blocks
can be used to teach place values, whole number operations, comparing numbers, area
and volume, etc.
bar diagram
solve for an unknown value using one of the four operations, solve word problems
counters
come in different shapes and colors (bears, bugs, chips) and are used for sorting and
counting
geoboard
pegboard grids to which students stretch rubber bands to make geometric shapes. used
to teach basic shapes, perimeter, area, etc.
fraction strips
help to show the relationship between the numerator and the denominator of a fraction
and how parts relate to the whole
snap cubes
can be used to teach number sense, basic operations, counting, patterns and place
value
tiles
can be used to teach counting, estimating, perform operations with fractions, etc.
place values in order
millions, hundred thousandths, ten thousands, thousands, hundred, tens, ones, AND,
tenths, hundredths, thousandths
expanded form
A way to write numbers that shows the place value of each digit. Example 872 in
expanded form is 800 +70+2
expanded notation
where each digit in written as a product of its place value. Example 872 in expanded
notation would be
(8 x 100) + (7 x 10) + (2 x 1)
Solutions
5 counting principles
stable order, one to one correspondence, cardinality, abstraction, order irrelevance
one-to-one correspondence
counting and quantity principe that refers to the understanding that each object in a
group can be counted once and only once
Subitizing
ability to quickly identify a number of items in a small group without having to count
them, regardless of the arrangement of items. Example dots on a dice
conservation of numbers
a person is able to understand that the number of objects remains the same even when
rearranged
cardinality
understanding that the last number spoken in a counting sequence names the quantity
for that set
stable order
understanding the verbal sequence of counting; being able to say the number names in
sequential order
abstraction
understanding that no matter what the student is counting, how the student counts stays
the same
order irrelevance
knowledge that the order that items are counted in is irrelevant
manipulatives (physical modes)
used to represent counting, patterns, operations, physical attributes of geometric figures
and formulas
, attribute blocks
can be used for sorting, patterns and attributes of figures
base-10 blocks
can be used to teach place values, whole number operations, comparing numbers, area
and volume, etc.
bar diagram
solve for an unknown value using one of the four operations, solve word problems
counters
come in different shapes and colors (bears, bugs, chips) and are used for sorting and
counting
geoboard
pegboard grids to which students stretch rubber bands to make geometric shapes. used
to teach basic shapes, perimeter, area, etc.
fraction strips
help to show the relationship between the numerator and the denominator of a fraction
and how parts relate to the whole
snap cubes
can be used to teach number sense, basic operations, counting, patterns and place
value
tiles
can be used to teach counting, estimating, perform operations with fractions, etc.
place values in order
millions, hundred thousandths, ten thousands, thousands, hundred, tens, ones, AND,
tenths, hundredths, thousandths
expanded form
A way to write numbers that shows the place value of each digit. Example 872 in
expanded form is 800 +70+2
expanded notation
where each digit in written as a product of its place value. Example 872 in expanded
notation would be
(8 x 100) + (7 x 10) + (2 x 1)
