Introduction to Tens and Ones
Place Value Manipulatives
Understanding Manipulatives:
There are many different manipulatives (concrete materials) that can be used to show place value.
Each one of these has its own unique properties that help students understand the grouping of ten
ones into one ten.
The table below shows manipulates in the order in which they should be introduced, from the easiest
to the most advanced.
Manipulatives
Tens
Ones
Properties
easily counted and manipulated by young
children
• individual cubes join together to make a ten
stick (use single shade per stick of ten so that
the whole stick is easily recognised)
• can be separated easily
• can be used on a ten frame to show tens and
ones
•
Unifix cubes
students should already be familiar with ten
frames for showing numbers to 20
• printed ten frames showing 10 can be used to
reduce the need for lots of counters
• the best resource for helping children
recognize numbers without counting
•
ten frames
individual sticks join together to make a ten
bundle with a rubber band
• can be separated and re-bundled easily
• ten bundles of ten can be joined later to make
a hundred
•
bundling sticks
ten blocks are easily manipulated and always
show groups of exactly 10
• need to exchange or trade 10 ones for 1 ten
(higher level of understanding required)
• can later show large numbers easily and
quickly showing into the hundreds and
thousands with consistent representations
•
base ten blocks
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Manipulatives
Tens
Ones
sets of objects
• marbles
Properties
•
•
•
pencils
•
gum
•
•
•
Virtual
Manipulatives
Software
•
Tens
Ones
clearly displays groups of 10
individual objects making up a
larger group that can be handled
both as one group and a set of 10
individual ones
can be separated and regrouped
easily
real objects from everyday life
helps students see the
commonality of grouping and
handling groups
larger numbers may be shown
later, but are less easily recognised
N.B. make sure the group does
have 10 and not 8 or 12 as is
common for some items
Properties
represent physical manipulates on
screen
• can show numbers accurately and
quickly (no accidental dropped
counters or cubes, or bundles with
only 9 in them)
•
Ten Frames
should be used after students are
familiar with the concepts and if
possible handling the actual item
• allow students to self correct as the
screen can display more
information such as the numeral
and the written NAME
• allows for whole class seeing
exactly the same number
•
allows for counting quickly and
accurately
• allows for counting in 2s and 5s
• can extend well beyond tens and
ones to millions
•
•
Odometer
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Introduction to Hundreds Tens and Ones
Place Value Manipulatives
Using manipulatives to represent 3-digit numbers:
The different manipulatives (concrete materials) that can be used to show place value have their
own unique properties.
The table below shows manipulates which can be extended into the hundred and beyond.
As the place value increases so does the difficulty in representing them. Larger numbers are
inherently harder to conceptualize so their use is critical in developing mathematical understanding.
Manipulatives
Hundreds
Tens
Ones
Properties
individual sticks join together to
make a ten bundle with a rubber
band
• can be separated and bundled
easily
• 10 sets of ten can be joined
again to make a hundred
• class can join together 10
hundreds to make a thousand
(use hair ties or scrunchies)
•
bundling sticks
groups of ten and hundred are
easily manipulated (do not break
apart)
• need to exchange or trade 10
ones for 1 ten and 10 tens to
make 1 hundred (higher level of
understanding required) can
show large numbers easily and
quickly
• shows places into the hundreds
and thousands with consistent
•
base ten blocks
•
•
abacus
•
•
•
the abacus is the most abstract
representation for base ten
numbers; beads do not show
the value of different places
beads are not easily dropped or
lost
large numbers may be
represented and manipulated
quickly and easily
some abacuses allow for trading
or exchanging of 10 ones for 1
ten
later the abacus can be used to
display decimal fractions
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Manipulatives
Hundreds
Tens
Ones
sets of objects
• marbles
Properties
•
•
•
pencils
•
•
•
•
gum
Virtual
Manipulatives
Software
• Odometer
Hundreds
Tens
Ones
real objects from everyday life
helps students see the
commonality of grouping and
handling groups
individual items join together to
make a ten group then a hundred
that can be handled both
individually or as a set of 10 ones
or 10 tens
can be separated and ungrouped
for demonstration
larger numbers can be shown
and can be easily recognised as
such
N.B. make sure the group does
have 10 and not 8 or 12 as is
common for some items: also
check the package/box does
contain 10 tens or 100
Properties
•
•
•
•
•
•
•
•
represent physical manipulates
on screen
should be used after students are
familiar with the concepts and if
possible the actual item
can show numbers accurately
and quickly (no accidental
dropped counters or cubes, or
bundles with only 9 in them)
allow students to self correct as
the screen displays the correct
number
allows for whole class seeing
exactly the same number
allows for counting quickly and
accurately (no errors)
allows for counting in 2s and 5s
in any place
can extend well beyond
hundreds, tens and ones to
millions and even decimal places
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