Transcript The place value framework

The place value
framework
Bernard Tola
The concept of place value
Understanding the structures
that underpin the four
operations with number.
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The concept of place value
The basis of all work on:
•decimals,
•the metric system,
•money,
•standard units of length, area and volume,
•conversions between units of measurement.
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Ten as a count (PV0)
• Ten is a numerical unit constructed out of ten
ones.
• The student may know the sequence of
multiples of ten.
• The student must be able to ‘count on’ to be at
this level.
• NS1.2
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Adding with a model
• Play in groups of 4.
• Each group has a model of a two-digit number
and a pack of cards.
• Players take turns to draw two cards, make a
two-digit number and add this number to the
number represented by the model.
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Ten as a unit (PV1)
• Ten is an abstract composite, seen as
either ‘one ten’ or ‘ten ones’, as needed
• The student can increment by tens and
ones from the middle of a decade with
only one representation available.
• NS1.2
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Addition challenge
• 4 players, cards Ace to 9.
• Each player turns over two cards and makes a two-digit
number which can no longer be changed.
• Players draw two more cards in turn, make a two-digit
number and add it to the first.
• The winner is the player with the largest total smaller
than 100.
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Tens and ones (PV2)
• Students use place value to solve two-digit
addition and subtraction mentally
• Two important methods:
– Jump method
– Split method
– NS2.2
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One Thousand or Bust
• Each player has a recording sheet
• One player rolls the die. All players must place
that number in one space on the recording sheet
• When two three-digit numbers have been made,
each player subtracts them mentally
• The player with the largest number wins.
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Hundreds, tens and ones (PV3)
• Students can add and subtract three-digit
numbers mentally.
• Students use place value to partition
three-digit numbers flexibly.
• Important methods: jump, split.
• NS2.2
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Decimal place value (PV4)
• The student represents fractional parts
with an understanding of the positional
value of decimals.
• The student has a multi-unit sense of
decimals.
• NS2.4
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System place value (PV5)
• The place value system can be extended
indefinitely to the left and right of the decimal
point.
• The student can explain what happens when a
number is multiplied or divided by a given power
of ten.
• NS3.2, NS3.4
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