The place value The place value frameworkframework

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.

• NS1.2CMIT Facilitator training 2009 7

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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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