Learning objective:

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Learning objective To be able to use
partitioning to double or halve numbers.
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Place value

• Numbers are categorised as being either
  units/ones, tens, hundreds or thousands etc.
• The position of the digit within an number shows
  its value according to its place.
• In whole numbers the number on the far right is
  always the units/ones column, next on the left
  comes the tens, then the thousands etc.

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Th H T U
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Partitioning

• Partitioning is the breaking down of a number
  into several components according to its place
  value.
• E.g. 485 400 80 5
• The zeros represent a place holder of the other
  digits ( e.g. tens and units) and without them
  the number would simply look like a single unit
  of 4.
• ..\..\..\..\Desktop\Maths ITP\placevalue_pc.EXE

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Partitioning and doubling

• Why do we need to partition when doubling?
• By partitioning a number we can use known doubles
  of smaller numbers and then add these together to
  calculate the answer.
• E.g. double 47 is not a double that most people
  know of by heart.

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• BUT of you partition it into tens and units
  
• ( 40 7)
• Double 40 is relatively easy 40x 2 80
• Double 7 is a known double 7 x 2 14
• Add these together ? 80
• 14
• 94

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• Have a go at this calculation using your
  knowledge of partitioning and known doubles.
• Q. What is double 67?

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Partitioning and halving

• Why do we need to partition when halving?
• By partitioning a number we can use known halves
  of smaller numbers and then add these together to
  calculate the answer.
• E.g. half of 58???????????

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• Partition 58 into tens and units
• (50 8)
• Half of 50 25 ( ½ or divide by 2)
• Half of 8 4
• Add these together ? 25
• 4
• 29

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• Have a go at this calculation using your
  knowledge of partitioning and known halves.
• Q. What is half of 38?

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• Remember ? if the number you are halving is an
  even number it will always halve exactly.
• Whereas if the number is an odd number the answer
  will always have the fraction of a half in it (
  e.g. half of 13 6 ½ )
• The easiest way to halve odd numbers is to half
  the even number just before it and then add on a
  half to that number (e.g. 13 ? half of 12 is 6
  ½ 6 ½ )

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• Well done you can now partition numbers to find
  doubles and halves!
• ?

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• Main activity
• With your partner, roll 2 dice to find 2-digit
  numbers. Then partition them into tens/units and
  find the doubles/halves and record in your
  exercise books.
• E.g. 34 ? 30 4
• 30 60 15
• 4 8 2
• Therefore 34 68 (60 8) 17 (15 2)
• Please remember to write the long date along with
  the title. LO To be able to use partitioning to
  double or halve numbers.
• Year 3s to work on numbers between 1-50 first (x
  10) then go onto numbers 50-100. ( x 5)
• Year 4s to work on numbers between 1-100. (x 10)
• Extension roll dice 3 times to create 3-digit
  numbers and find doubles/halves by partitioning
  into hundreds/tens/units (x 5)