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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. 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. 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. 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. Partitioning is the breaking down of a number into several components according to its place value. E.g. 485 = 400 + 80 + 5 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. 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..\..\..\..\Desktop\Maths ITP\placevalue_pc.EXE..\..\..\..\Desktop\Maths ITP\placevalue_pc.EXE..\..\..\..\Desktop\Maths ITP\placevalue_pc.EXE

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Partitioning and doubling Why do we need to partition when 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. 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. 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 BUT of you partition it into tens and units ( 40 + 7) ( 40 + 7) Double 40 is relatively easy = 40x 2 = 80 Double 40 is relatively easy = 40x 2 = 80 Double 7 is a known double = 7 x 2 = 14 Double 7 is a known double = 7 x 2 = 14 Add these together 80 Add these together 80 +14 +14 94 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? 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. 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??????????? E.g. half of 58???????????

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

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Have a go at this calculation using your knowledge of partitioning and known halves. Have a go at this calculation using your knowledge of partitioning and known halves. Q. What is half of 38? 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. 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 ) 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 ) 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. 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 E.g. 34 30 + 4 30 = 60 = 15 30 = 60 = 15 4 = 8 = 2 4 = 8 = 2 Therefore 34 = 68 (60 + 8) = 17 (15 + 2) Therefore 34 = 68 (60 + 8) = 17 (15 + 2) Please remember to write the long date along with the title. LO: 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 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) 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) Extension: roll dice 3 times to create 3-digit numbers and find doubles/halves by partitioning into hundreds/tens/units (x 5)

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