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

1. Learning objective: To be able to use partitioning to double or halve numbers.

2. 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.

3. Th H T U

4. 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

5. 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.

6. 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

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

9. 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???????????

10. 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

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

13. 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 )

14. Well done you can now partition numbers to find doubles and halves! ☺

15. 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 3’s to work on numbers between 1-50 first (x 10) then go onto numbers 50-100. ( x 5) • Year 4’s 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)