Written Methods for Division

Aim
To explain some of the strategies that we use to
teach +, -, x and ÷.
• Concrete/practical/objects
• Pictorial
• Abstract (‘writing it down’)
• We always try to relate calculations to real-life
and to solving problems
• Mental as well as pencil-and-paper methods
• Develop rapid, confident recall of number
facts and Times Tables
•
•
•
•
Add
Plus
More than
Count on
Addition
Laying the foundations……
•
•
•
•
•
•
Number lines
Practical equipment
Multilink cubes
Real life contexts
Number bonds
Patterns
Use of a number line
6+5=
1
2
3
4
5
6
7
8
9
10
11
12
13
Use of a 100 square
34+14 =
Partitioning……..
• Place value
• Partitioning
• Recombining
Children use their knowledge to move
towards the ‘standard’ written method:
• Continue to use partitioning
• 58 + 43
50 + 8
40 + 3
90 + 11 = 101
Column addition….
• The final step, when the children have a sound
grasp of place value & of the whole process…
364
+ 54
418
1
Subtraction
Subtraction
Taking away practically.
3-2=
Use of a number line/100 square
12-6=6
1
2
3
4
5
6
7
8
9
10
11
12
13
Written methods for Subtraction
Partitioning
Subtraction can be recorded using partitioning
to write equivalent calculations that are easier
to carry out mentally. For 74 - 28 this involves
partitioning the 28 into 20 and 8, then
subtracting 20 and 8 in turn.
74 – 28 is the same as 74 – 20 – 8
74 – 20 = 54
54 – 8 = 46
Written methods for Subtraction
Stage 4: Column method
The expanded method is eventually reduced to:
Multiplication
Multiplication- repeated addition
3x5=
(3 groups of 5)
xx
xx
x
5
xx
xx
x
+ 5
xx
xx
x
+
5= 15
Arrays
Children should be able to model a multiplication calculation using an array.
This knowledge will support with the development of the grid method.
3x5
5x3
Grid Method
Using partitioning, we can look at 8 x 13 = 104 as
8 x 10 plus 8x3:
80 + 24 = 104
Standard Written Method
Division
÷
Written methods for Division
Initially division is introduced as ‘sharing’ using real
objects or pictures.
Share 10 apples equally between
2 children which eventually
becomes 10 ÷ 2 = 5
• Remainders:
Written Methods for Division
• ‘Short’ division
Written methods for Division
Long division for HTU ÷ TU
The next step is to tackle HTU ÷ TU.
This is the 'long division' method. The 20, or 2 tens, and the 3 ones
forming the answer are recorded above the line, as in the second version.

Download Report