Formal Written Methods of Calculation - Policy Statement
It is the policy of Dovedale Primary School that no formal written methods be taught to children until the beginning of Y4.
Written calculations will follow in the following progression. Average children will work at age appropriate levels (see section 6 of the NNS) Children with SEN and higher attainers will work at the appropriate stage for their ability.
If at any time a child is failing with one strategy they will be directed to return to a method which may not be as compact but which is reliable for that child.
Children will be encouraged to estimate, calculate and check for accuracy.
Addition (NNS Section 6 pages 48, 49)
Children will always be presented with written calculations in horizontal form to enable them to choose a mental method if appropriate, particularly the use of informal jottings and a number line.
45+23=
+20 +3
45 65 68
Children will be taught to write more complicated addition calculations in vertical form and at this point to add the most significant digits
256
+ 385
500
130
1 1
64 1
(Children to add using a mental method 500+130+11)
Children will move to adding the least significant digits in preparation for carrying.
256
+ 385
11
130
500
641
(Children to add using a mental method 500+130+11)
Children will progress to a compact method of addition:
147
+ 389
536
1 1
This will be extended to four digit numbers, numbers with any number of digits and decimals
Subtraction (NNS section 6 pages 50,51)
Children will be reminded of how to subtract by using a mental method including a number line and will use these methods where appropriate:
+4 +20 +4
56 60 80 84
Children will do this first not crossing the tens or hundreds boundary, then crossing either the tens or the hundreds boundary.
This will be extended to decimal numbers and problem solving situations.
The compact written form will be taught to more able Y6 children. When moving to the compact written form, the expanded method will be shown alongside to aid understanding if necessary e.g. 754 - 86
700 + 50 + 4
- 80 + 6
4 1
700 + 40 +14 754
- 80 + 6 86
6 14 1
600 + 140 + 14 754
80 + 6 86
600 + 60 + 8 668
Multiplication (NNS Section 5 p47, Section 6 pages 66,67)
Informal methods of multiplication including:
- repeated addition
- describing arrays
- scaling
will be taught to lay the foundations for more formal written methods
Children will be taught both the grid method of multiplication and short multiplication by single digit numbers:
20 3
|
8 |
160 |
24 |
184 |
Like addition, calculations will be presented in a horizontal format and children will be encouraged to make an estimate.
For more able children, when moving to short multiplication, children will be taught to consider the least significant digit is first:
23 23 2.3
x 7 leading to x7 extending to x7
21 161 16.1
140 ˛ ˛
161
Division (NNS section 6 pages 68,69)
Children in Y4,Y5,Y6 will be taught to think of division as grouping rather than sharing 12÷4= as 12 grouped in 4s or as the inverse of 4x3=12
When introduced to division the teacher will use concrete apparatus to group a large number (eg 100) of objects in 7s to give children a mental model for their ‘chunking’
__ ____ ____
9( 97 6)196 6)196
- 90 (10 x 9) leading to - 60 (10 x 6) contracting to - 120 (20 x 6)
7 136 76 (10 x 6)
- 60 (10 x 6) - 60 (10 x 6)
10 r 7 76 16
- 60 (10 x 6) - 12 (2 x 6)
16 4
- 12 (2 x 6)
4 32 r 4
32 r 4
Children will be taught to estimate and these estimates will aid the chunking.
There is recognition that some children will need help with subtraction when dividing in this way.
The traditional methods of short and long division will be taught to able Y6 children.