Download Written Calculations Booklet Nov 2012

John of Rolleston Primary
School
Written Calculations
This document shows when the different methods of written calculation are introduced to
each year group, following guidance from the Primary Framework. However there is
flexibility in this, dependent on the needs and abilities of each child, consequently, any of
these methods could be used in any year group.
This is particularly so with the use of number lines which we positively encourage as a
preferred method of calculation. Children are able to use number lines consistently and
accurately which is vital for the consolidation of their understanding and the accuracy of
their work.
Time will also be given for more ‘compact’ or ‘traditional’ methods during Key Stage 2.
October 2012
+ Addition + + Addition + + Addition + + Addition + + Addition +
Progression
Foundation
Year 1
Written Method
Counting objects - one more etc
Practical activities
Numbers to 10
1+2=
Number line jumps to 20 – jump forward – count on
Counting objects – draw more
10 + 2 =
Year 2
+ 2 = 8 missing numbers
Use of number line and hundred square
Adding 2 digit + 1 digit numbers
26 + 6 =
Adding 3 numbers
34 + 2 + 1 =
Partitioning when adding 2 digit plus 2 digit numbers
Use of empty number line
13 + 15 = 28
10 + 3 + 10 + 5
20
8
24 + 15 = 39
+10
+5
____________________________________
24
34
39
Use of numbers up to 100
Year 3
Use of number lines
56 + 37 =
+10
+10
+10
+7
____________________________________________________
56
66
76
86
93
Horizontal partitioning
72 + 28 =
72 + 20 = 92
92 + 8 = 100
72 + 28 =
70 + 20 = 90
2 + 8 = 10
90 + 10 = 100
Use of numbers up to 1000
Year 4
Use of number lines 135 + 48 =
+20
+20
+5
+3
__________________________________________________
135
155
175
180
183
Partitioned column addition
133 + 223 =
100 + 30 + 3
200 + 20 + 3
300 + 50 + 6 = 356
Addition of decimals
Use of numbers up to 1000 and decimals to 1 decimal place
Year 5
Use of number lines 1048 + 243 =
+200
+40
+3
___________________________________________________
1048
1248
1288
1291
Horizontal partitioning
394 + 257 = 300 + 90 + 4
200 + 50 + 7
600 + 50 + 1 = 651
1
1
Column addition
23.6
+ 14.1
37.7
Use of numbers up to 10,000 and decimals to 2 decimal places
Year 6
Use of number lines 37.6 + 25.8
Horizontal partitioning
+0.4
+20.0
+5.0
+0.4
__________________________________________________
37.6
38.0
58.0
63.0
63.4
Column addition
569 . 375
+ 277 . 648
847 . 023
111 11
Use of numbers up to 100,000 and decimals to 3 decimal places
- Subtraction - - Subtraction - - Subtraction - - Subtraction - - Subtraction Progression
Foundation
Written Method
Counting objects - one less, taking away, fewer than etc
Practical activities
Numbers to 10
Year 1
Number lines to 20 – jump back , count back
Counting objects – cross off
10 – 7 =
Year 2
20 --
= 16 finding missing numbers
Use of number line and / or hundred square to count back
Use of empty number line
28 - 11 = 17
-1
-10
____________________________________
17
18
28
100 --
Year 3
= 80
taking away multiples of 10
Use of number lines counting on to find the difference
57 – 34 = 23
+6
+10
+7
________________________________________
34
40
50
57
Horizontal subtraction with partitioning
123 - 24 =
123 - 20 = 103
103 - 4 = 99
Use of numbers up to 1000
Year 4
inverse to check answers
Use of number lines counting on to find the difference
123 - 64 = 59
+6
+30
+20
+3
__________________________________________________
64
70
100
120
123
Year 5
Use of number lines counting on to find the difference
568 - 384 = 184
Horizontal subtraction with partitioning
Partitioned column subtraction
262 - 141 = 200 + 60 + 2
100 + 40 + 1
100 + 20 + 1 = 121
Use of numbers up to 10,000 and decimals to 1 decimal place
Partitioned column subtraction with exchange
224 - 147 =
+16
+100
+68
___________________________________________________
384
400
500
568
200 + 20 + 4
-- 100 + 40 + 7
0 + 70 + 7 = 77
Some column subtraction
Use of numbers up to 100,000 and decimals to 2 decimal places
Year 6
Use of number lines counting on to find the difference
23.5 - 16.4 = 7.1
+0.6
+3.0
+3.5
__________________________________________________
16 . 4
17.0
20.0
23.5
Partitioned column subtraction
268.5 - 136.3 =
200 + 60 + 8 + . 5
100 + 30 + 6 + . 3
100 + 30 + 2 + . 2 = 132.2
Column subtraction
--
2394
1234
1160
Use of numbers up to 100,000 and decimals to 3 decimal places
X Multiplication X X Multiplication X X Multiplication X
Progression
Written Method
Foundation
Oral counting in tens
10 20 30 40 50
Year 1
Counting in 10s, 2s, and 5s
Writing out tables in order 2X, 10X and 5X ( some may progress to 3X and 4X)
1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 =12 7 x 2 = 14 8 x 2 = 16
Year 2
9 x 2 = 18
10 x 2 = 20
Use of apparatus, drawings and arrays
Times tables 2X 10X 5X 3X 4X
Arrays
2 X 4
4 X 2
****
****
Finding answers
3X4=
Link to doubles
2X5=
Repeated addition 5 + 5 + 5 =
3 lots of 5 3 times 5 5 times 3
Year 3
*
*
*
*
*
*
*
*
2 digit X 1 digit
X
3
10
30
12 X 3 = 36
2
6
=
Use of number lines for repeated addition
12 X 4 =
Use of numbers up to 1000
Use of number lines for repeated addition
36 x 3 = 108
+36
+36
+36
________________________________________
0
36
72
108
Grid multiplication
2 digit X 1 digit 14 X 5 =
X
5
10
50
4
20
2 digit X 2 digit
X
10
5
10
100
50
Use of numbers up to 1000
Number lines for repeated addition
46 x 13 = 598
+ 46 X 10
+ 46 X 1
+ 46 x 1
+ 46 X 1
____________________________________________________
0
460
506
552
598
=
50 + 20 = 70
13 X 15 = 210
3
30
30
=
100 + 30 = 130
50 + 30 =
80
X
6
20
120
4
24
X
10
8
30
300
240
=
120 + 24 = 144
=
300 + 50 = 350
240 + 40 = 280
X
6
70
420
6
36
100
1000
500
=
Use of numbers up to 100,000
=
420 + 36 = 456
138 X 15 = 2070
30
300
150
8
80
40
1000 + 300 + 80 = 1380
500 + 150 + 40 = 690
=
=
Use of numbers up to 10,000
+ 12.25 x 10
+ 12.25 x 5
________________________________________
0
122.50
183.75
=
= 630
Grid multiplication
2 digit X 1 digit 76 X 6 = 456
X
10
5
Number lines for repeated addition
12.25 x 15 = 183.75
=
35 X 18 = 630
5
50
40
3 digit X 2 digit
Year 6
=
= 210
Grid multiplication
2 digit X 1 digit 24 X 6 = 144
2 digit X 2 digit
Year 5
30 + 6 = 36
5X3 3X5
+12
+12
+12
+12
_________________________________________________
0
12
24
36
48
Year 4
Grid multiplication
2070
=
Grid multiplication
Larger numbers and decimals
56.4 X 2.8 = 157 .92
X
2
0.8
50
100
40.0
6
12
4.8
0.4
0.8
0.32
=
100 + 12 +0.8 = 112.8
40 + 4.8 + 0.32 = 45.12
157.92
÷ Division ÷ ÷ Division ÷ ÷ Division ÷
Progression
Written Method
Foundation
Year 1
Year 2
Use of pictures and objects – share into equal groups - lots of …
Grouping 10 ÷ 2 =
sharing equally 6 ÷ 3 =
Find the missing number
Year 3
Use of number lines
10 ÷
= 2
- How many 3s in 30 ?
30 ÷ 3 = 10
3
3
3
3
3
3
3
3
3
3
__________________________________________________________________________________
0
3
6
9
12
15
18
21
24
27
30
Year 4
Use of number lines
- How many 6s in 36 ?
36 ÷ 6 =
6
6
6
6
6
__________________________________________________
0
6
12
18
24
30
36
Year 5
Division by 10, 100 and 1000 by moving digits (place value)
Number lines 117 ÷ 9 = 13
10 x 9
2x9
1x9
___________________________________
0
90
108
117
Year 6
Number lines
More formal method of chunking towards the end of the year. (Use of inverse – division through multiplication)
October 2012