Stage 6
Addition
Subtraction
+ and = signs and missing numbers
Continue using a range of equations as in
Year 1 and 2 but with appropriate numbers.
Partition into hundreds, tens, ones and
decimal fractions and recombine
Either partition both numbers and recombine
or partition the second number only e.g.
35.8 + 7.3 = 35.8 + 7 + 0.3
= 42.8 + 0.3
= 43.1
+7
35.8
This can be modelled on an empty number
line (see complementary addition below).
+0.1
+0.09
x and = signs and missing numbers
Continue using a range of equations as in
Year 2 but with appropriate numbers
Pencil and paper procedures
Grid method
X
4000
800
30
6
8
32000
6400
240
48
Division
÷ and= signs and missing numbers
Continue using a range of equations as in
Year 2 but with appropriate numbers.
Sharing and grouping
Continue to understand division as both
sharing and grouping (repeated subtraction
Pencil and paper procedures
8
0.4
0.31
+0.3
42.8
Multiplication
- and = signs and missing numbers
Continue using a range of equations as in
Year 1 and 2 but with appropriate numbers.
Find a difference by counting up
e.g. 0.5 – 0.31 = 0.19
0.5
Subtract the nearest multiple of 10, 100 or
1000, then adjust
43. Continue as in Year 2, 3, 4 and 5 but with
appropriate numbers.
Add the nearest multiple of 10, 100 or
1000, then adjust
Continue as in Year 2, 3, 4 and 5 but with
appropriate numbers including extending to
adding 0.9, 1.9, 2.9 etc
G+T
Pencil and paper procedures
Complementary addition
6467 – 2684 = 3783
+16
Pencil and paper procedures
Extend to numbers with any number of digits
and decimals with 1, 2 and 3 decimal places.
4165 + 7983 = 12,148
4165
+ 7983
12148
11
14.685 + 3.9 + 4 + 7.030 = 21.615
14.685
3.900
4.000
+ 7.030
29.615
11
2684
2700
3000
OR 6467 – 2684 = 3783
16 (2700)
300 (3000)
3467 (6467)
3783
Expanded to explain decomposition
5000
1300
300
160
6000 and400 and60 and 7
- 2000 and600 and80 and 3
3000
700
80
4
Using decomposition
6 4 6 7
- 2 6 8 3
3 7 8 4
4836
x8
48
240
6400
32000
38688
+3467
+300
14 16
Revert to expanded methods if the children
experience any difficulty.
Extend to decimals (either one or two decimal
places).
32000
6400
240
+ 48
38688
4836
X8
3868 8
8
599r4
4796
- 4 0 0 0 (500x8)
796
- 6 4 0 (80x8)
156
- 8 0 (10x8)
76
- 7 2 (9x8)
4
599r4
7 7
8
4 796
1 4 9 r 47
(7x6)
(7x40)
(7x700)
(40x6)
(40x40)
(40x700)
121
decimals
approximate first.
4.62 x 3 is about 15
4.62
x 3
13.86
1
G+T
624
6467
746
x47
42
280
4900
240
1600
28000
35062
4796
-800
3996
- 800
3196
- 800
2396
- 800
etc.
GT
746
x4 7
5222
29840
35062
49 7 3 4 8
-4900
(100x49)
2448
- 980
(20x49)
1468
- 980
(20x49)
488
- 245
(5x49)
343
- 196
(4x49)
47
decimals 87.5 - 7
7
87.5
- 70.0
1 7.5
- 1 4.0
3.5
- 3.5
0.0
(10x7)
(2x7)
(0.5x 7)
answer 12.5