Transcript Maths – INSET 20th April 2009

Calculations – years 1-6
Dear Parents/Carers
Over recent months several parents have asked us to explain the way we teach calculations in maths.
In order to help you support your child we are sending out guidance which is adapted from the school
calculations policy.
This is in line with Government recommendations.
The booklet is organised into three sections:
Year 1 and 2
Year 3 and 4
Year 5 and 6
Most children will perform calculations in line with their relevant phase of learning.
Some children, however, will naturally progress more slowly or more quickly. Those
progressing more quickly will be extended onto the type of calculations shown for the
next year group when their teacher feels they are ready and vice versa.
If you require further information about typical progression in a year group this can be
found in the national guidelines website:
http://nationalstrategies.standards.dcsf.gov.uk/search/primary/results/nav:49930
Year 1 /Year 2
Addition : horizontal format e.g. 7 + 3 = 10
23 + 12 = 35
20 +10 =30
3+2=5
30 + 5 = 35
Subtraction: Horizontal format again. Children encouraged to use a number line to find the difference between
two numbers when apparatus not appropriate:
9–4=5
+1
+1
+1
+1
+1
____________________________________________________________________________________
4
5
6
7
8
9
They move onto larger numbers when ready, counting to the next multiple of 10 first. eg. 41-26
+4
+10
+1
_________________________________________________________________________________
26
30
40
10 +4 +1 = 15
41
Multiplication and division
Introduced as “groups of” (arrays) and repeated addition/subtraction.
4 groups of 2
4x2=8
Number lines are used too:
eg 3jumps of 5 to make 15.
+5
+5
3 x 5 = 15
+5
____________________________________
0
5
10
15
Division is introduced in terms of sharing and is linked very closely to the multiplication facts
the children are becoming familiar with:
8÷2=4
or on a number line:
-2
-2
8 ÷ 2 = 4 jumps
-2
-2
________________________________________________________
0
2
4
6
8
Year 3 and 4
Addition – children develop partitioning using a horizontal method in Y3/4, partitioning into
HTU
Eg 36 + 42 = 78
30 + 40 = 70
6+2=8
70 + 8 = 78
They move towards standard written methods:
39
+ 56
80
15
95
Subtraction – continue to use the number line method – counting up from the smaller
number to the larger number as well as backwards using efficient jumps:
57 – 29 = 28
+1
+10
+10
+7
_________________________________________________________________________
29
30
40
50
57
Multiplication – start with horizontal format
Eg 8 x 4 = 32
Continue to show as jumps on a number line
+4
+4
+4
+4
_____________________________________________
4 + 4 + 4 + 4 = 16
18 x 3
10 x 3 = 30
8 x 3 = 24
30 + 24 = 54
Move onto grid method:
43 x 6
240 + 18 = 258
x
6
40
240
3
18
Division – horizontal format with informal jottings:
Eg 27 divided by 3 = 9
37 divided by 6 = 6 r1
+6
+6
+6
+6
+6
+6
r1
_______________________________________________________________
0
6
12
18
24
30
36 37
Year 5 and 6
Addition – children are taught to choose an efficient method for solving their calculations:
mental, written or calculator:
Methods include partitioning and standard written methods, including carrying.
Addition of decimals – up to 2 decimal places.
When ready, the number of digits and decimal places is extended.
Eg
16 . 25
+ 25. 03
30 . 00
11 . 00
0. 20
0. 08
41 .28
2468
+ 4927
6000 (2000+4000)
1300 (400+900)
80 (60 +20)
15 (8 + 7)
7395
+
16 . 25
25 . 08
41 . 28
2468
+ 4927
7395
Subtraction
Y5 continue to use the number line method where they count up to the larger number
(this is linked to mental maths skills)
Y6 move onto standard decomposition, after the SATs
eg 376 – 149
+1
+50
+100
+76
_______________________________________________________________________
149
150
200
300
376
100 + 76 + 50 + 1 = 227
or
376 – 149 = 227
149
+1
150
+50
200
+100
300
+76
376
376
_ 149
1
50
100
76
227
(
(
(
(
50)
200)
300)
376)
Multiplication
Grid method
246 x 4 = 984
x
200
40
6
+
4
800
160
24
800
160
24
984
24 x 13
x
20
4
10
200
40
= 240
3
60
12
=
72
312
short multiplication by partitioning
24
X 13
12
60
40
200
312
x
(3x4)
(3x20)
(10x4)
(10x20)
246
4
24 (4x6)
160 (4x40)
800 (4x200)
984
The multiplication of decimals is included. The grid method is used first followed by short
multiplication partitioning.
12 . 5 x 6 = 75
x
x
10
2
0.5
6
60
12
3
60
12
3
75
Moving onto long multiplication:
124
X 16
744 (6x124)
1240 (10x124)
1984
264
x 4
1056
12 . 5
6
60 (6x10)
12 (6x2)
3 (6x0.5)
75
Division
The “chunking” method is used – “chunks” of the multiple are taken away – this
reinforces the use and application of times table facts.
125 divided by 4 = 31 r1
(10 lots of 4)
(10 lots of 4)
(10 lots of 4)
(1 lot of 4)
125
40
85
40
45
40
5
4
1
Add up how many 4s there were: 10+10+10+1 = 31 r1
The children move onto efficient chunking when ready – this is where they begin to take
away larger “chunks” of the multiple, making this method faster.
125 divided by 4 = 31 r1
(30x4)
(1x4)
31
125
120 5
4 r
1