Download Written mathematical methods - multiplication and division

Multiplication
Number lines: multiplication

16 x 4 = 64
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
_________________________________________________________________
0
4
8
12 16 20 24 28 32 36 40 44 48 52 56
60 64
Using chunking to speed the process: If a child is very secure with the above method
they can then move onto using ‘chunking’ with their number lines.
16 x 4 = 64
10x4=40
6x4=24
______________________________________________
0
40
64
Grid method: short multiplication
Partition the 2 or 3 digit number and lay the calculation out in a grid form. Multiply
the sections, then add the total.
23 x 4 = 92
20
3
X 2 0 3
4 80 12
80
+ 1 2
92
Grid method: long multiplication
As for short multiplication, but partition both numbers this time.
36 x 43
30
40
6
3
X
40
3
3 0
1200
6
240
1440
90
18
108
1200
240
90
+ 1 18
1548
1548
Expanded vertical method: multiplication
Multiply the units first and layout the stages underneath each other.
23
x 4
1 2 (4 x 3)
8 0 ( 4 x 20)
9 2
Standard compact method: short and long multiplication
35 x 7 = 245
35
x 3 7
245
23 x 47 =
2 3
x 4 7
1 62 1
91 2 0
10 8 1
Division
Number line
56 ÷ 4 = 14
14x4
13x4
12x4
11x4
10x4
9x4
8x4
7x4
6x4
5x4
4x4
3x4
2x4
1x4
_________________________________________________________
0
4
8
12 16 20 24 28 32 36 40 44 48 52 56
Chunking on a number line
56 ÷ 4 = 14
10x4=40
2x4=8
2x4=8
_________________________________________________________
0
40
48
56
Vertical chunking method: short division
Make repeated subtractions of groups, using the favourite numbers as much as
possible.
219r3
4) 879
- 4 0 0 100 x 4
479
- 4 0 0 100 x 4
79
- 4 0 10 x 4
39
-20 5x4
19
- 8 2 x4
0 1 11
- 8 2x4
r3
219
Favourite numbers
1000
100
10
5
2
1
Vertical chunking method: long division
48r5
14 ) 56 7 7
-2 8 0
397
-280
1
0 1 1 7
- 70
1
34 7
-2 8
1 9
-1 4
r 5
20 X 14
20 X 14
5 x 14
2 x 14
1 x 14
48
Favourite numbers
1000
500
200
100
50
20
10
5
2
1
Standard compact method: short division
197 ÷ 7 = 28 r 1 or 28 1/7
2 8 r1
7 1 9 57