Transcript Progression from Mental to Written Strategies

A Presentation for Parents
• To consider the skills involved in mental
calculations
• To discuss children’s expected
progression from mental to written
methods
• To consider how ICT can support
teaching and learning
• An ability to calculate mentally lies at the heart
of numeracy.
• An emphasis on mental calculation does not
mean that written methods are not taught in
the primary years but the balance between
mental and written methods, and the way in
which pupils progress from one to the other, is
very important.
• Counting of objects and mental counting
• Early stages of mental calculation and learning
of number facts, with recording
• Work with larger numbers and informal
jottings
• Expanded written methods, first with
whole numbers then with decimals
(introduced in late Year 3)
• Compact written methods (introduced in
Year 4)
• Use of calculators for more difficult
calculations (introduced in Year 5)
Children still need to practise,
and extend, mental methods even
after written methods have been
introduced.
Continued development of mental
strategies can reduce the number of
steps needed when using informal
written methods to calculate.
R
Y6
MENTAL
RECALL
MENTAL
RECALL
MENTAL
CALCULATION
MENTAL
RECALL
MENTAL
CALCULATION
MENTAL CALC.
WITH JOTTINGS
MENTAL
RECALL
MENTAL
RECALL
MENTAL
MENTAL
CALCULATION
MENTAL CALC.
WITH JOTTINGS
INFORMAL
WRITTEN
METHODS
MENTAL
RECALL
CALCULATION
MENTAL CALC.
WITH JOTTINGS
INFORMAL INFORMAL
WRITTEN
WRITTEN
METHODS METHODS
STANDARD STANDARD
WRITTEN
WRITTEN
METHODS
METHODS
CALCULATOR
• place value and partitioning;
• knowledge of number facts, such as
number bonds to 10 and 100;
• the size of numbers and where they
fit into the number system;
• the relationship between operations.
A written method needs to
be efficient in its process,
compact in its recording,
and have general
application.
Mental method using partitioning.
47 + 76 = (40 + 70) + (7 + 6)
or
47 + 76 = (47 + 70) + 6
47 + 76 = (40 + 70) + (7 + 6) = 110 + 13 = 123
4 7
+
7 6
1
1 0
1
1 3
2 3
Expanded vertical method
mirroring the mental method
Progress to expanded
vertical layout adding the
units first
+
4 7
7 6
1
3
1
1
0
1
2 3
One ‘carry’
4 7
+2 6
1 3
6 0
7 3
4 7
+
2 6
3 68
3 6
8
36 8
4 9
1
49 1
9
85 9
1 5
0
1
7 00
7 0
0
7 91
8 5
9
+4
23
7 3
11
1
80
3 6 8
+
4 2 3
+
7 9 1
1
+3
27
7 4
- 2 7
3
4 0
4
4 7
+ 40
30
3 0
7 0
7 4
+4
70
74
Show children the
vertical layout for a
calculation they can do
mentally
+2
+20
178 180
+100
200
300
3 2 6
-1 7 8
2
1 8 0
2 0
2 0 0
1 0 0
3 0 0
2 0
3 2 0
6
3 2 6
1 4 8
+20
+6
320
Show the children how
this form of recording
can help organise the
steps in subtracting
3-digit numbers.
Estimate first
326
+22
178
+126
200
3 2 6
-1 7 8
2 2
2 0 0
1 2 6
3 2 6
1 4 8
326
Reduce the number of
stages further by using
knowledge of pairs of
numbers that total 100
563 – 241 =
5 0 0
+ 6 0
+ 3
5 6 3
- 2 0 0
+ 4 0
+ 1
- 2 4 1
3 0 0
+ 2 0
+ 2
3 2 2
563 – 248 =
5 0 0
+ 6 0
+ 3
- 2 0 0
+ 4 0
+ 8
5
13
5 0 0
+ 5 0
+13
5 6 3
- 2 0 0
+ 4 0
+ 8
- 2 4 8
3 0 0
+ 1 0
+ 5
3 1 5
Mental method using partitioning
38 x 7
=
=
=
( 30x7)
21 0
266
+
+
( 8x7)
56
38 x 7
x
7
=
=
=
30
21 0
( 30x 7)
21 0
266
8
56
266
+
+
( 8x7)
56
Grid layout,
expanded working.
Note the link to
the mental method
56 x 27 =
Estimate: 60 x 30 = 1800
x
50
20 1 0 0 0
7
350
1 350
6
1 201 1 20
42
392
1 621 51 2
Extend to
bigger numbers
x
30
8
7
2 1 0
56
2 66
Vertical format,
expanded working.
Note the link to
the grid method
3 8
x
7
2 1 0
5 6
2 6 6
3 0 x
8 x
7
7
Problem:
20 cakes are to be divided between 4
people.
How many does each person get?
Problem:
21 eggs are packed in boxes of 6.
How many boxes are needed?
275 ÷ 8 =
2
1
7
8
9
5
0
5
1
-
8
1
8
3
0
5
0
5
-
3
2
3
10 
8
10 
8
10 
8

8
4
275 ÷ 8 = 34 remainder 3
34
2 7
5
2 4
0
3
5
3
2
30

8
4

8
3
34
275 ÷ 8 = 34 remainder 3
196 ÷ 6 =
6
1
1
3
9
8
2
6
0
1
1
6
2
4
R4
1 9 6
1 8 0
1 6
1 2
4
196 ÷ 6 = 32 remainder 4
30  6
2
32
 6