Transcript Year 1 - Simonstone St Peters CE School

Progression through
the teaching of
addition and
subtraction
Maths has changed!
The maths work your child is doing at school
may look very different to the kind of ‘sums’
you remember. This is because children are
encouraged to work mentally, where
possible, using personal jottings to help
support their thinking.
‘Formal’ calculations are introduced from Year
3 onwards. Children are then encouraged to
use these methods for calculations they
cannot solve in their heads.
Parents Meeting on:
Progression through Calculations
When faced with a problem, we want children to
ask themselves….
Do I need
jottings ?
Shall I use a
pencil and
paper method?
Can I do
it in my
head?
Do I need to
use a
calculator?
Lancashire Mathematics Team
How would you solve these calculations?
76 + 75 =
47 + 19 =
5321 – 2847 =
6003 - 5997 =
27 – 5 =
81 – 35 =
52 + 30 =
Laying the foundations for addition
and subtraction
o Partitioning
o Rounding
o Compensating
o Counting on and back
o Bridging through 10s, 100s, 1000s boundaries
o Addition and subtraction facts
Lancashire Mathematics Team
Addition +
THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE
MAJORITY OF CHILDREN TO ACHIEVE.
Reception and Year 1
Children are encouraged to
develop a mental picture of
the number system in their
heads to use for
calculation. They develop
ways of recording
calculations using pictures.
A number line is
just a ‘picture’ of
how we work out
some calculations
in our heads!
They use number lines and practical resources to support
calculation and teachers demonstrate the use of the number line.
3+2=5
+1
+1
___________________________________________
0
1
2
3
4
5
6
7
8
9
Children then begin to use number lines to support their own
calculations using a numbered line to count on in ones.
8 + 5 = 13
0
1
2
+1 +1 +1 +1 +1
3
4
5
6
7
8
9
10 11
12
13 14 15
Bead strings or bead bars can be used to illustrate addition including
bridging through ten by counting on 2 then counting on 3.
Year 1
Year 2
Children will begin to use ‘empty number lines’ themselves
starting with the larger number and counting on.
 First counting on in tens and ones.
34 + 23 = 57
+10
+10
+1 +1 +1
34
44
54 55 56 57
 Then helping children to become more efficient by adding the units in one
jump (by using the known fact 4 + 3 = 7).
34 + 23 = 57
+10
+10
+3
34
44
54
57
 Followed by adding the tens in one jump and the units in one jump.
Your turn!
64 + 25 = 89
+20
+10
64
+10
74
+5
84
89
Year 3
Children will continue to use empty number lines with
increasingly large numbers, including compensation where
appropriate.
 Count on from the largest number irrespective of the order of the
calculation.
38 + 86 = 124
+4
+30
+4
_______________________________________________
86
90
120
124
 Compensation
Year 3
+50
49 + 73 = 122
-1
73
122 123
Children will begin to use informal pencil and paper methods (jottings) to
support, record and explain mental methods building on existing mental
strategies.
Stage 1: Adding the most significant digits first, then moving to adding
least significant digits.
67
267
+ 24
+ 85
80 (60 + 20)
200 (200 + 0)
11 (7 + 4)
140 (60 +80)
91
12 (7 + 5)
352
Year 3
Moving to adding the least significant digits first in preparation for
‘carrying’.
67
+ 24
11 (7 + 4)
80 (60 + 20)
91
267
+ 85
12 (7+5)
140 (60+80)
200 (200+0)
352
Your turn!
72 + 46 =
72
+ 46
8
110
118
(2 + 6)
(70 + 40)
Year 4
Children will in Year 4 be introduced to carrying above the line.
625
+ 48
1
673
783
+ 42
367
+ 85
1
11
825
452
Using similar methods, children will:
Add several numbers with different numbers of digits;
Begin to add 2 or more 3-digit sums of money, with or without
adjustment from pence to pounds;
Know that the decimal points should line up under each other,
particularly when adding or subtracting mixed amounts, e.g
£3.59+78p
Year 5
Following formal addition methods with carrying above the line
being introduced at Year 4, children should at Year 5, extend the
carrying method to numbers with at least four digits.
587
+ 475
11
1062
3587
+ 675
111
4262
Using similar methods, children will:
Children would use
rounding to estimate
the answer to the
calculation.
So 587 + 475 is
about 600 + 500,
which is
approximately 1100.
 Add several numbers with different numbers of digits;
 Begin to add two or more decimal fractions with up to three
digits and the same number of decimal points
 Know that decimal points should line up under each other,
particularly when adding or subtracting mixed amounts, e.g 3.2m –
280cm
Year 6
Children should extend the carrying method to numbers with
any number of digits.
7648
+ 1486
111
9134
6584
+ 5848
111
12432
Using similar methods, children will:
Add several numbers with different numbers of digits;
Begin to add two or more decimal fractions with up to four
digits and either one or two decimal places;
Know that decimal points should line up under each other,
particularly when adding or subtracting mixed amounts, e.g 401.2
+ 26.85 + 0.71
Vocabulary.
•
•
•
•
•
•
•
•
•
Add
Plus
Altogether
Addition
Total
Count on
Increase
Sum
Make
Subtraction THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE
MAJORITY OF CHILDREN TO ACHIEVE.
Reception and Year 1
Children are encouraged to
develop a mental picture of
the number system in their
heads to use for calculation.
They develop ways of
recording calculations using
pictures etc.
There are five frogs. If 2 frogs jumped into
the lake how many would be left?
Year 1
They use number lines and practical resources to support calculation.
Teachers demonstrate the use of the number line.
6 – 3 = 3
-1
0
1
2
3
-1
4
-1
5
6
7
8
9
10
The number line should also be used to show that 6 - 3 means the ‘difference
between 6 and 3’ or ‘the difference between 3 and 6’ and how many jumps they
are apart.
0
1
2
3
4
5
6
7
8
9
10
Year 1
Children then begin to use numbered lines to support their own
calculations - using a numbered line to count back in ones.
13 – 5 = 8
-1 -1 -1 -1 -1
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Bead strings or bead bars can be used to illustrate subtraction including
bridging through ten by counting back 3 then counting back 2.
13 – 5 = 8
Year 2
Children will begin to use empty number lines to support calculations.
Counting back

First counting back in tens and ones.
47 – 23 = 24
-1
24
-1
25
- 10
-1
26
27
- 10
37
47

Then helping children to become more efficient by subtracting the
units in one jump (by using the known fact 7 – 3 = 4).
47 – 23 = 24
- 10
-3
24

- 10
Year 2
27
37
47
Subtracting the tens in one jump and the units in one jump.
- 20
-3
24
27
47
Your turn!
64 - 26 = 38
-20
-6
38
44
64
Counting on
If the numbers involved in the calculation are close
together or near to multiples of 10, 100 etc, it can be more
efficient to count on.
Year 2
73 – 68 = 5
+2
68
+3
70
73
82 – 47 = 35
+3
47
+ 10
50
60
+ 10
70
+ 10
80
+2
82
Year 3
Children continue to use empty number lines with increasingly
large numbers.
Children are then taught this expanded method using partitioning.
89 =
- 57
80 + 9
50 + 7
30 + 2 = 32
Initially, the children are taught using examples that do not need the children to
exchange.
Year 3
From this the children move to exchanging;
71
- 46
=
Step 1:
Step 2:
70 + 1
40 + 6
60 + 11
- 40 + 6
20 + 5 = 25
This would be recorded by the children as
60
1
70 + 1
- 40 + 6
20 + 5
= 25
Your turn!
73
- 26
60
1
70 + 3
20 + 6
40 + 7
= 47
Year 4
Partitioning and decomposition
754
86
=
Step 1
700 + 50 + 4
80 + 6
Step 2
700 + 40 + 14
80 + 6
Step 3
600 + 140 + 14 (adjust from H to T)
80 + 6
600 + 60 + 8 = 668
(adjust from T to U)
This would be recorded by the children as:
600
140 1
700+ 50 + 4
80 + 6
600 +60 +8 = 668
As decomposition this would look like this:
6 14 1
754
- 86
668
Year 4
Common calculation errors!
945
- 237
712
1 1
1
2000
- 108
902
Year 4
Children should:
• Be able to subtract numbers with different numbers of digits;
• Using this method, children should also begin to find the difference
between 2 3-digit sums of money, with or without adjustment from the
pence to pounds;
• Know that decimal points should line up under each other.
For example:
£8.95 =
- £4.38
8 + 0.9 + 0.05
4 + 0.3 + 0.08
8 + 0.8 + 0.15
4 + 0.3 + 0.08
4 + 0.5 + 0.07
leading to
81
8.95
- 4.38
= £4.57
Alternatively, children can set the amounts to whole numbers, i.e. 895 –
438 and convert to pounds after the calculation.
Year 4
Where the numbers are involved in the calculation are close
together or near to multiples of 10, 100 etc. counting on using a
number line should be used.
511 – 197 = 314
+300
+11
+3
197
200
500
511
Year 5
The teaching of subtraction continues from Year 4 where an
expanded method will have been introduced.
This expanded method uses partitioning
Step 1:
754 = 700 + 50 + 4
- 286
200 + 80 + 6
Step 2:
700 + 40 + 14 (adjusting from T to U)
- 200 + 80 + 6
Step 3:
600 + 140 + 14 (adjusting from H to T)
- 200 + 80 + 6
400 + 60 + 8 = 468
600
This would be recorded by the children as
140
700 + 50 + 4
200 + 80 + 6
400 + 60 + 8 = 468
Year 5
Decomposition
6 14 1
754
- 286
468
Children would use rounding
to estimate the answer to the
calculation.
So 754 – 286 is about 800 300, which is approximately
500.
Children should:
•Be able to subtract numbers with different numbers of digits
•Begin to find the number between two decimal fractions with up to
three digits and the same number of decimal places this could be in
the context of money or measures
•Know that decimal points should line up under each other.
Year 5
Where the numbers are involved in the calculation are close
together or near to multiples of 10, 100 etc. counting on using a
number line should be used.
1209 – 388 = 821
+ 800
+9
+12
388
400
1200
1209
Year 6
Decomposition
5 13 1
6467
- 2684
3783
Now using 4 digit
numbers and
beyond.
Children should:
•be able to subtract numbers with different numbers of digits;
•Be able to subtract two or more decimal fractions with up to three digits and either
one or two decimal places; this could be in the context of money or measures
•know that decimal points should line up under each other.
Year 6
Where the numbers are involved in the calculation are
close together or near to multiples of 10, 100 etc.
counting on using a number line should be used.
3002 -1997 = 1005
+ 1000
+2
+3
1997
2000
3000
3002
Subtraction Vocabulary
How many are left?
Take (away)
How many have gone?
Difference between
Decrease
1 less
How many fewer is ... than ...
10 less
How many are left over?
Count back
Key messages
• Children need to develop skills such as counting,
partitioning and recombining numbers
• They need to build an awareness of the number
system, value of numbers and number
relationships
• They need to recall facts such as halving and
doubling, number bonds and multiplication facts
• From all of these they learn to construct strategies
that they can apply in many different areas.
• The questions at the forefront of their minds: ‘Can
I do it in my head? If not which method will help
me?’
Thank you for
attending our workshop
on the progression
through addition and
subtraction.