Mental and written addition and subtraction
Year 6 Autumn 6
Add or subtract mentally a near multiple of 10, 100 or 1000, or a near multiple of £1, and adjust, e.g.3127 + 4998, 5678 – 1996, £5.00 ± £2.99
Previous learning
Core for Year 6
Extension
Use, read and begin to write these words:
Use, read and write these words:
Use, read and write these words:
add, count on, sum, total, altogether,…
subtract, take away, count up, count back, how many are left,
difference between, how many more, how many less, how
many more to make? … number sentence, answer, …
add, count on, sum, total, altogether,…
subtract, take away, count up, count back, how many are left,
difference between, how many more, how many less, how
many more to make? … number sentence, answer, …
add, count on, sum, total, altogether,…
subtract, take away, count up, count back, how many are left,
difference between, how many more, how many less, how
many more to make? … number sentence, answer, …
and use the plus (+), minus (–) and equals (=) signs.
and use the plus (+), minus (–) and equals (=) signs.
and use the plus (+), minus (–) and equals (=) signs.
Add a near multiple of 100 or 10 and adjust, e.g.
Add a near multiple of 1000 and adjust, e.g.
• 465 + 503 = 465 + 500 + 3
= 965 + 3
= 968
• 3127 + 4998 = 3127 + 5000 – 2
= 8127 – 2
= 8125
• 248 + 39
Add a near multiple of £1 and adjust, e.g.
= 248 + 40 – 1
= 288 – 1
= 287
• £5.00 + £2.99 = £5 + £3 – 1p = £7.99
Subtract a near multiple of 100 or 10 and adjust, e.g.
Subtract a near multiple of 1000 and adjust, e.g.
• 678 – 199 = 678 – 200 + 1
= 478 +1
= 479
• 5678 – 1996 = 5678 – 2000 + 4
= 3678 + 4
= 3682
• 527 – 202 = 527 – 200 – 2
= 327 – 2
= 325
Subtract a near multiple of £1 and adjust, e.g.
• £5.00 – £2.99 = £5 – £3 + 1p = £2.01
© 1 | Year 6 | Autumn TS6 | Mental and written addition and subtraction
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Use strategies for adding or subtracting two-digit whole numbers and place value to add or subtract three-digit multiples of 10 and pairs of decimals
Previous learning
Core for Year 5
Extension
Add two-digit numbers mentally, e.g. 75 + 58
Use strategies for adding two-digit numbers mentally to add
pairs such as 420 + 250 or 7.4 + 2.3, e.g.
Use strategies for adding two-digit numbers mentally to add
pairs such as 0.74 + 0.23, e.g.
First work out 75 + 58 = 133,
either by counting on in 10s and 1s,
or by partitioning and recombining,
or by adding a multiple of 10 and adjusting.
First work out 75 + 58 = 133
by your preferred method.
Count on in 10s and 1s
• 75 + 58 = 75 + 50 + 8 = 125 + 8 = 133
Partition and recombine
• 75 + 58 = 70 + 50 + 5 + 8
= 120 + 13
= 133
Then use place value to derive:
Then use place value to derive:
• 0.75 + 0.58 = 1.33
• 750 + 580 = 1330
• 7.5 + 5.8 = 13.3
Add a multiple of 10 and adjust
• 75 + 58 = 75 + 60 – 2 = 135 – 2 = 133
Add near doubles, e.g.
• 25 + 26 = double 25 plus 1 = 50 + 1 = 51
Subtract two-digit numbers mentally, e.g. 75 – 38
Count back in 10s and 1s
• 75 – 38 = 75 – 30 – 8 = 45 – 8 = 37
Count up from the smaller to the larger number,
• 38 + 2 = 40, and 40 + 35 = 75, so 75 – 38 = 2 + 35 = 37
For near doubles, first work out 25 + 26 = 51.
For near doubles, first work out 25 + 26 = 51.
Then use place value to derive:
Then use place value to derive:
• 250 + 260 = 510
• 0.25 + 0.26 = 0.51
• 2.5 + 2.6 = 5.1
Use strategies for subtracting two-digit numbers to subtract
pairs such as 750 – 380 or 7.5 – 3.8, e.g.
Use strategies for subtracting two-digit numbers to subtract
pairs such as 0.75 – 0.38, e.g.
First work out 75 – 38 = 37,
either by counting back in 10s and 1s.
or by counting up from the smaller to the larger number,
or by subtracting a multiple of 10 and adjusting.
First work out 75 – 38 = 37
by your preferred method.
Then use place value to derive:
75
Then use place value to derive:
• 0.75 – 0.38 = 0.37
• 750 – 380 = 370
– 38
2
(40)
+ 35
(75)
• 7.5 – 3.8 = 3.7
37
Subtract a multiple of 10 and adjust
• 75 – 38 = 75 – 40 + 2 = 35+ 2 = 37
Approximate first before calculating
Previous learning
Core for Year 6
Extension
Use rounding to estimate results of calculations and use the
estimate to check answers, e.g.
Use rounding to estimate results of calculations and use the
estimate to check answers, e.g.
Use rounding to estimate results of calculations and use the
estimate to check answers, e.g.
• 321 + 487
Estimate: 300 + 500 = 800
• 2321 + 5487
Estimate: 2000 + 5000 = 7000
• £32.15 + £64.87
Estimate: £30 + £60 = £90
• 924 – 382
Estimate: 900 – 400 = 500
• 4724 – 2982
Estimate: 5000 – 3000 = 2000
• £50.00 – £38.82
Estimate: £50 – £40 = £10
© 2 | Year 6 | Autumn TS6 | Mental and written addition and subtraction
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Revise adding any pair of four-digit numbers using vertical addition
Previous learning
Core for Year 5
Extension
Add four-digit numbers using expanded vertical addition,
lining up equivalent units, and estimating first, e.g.
Add any pair of four-digit numbers using compact vertical
addition, with carrying figures below the total line, e.g.
Add more than two four-digit numbers, including money,
using compact addition, with carrying below the line, e.g.
• 4875 + 3359
• 4875 + 3359
• 4875 + 3359
4875
+ 3359
14
120
1100
7000
8234
Estimate: 5000 + 3000 = 8000
4875
+ 3359
8234
1 1 1..
Answer: 8234
Estimate: 5000 + 3000 = 8000
Estimate: 5000 + 3000 = 8000
£.00
48.75
21.34
+ 33.59
103.68
1 1 1..
4875
2134
+ 3359
10368
1 1 1..
Answer: 8234
Answer: 10 368
Answer: £103.68
Revise adding two numbers with the same number of decimal places using vertical addition, including amounts of money, e.g. £35.75 + £26.78
Previous learning
Core for Year 6
Extension
Add money using expanded vertical addition, lining up
equivalent units, and estimating the answer first, e.g.
Add numbers with same number of decimal places, using
compact addition, lining up units, estimating the first, e.g.
Add numbers with different numbers of decimal places using
expanded then compact vertical addition, e.g.
Money•
Money
Different numbers of decimal places
• £48.75 + £33.59
£.00
48.75
+ 33.59
0.14
1.20
11.00
70.00
82.34
Estimate: £50 + £30 = £80
• £48.75 + £33.59
£.00
48.75
+ 33.59
82.34
1 1 1..
Answer: £82.34
Estimate:£50 + £30 = £80
Answer: £82.34
One decimal place
• 17.8 + 28.6
17.8
+ 28.6
46.4
1. 1 .
Estimate: 20 + 30 = 50
• 4.76 + 13.8
4.76
+ 13.80
0.06
1.50
7.00
10.00
18.56
Answer: 18.56
Estimate: 5 + 14 = 19
4.76
+ 13.80
18.56
1.. .
Answer: 18.56
Answer: 46.4
Two decimal places
• 4.76 + 3.82
4.76
+ 3.82
8.58
1.. .
© 3 | Year 6 | Autumn TS6 | Mental and written addition and subtraction
Estimate: 5 + 4 = 9
Answer: 8.58
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Revise subtracting four digit numbers by counting up, including amounts of money, e.g. 5431 – 2789 or £35.75 – £26.78
Previous learning
Core for Year 6
Extension
Subtract four-digit numbers by counting up, drawing own
empty number line, e.g.
Subtract four-digit numbers by counting up, recording
vertically and more efficiently, e.g.
• 5431 – 2789
• 5431 – 2789
5431
– 2789
+11
2789
+200
2800
+2431
3000
211
(3000)
+ 2431
(5431)
5431
2642
Answer: 2642
Begin to record the steps vertically, e.g.
• £35.75 – £26.78
5431
– 2789
£.00
11
(2800)
35.75
200
(3000)
–26.78
+ 2431
(5431)
3.22
(£30.00)
+ 5.75
(£35.75)
2642
Answer: 2642
8.97
Answer: £8.97
Subtract three-digit then four-digit whole numbers using decomposition
Previous learning
Core for Year 6
Extension
Subtract three-digit numbers by decomposition, first
expanded and then compact, e.g.
Subtract four-digit numbers by decomposition, first expanded
and then compact, e.g.
Subtract four-digit numbers using a fully compact
decomposition method, e.g.
• 751 – 286
Estimate: 800 – 300 = 500
• 3754 – 1286
Estimate: 4000 – 1000 = 3000
• 751 – 286
Estimate: 800 – 300 = 500
Expanded
Compact
Expanded
751
– 286
3751 = 3000 + 700 + 50 + 1
– 1286 = 1000 + 200 + 80 + 6
37 5 1
– 12 8 6
= 700 + 40 +11
– 200 + 80 + 6
= 7 411
– 286
= 3000 + 700 + 40 +11
– 1000 + 200 + 80 + 6
= 3 7 411
– 12 8 6
1
1
= 600 + 40 + 1
– 200 + 80 + 6
1 1
= 641
– 286
1
1
= 3000 + 600 + 40 + 1
– 1000 + 200 + 80 + 6
1 1
= 36 4 1
– 12 8 6
= 400 + 60 + 5
= 465
= 2000 + 400 + 60 + 5
= 24 6 5
Answer: 465
Answer: 465
© 4 | Year 6 | Autumn TS6 | Mental and written addition and subtraction
Answer: 2465
Fully compact
Compact
751 = 700 + 50 + 1
– 286
200 + 80 + 6
Answer: 2468
6467 – 2684
Estimate: 6000 – 3000 = 3000
Answer: 465
Answer: 3783
Extend to money and to decimals, first with the same number
of decimal places, then with different numbers of decimal
places.
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Subtract numbers with the same number of decimal places by counting up, including amounts of money, e.g. 25.3 – 15.7, 5.24 – 2.76, £50.00 – £26.78
Previous learning
Core for Year 5
Extension
Subtract decimals with the same number of decimal places
by counting up from the smaller to the larger number, e.g.
Subtract decimals with the same number of decimal places
by counting up from the smaller to the larger number, e.g.
Subtract decimals with different numbers of decimal places
by counting up from the smaller number, e.g.
One decimal place
One decimal place
Two subtract one decimal places
• 25.3 – 15.7
• 25.3 – 15.7
• 5.24 – 3.7
Record the steps vertically:
25.3
– 15.7
+0.3
+4
15.7
16
+5.3
20
0.3
25.3
Answer: 9.6
(16)
4.0
(20)
+ 5.3
(25.3)
Record the steps vertically, filling trailing empty decimal
places with zeroes:
5.24
– 3.70
9.6
Answer: 9.6
0.30
(4)
+ 1.24
(5.24)
1.54
Answer: 1.54
Two decimal places
Two decimal places
One subtract two decimal places
• 5.24 – 2.76
• 5.24 – 2.76
• 9.4 – 5.78
5.24
– 2.76
0.04
+0.04
2.76
+0.2
2.8
+2.24
3
5.24
Answer: 2.48
(2.8)
0.20
(3)
+ 2.24
(5.24)
2.48
Record the steps vertically, filling trailing empty decimal
places with zeroes:
9.40
Answer: 2.48
– 5.78
0.02
(5.8)
0.20
(6)
+ 3.40
(9.4)
3.62
Answer: 3.62
© 5 | Year 6 | Autumn TS6 | Mental and written addition and subtraction
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 5
Money
Money
• £50.00 – £27.89
• £50.00 – £26.78
Extension
Record the steps vertically.
Count up from £27.89, using two or three steps.
£0.00
50.00
– 26.78
11p
£27.89
£22
£28
£50
Answer: £22.11
0.22
(£27)
+ £23.00
(£50)
£23.22
Answer: £23.22
Choose an efficient method to subtract for a variety of calculations, such as 5412 – 3006, 1524 – 320 or 1524 – 978
Previous learning
Core for Year 5
Extension
When solving word problems, write down the subtraction
calculation resulting from problems involving a range of
subtraction contexts:
When solving word problems, write down the subtraction
calculation resulting from problems involving a range of
subtraction contexts:
When solving word problems, write down the subtraction
calculation resulting from problems involving a range of
subtraction contexts.
• taking away from a quantity to find how many are left, e.g.
• taking away to find how many are left;
5412 people want to buy tickets for a concert.
There are only 3006 tickets for sale.
How many people will not be able to buy a ticket?
• comparing two quantities, to find how many more or how
many less one quantity is than another, or to find the
difference between them, e.g.
• making a comparison:
– finding how many more or how much more A is than B;
– finding how many fewer or how much less A is than B;
– finding a difference between A and B;
• complementary addition to find how many more or how
much more to make a given number or quantity.
A red string is 1524 cm long. A blue string is 320 cm long.
How much longer is the red string than the blue string?
How much shorter is the blue string than the red string?
What is the difference between the lengths of the strings?
• complementary addition to find how many more or how
much more to make up a given number or quantity, e.g.
Sarah has £9.78 in her purse. She wants to buy a T-shirt
that costs £15.24. How much more money does she need?
© 6 | Year 6 | Autumn TS6 | Mental and written addition and subtraction
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Choose mental, written or calculator methods to work out addition and subtraction calculations
Previous learning
Core for Year 6
Extension
Understand that once you have decided on the calculation to
do it can be worked out by any efficient method.
Understand that once you have decided on the calculation to
do it can be worked out by any efficient method.
Understand that once you have decided on the calculation to
do it can be worked out by any efficient method.
When working without a calculator, decide how to work out
calculations such as:
When working without a calculator, decide how to work out
calculations such as:
When working without a calculator, decide how to work out
calculations such as:
423 + 268
423 + 205
4123 + 210
3278 + 2995
3278 – 247
3278 + 3020
• 52.85 + 143.6
4672 + 3275
£34.27 – £12.99
£15.38 + £27.67
278 + 2456
1524 – 320
£25.99 + £17.99
• 15.05 – 14.84
1524 – 1203
1524 – 320
1524 – 978
1524 – 978
3997 + 2456
5412 – 3006
When calculators are available, choose to use a calculator,
or a written or mental method to solve problems such as:
When calculators are available, choose to use a calculator,
or a written or mental method to solve problems such as:
When calculators are available, choose to use a calculator,
or a written or mental method to solve problems such as:
• Calculate 1202 + 45 + 367.
• Rachel flies 4227 miles from London to Atlanta.
She flies a further 946 miles to New Orleans.
How far does she travel altogether?
• A drink and a box of popcorn together cost 90p.
2 drinks and a box of popcorn together costs £1.45. What
does a box of popcorn cost?
• Mandy is saving for a car that costs £8765.
She has already saved £4927.
How much more does she have to save?
• Write in the missing number.
• Ryan buys some sunglasses for £4.69 and a sun hat for
£3.29. What is the total cost?
• Charles is driving 1454 km from Paris to Lisbon.
He has already driven 1086 km.
How much further does he have to drive?
© 7 | Year 6 | Autumn TS6 | Mental and written addition and subtraction
100 – (22.75 + 19.08) = F
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999