Idea Transcript
SUBTRACTION
YR
Subtraction as ‘taking away’ from a group
Subtraction as ‘taking away’ and ‘difference’ (by counting on) Y1
O– O TO – O (bridging 10)
Rapid Recall
Recording
AGE-RELATED EXPECTATIONS Practical or recorded using ICT (eg digital photos / pictures on IWB)
Pictures / Objects
Symbols
I have five cakes. I eat two of them. How many do I have left?
Mum baked 9 biscuits. I ate 5. How many were left?
Practical or recorded using ICT
Taking away – jumps of 1 (modelled using bead strings)
Might be recorded as: 5–2=3
Counting on – jumps of 1 (modelled using bead strings)
13 – 5 = 8
11 – 8 = 3
13 – 5 =8 -2
8 -1
(see above)
-1
-1
-1
-1
8
9
10
11
12
Counting on (efficient jumps) Number line / no number line
-3
10
13
8 + 2 = 10 10 + 1 = 11
+1 +1 +1
0 1
Subtraction as inverse of addition TO – TO (bridging 10s)
Number lines – counting on
Partitioning
74 -27 = 47
74 - 27
74 -27 = 47 +3
74 – 20 = 54 54 – 4 = 50 50 – 3 = 47
+41 -8
248 89
100
141
Y4
+ 500
+ 54
754 – 100 = 654 654 – 80 = 574 574 – 6 = 568
186 200 700 Vertical number line may be used to record calculation Number lines – counting on ThHTO – HTO
72.5 – 40 = 32.5 32.5 – 5 = 27.5 27.5 – 0.7 = 26.8 45.7
Y6
Partitioning
+ 2.5
Decimals up to 2dp (72.5 – 45.7)
Consolidate / extend Y5 including: Decimal to 3 dp relating to measures
50
70
72.5
Recognise when one written method is more efficient. (See Y5 methods of recording)
Decomposition 723 – 458 = 265 [Red Alert] 700 400
20 50
70 40
2 8
200
60 40
12 8
200
20
4
Decomposition (compact method)
3 8
600 110 13 400 50 8 200 60 5 Decomposition 2362 – 548 = 1814 [Red Alert]
72.5 – 45.7 + 20
200 -
754
72.5 – 45.7 = 26.8 + 4.3
Y5
70 = 256 6 = 250 2 = 248
74
754 - 186
+14
Decimals: money (£7.85 - £3.49)
272 – 48 = 224 [Red Alert]
326
Partitioning
754 – 186 = 568
326 - 78
Vertical number line may be used to record calculation
Number lines – counting on HTO – TO HTO – HTO
Decomposition
326 256 250 256
70
Partitioning
-70
+11
Y3
Estimation and checking
326 – 78 = 248
141 - 89 = 52
+4
0 27 30 [Also jumps can be in 10s and 1s]
[Also jumps can be in 10s and 1s] Number line – counting on Number line - taking away TO – TO HTO – TO HTO – HTO
Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7= –9
10 less Number bonds, subtraction: 20, 12, 13 Number bonds, subtraction: 14, 15 Subtract 1 digit from 2 digit by bridging Partition second number, count back in 10s then 1s Subtract 10 and multiples of 10 Number bonds, subtraction: 16, 17 Subtract near multiples of 10 Difference between Number bonds, subtraction: 18, 19
Add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
13
Number lines - taking away
45 – 22 = 23
Number bonds, subtraction: 5, 6 Count back Number bonds, subtraction: 7, 8 Subtract 10. Number bonds, subtraction: 9, 10 Teens subtract 10. Difference between
2 3 4 5 6 7 8 9 10 11
+40 Y2
(see recording)
No number line: 13 – 3 = 10 10 – 2 = 8
Pictures / Symbols
1 less
[Might be recorded as: 9 – 5 = 4]
Taking away (efficient jumps)
Pictures / Symbols
With Jotting
There was 2.5 litres in the jug. Stuart drank 385 ml. How much was left? 18.07 km – 3.243 km
2000
300 500
60 40
1000
1300 500 800
50 12 40 8 10 4
1000
2 8
Decomposition (compact method)
Subtract multiples of 10 and 100 Subtract single digit by bridging through boundaries Partition second number to subtract Difference between Subtract near multiples of 10 and 100 by rounding and adjusting Difference between Subtract multiples of 10s , 100s, 1000s,tenths, Fluency of 2 digit - 2 digit including with decimals Partition second number to subtract Difference between Adjust numbers to subtract Difference between Subtract multiples of 10s , 100s, 1000s,tenths, Fluency of 2 digit - 2 digit including with decimals Partition second number to subtract Difference between Adjust numbers to subtract Difference between Subtract multiples of 10s , 100s, 1000s, tenths, hundredths Fluency of 2 digit - 2 digit including with decimals Partition second number to subtract Use number facts bridging and place value Adjust numbers to subtract Difference between
* a 2-digit number and ones * a 2-digit number and tens * 2 2-digit numbers * adding 3 1-digit number Add and subtract numbers mentally, including: * a 3-digit number and ones * a 3-digit number and tens * a 3-digit number and hundreds
Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
Add and subtract numbers mentally with increasingly large numbers
Perform mental calculations, including with mixed operations and large numbers