mawsley primary school calculation policy addition and subtraction
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Mawsley Primary School Calculation Policy
Addition and Subtraction
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5 7
Models for addition
Adding on to a set (augmentation)
Counting on with a bead bar/number line
Combining two sets of objects (aggregation)
12
Issue:Tend to count one set, count the other and then count all.
5 6 7 8 9101112
Issue:Requires fluency with counting from any number.
12 5 0
+ 7 Issues:Bead bar is a useful bridge from cardinal to ordinal.Number line helps to stop counting all
Also:Bead bar and number line (showing 10s) encourages use of number bonds and place value for added efficiency.
10 +2+52
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Commutative Laws
The "Commutative Laws" say you can swap numbers over and still get the same answer ...
... when you add:
a + b = b + a
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Models and images
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Associative Laws
• The "Associative Laws" say that it doesn't matter how you group the numbers (i.e. which you calculate first) ...
... when you add:
(a + b) + c = a + (b + c)
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Vocabulary
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Foundation stage
• Recognise numbers 0 to 20, including Numicon.• Count beyond 10 everyday objects. • Find one more than a number• Count in ones and tens• Begin to relate addition to combining 2 groups• Count along a number line to add numbers
together• Begin to use + and = to record mental
calculations in a number sentence• Be able to calculate doubles
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Level 1
• Know by heart all pairs of numbers with a total of 10 and 20
• Know that addition can be done in any order
• Using a number line adding by counting up to the next ten then counting in ones.
• Draw own number lines to add
• Begin to partition numbers in order to add
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Level 2
• Add 2 single digits that bridge 10• Use base 10 apparatus to add two 2-digit
numbers together up to =100, exchanging ten units for a ten.
• add a number up to =50 on a number line, in jumps of 1, 5 or 10
• Adding two 2-digit numbers first without and then with bridging 10’s boundary
• Start to use partititioning
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Level 3
• Expanded method of addition
• Column method, first without and then with carrying
• Column addition to add money without carrying
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Level 4
• Continue with the strategies to add numbers up to 2 decimal places, including numbers which do not have the same number of decimal places
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Overview
Number line
Partitioning
Expanded method
Standard written method
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12
Models for subtraction
Removing items from a set (reduction or take-away)
- 1- 2- 3- 4- 5 = 7Issue:Relies on ‘counting all’, again.
Comparing two sets (comparison or difference)Issue:Useful when two numbers are ‘close together’, where ‘take-away’ image can be cumbersome
Seeing one set as partitioned
Seeing 12 as made up of 5 and 7
Issue:Helps to see the related calculations; 5+7=12, 7+5=12, 12-7 = 5 and 12-5=7 as all in the same diagram
N.B.When this is done on a bead bar, there are links with both counting back and difference on a number line
13
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Models for subtractionCounting back on a number line
Finding the difference on a number line
12 0
- 5
7
Issue:Number line helps to stop ‘counting all’.
Also:Knowledge of place value and number bonds can support more efficient calculating
12 0 5
7 Issue:Useful when two numbers are ‘close together’, use of number bonds and place value can help.
5 2 10
10 -2-3
14
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Subtraction key vocabulary
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Foundation stage
• Begin to count backwards in familiar contexts
• Continue the count back in ones from any given number
• Find one less than a number
• Count back in tens
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Level 1
• Draw on a number line to count back in ones
• Draw own number line to take away• Find the difference between 2 numbers
less than 20• Subtract single digit numbers bridging
through 10• Begin to find the difference by counting up
from the smallest.
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Level 2
• Know by heart subtraction facts for 10 and 20
• Subtract a single digit from a 2 digit number
• Begin to use partitioning
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Level 3
• Decide whether to count on or back
• Compensation method
• Take too much and add back
84 – 56
8424 28
(84 – 60) +4 = 28
-60
+4
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• Partitioning when there is an exchange:
57 – 28
50 & 7 40 & 17 50 & 7
- 20 & 8 - 20 & 8 - 20 & 8
20 & 9 20 & 9
•
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• Expanded method
500 + 30 40 + 10 + 3 - 100 + 20 + 7
400 + 10 + 6
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Level 4
• Formal column method
• Continue with the strategies to subtract numbers up to 2 decimal places, including numbers which do not have the same number of decimal places.
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Overview
Number line
Partitioning
Expanded method
Standard written method