Addition and Subtraction

Combining two sets of objects (aggregation)
7
Issue:
Tend to count one set, count the other and then count all.
Adding on to a set (augmentation)
Issue:
Requires fluency with counting from any number.
Counting on with a bead bar/number line
+ 7
0 5
+5
10
+2
12

The "Commutative Laws" say you can swap numbers over and still get the same answer ...
... when you add : a + b = b + a

• 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)

• 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

• 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

• 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

• Expanded method of addition
• Column method, first without and then with carrying
• Column addition to add money without carrying

• Continue with the strategies to add numbers up to 2 decimal places, including numbers which do not have the same number of decimal places

Number line
Partitioning
Expanded method
Standard written method

Removing items from a set (reduction or take-away)
N.B.
12 Relies on ‘counting all ’, again.
a number line
Comparing two sets (comparison or difference)
Seeing one set as partitioned
Issue:
Useful when two numbers are ‘close together’, where
‘take-away’ image can be cumbersome
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 13

Counting back on a number line
0 7
-3
- 5
10 -2
12
Also:
Issue:
Knowledge of place value
Number line helps to support more efficient calculating
Finding the difference on a number line
0 5 5
7
10 2 12
Issue:
Useful when two numbers are ‘close together’, use of number bonds and place value can help.
14

• 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

• 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.

• Know by heart subtraction facts for 10 and
20
• Subtract a single digit from a 2 digit number
• Begin to use partitioning

• Decide whether to count on or back
• Compensation method
• Take too much and add back
-60
84 – 56
+4
24
28
(84 – 60) +4 = 28
84

• Partitioning when there is an exchange:
57 – 28
50 & 7 40 & 17 50 & 7
•
- 20 & 8 - 20 & 8 - 20 & 8
20 & 9 20 & 9

• Expanded method
500 + 30 40 + 10 + 3
- 100 + 20 + 7
400 + 10 + 6

• 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.

Number line
Partitioning
Expanded method
Standard written method