Addition
Addition
Children should use the most efficient method accurately and with confidence. All calculations will begin with exploration and use manipulatives (objects) and visual representations (models). Children will then develop mental methods and written methods to support their addition. It is important that children’s mental methods of calculation are practised and secured alongside their learning and use of an efficient written method for addition. We must explain that in mental calculation we always start with the biggest number.
Key Vocabulary for Addition:
more plus count on greater than more than expression equation addend first/then/now sum 
Learning Pathway for Addition:  
Recognising I need more (Augmentation Addition: adding on to a group)  Children explore through play scenarios highlighting the need for more items. E.g setting the table for a tea party and some friends come to join. Children know “I need more cups, plates etc.” Or when painting/arts & crafts, running out of items “I need more paint, stones etc” 
Adding one more to numbers 09 (Augmentation Addition: adding on to a group)  Adding one more should be approached practically through play or everyday situations. For example: I can see that you have 3 sweets. Would you like one more? How many do you have now? Encourage children to group all of the sweets together and then count the whole amount. Use a maths story to support the stem sentence, First there were 3 sweets. Then mum gave me one more. Now there are 4 sweets.

Counting all to find a total less than 10. (Aggregation addition: combining more than one group)  Children will find the total of more than one group of objects/pictures. For example they may have 4 apples and 2 oranges. Example: Pointing to red dots say “1 2 3 4” then pointing to blue dots continues to count saying “5 6 7 8 9.” Children will point to each object/picture and say the numbers one at a time. They need to understand that the last number they say is the total of the groups. (Cardinality) Encourage and model to children the stem sentence “4 plus 5 is equal to 9”

Counting on to find a total less than 10. (Augmentation Addition: adding on to a group)  Children will explore counting objects or pictures in more than one group. But now they will progress to subitising the amount in the first group and hold this amount in their head. They will begin counting the second (or more) group of objects/pictures by saying the next number. Example Child will say “ 3” then pointing to the 2nd group count saying “4, 5 there are 5 tomatoes”, Encourage and model the stem sentence “First there were 3. Then I counted on 2 more, Now there are 5. So 3 plus 2 is equal to 5”

Successive doubling of numbers 1, 2 and 4 1 doubled is 2, 2 doubled is 4 4 doubled is 8  When children have 2 groups of objects/pictures ask “what do you notice about your groups? Are they equal?” Children need to understand that when we add 2 groups that are equal this is called doubling. Explore this successive doubling pattern practically, asking the children to continue doubling the total (do not go beyond 10). Encourage the use of the word ‘double’

Aggregation addition: combining more than one group Recording addition of amounts up to 10 in an expression. (no equals symbol used, sum not calculated)  Children recognise and use the + (plus) symbol to record their addition calculations. Children now need to explore the commutative law meaning that the groups can be added in any order. Encourage children to describe their maths orally. “There are 2 red hats plus 4 blue hats.” The use of the word addend should now be introduced and used to correctly describe the groups. Can you tell me an addend in this expression?

Aggregation addition: combining more than one group Recording addition of amounts up to 10 in an equation. (The equal symbol is used and the sum recorded)  Moving on to the next stage children are encouraged to record the sum of their addends and will begin to recognise and use the = symbol. It is vital from this stage that children say “is equal to (=)” refer to the answer as the “sum” of the addends and use the word equation. Children must also now develop a secure understanding that the amounts on each side of the = symbol MUST be equal to each other. This can be explored practically by using balance scales. This provides the foundation for the children in their maths journey when they later explore missing number equations and further still in secondary school with formulaic equations.

Augmentation Addition: adding on to a group Recording addition of amounts up to 10 in an expression. (no equal symbol used, sum not calculated) Recording addition of amounts up to 10 in an equation. (The equal symbol is used and the sum recorded)  Children recognise and talk about this type of addition using “First, Then, Next.” It is helpful for children to make up stories to become familiar with this type of addition, helping them to recognise the order of the additive events. e.g 3 + 4 First there were 3 ducks in a pond. Then 4 ducks flew over and landed in the pond. Now there are 7 ducks in the pond. As in the two steps previous to this children should first record as an expression, without any emphasis or need to find the sum. Then move on to finding the sum and recording as an equation, only once the child is confident at recording an expression writing + symbol and using the stem sentence language first, then, next , identifying and using the vocabulary of addend, and plus.

Find the missing addend where the sum and one addend is known. E.g ? + 2 = 5 3 + ? = 5  Children can use 2 methods to find the missing addend. They can count on from the known addend to the sum. Or they can count back (subtract) the known addend from the sum.

Addition where the sum is less than 20.  Children now develop the key skills described above but now they will work with numbers to 20. Recording addition of amounts up to 20 in an expression. (no equal symbol used, sum not calculated) Recording addition of amounts up to 20 in an equation. (The equal symbol is used and the sum recorded) Find the missing addend where the sum and one addend is known. 
Associative Law of Addition Addition of 3 single digit addends with a sum less than 20  First the children will explore the addition of 3 addends on tens frames, using 3 different coloured counters to represent the 3 different addends. This can be practised at home easily by using 3 different coloured lego pieces, or shapes of pasta for example
Then the children will be taught to use all of their number fluency and number fact skills they have developed so far to look for patterns or relationships they know which can help them solve the 3 addend equation most efficiently. See the examples below: 
Add using bonds of 10 to cross into the next ten (sum is 11 to 20)  Children will use their number bonds of 10 facts to support efficient addition calculations when crossing into the next group of 10. At this stage in the teens numbers only. They will partition the smallest addend into 2 parts, so that one of these parts can easily be added to the first addend to make 10. Then they will add the remaining part. See examples below. This will be done practically to begin, with the children using counters and 2x tens frames and also using number lines, before the children move on to recording as in the second example. The use of number lines and tens frames supports the children in being able to visualise and use linear understanding of numbers to complete these calculations in their heads. See the 4 steps below…. 
Add multiples of 10  Children use their place value knowledge to identify how many 10’s there are in each number and then use number fluency to add the single digit amounts.
Children will also use their number facts of counting in 10’s to count on in 10’s from the largest addend, knowing how many more groups of 10 they need to count on. Example 50 + 30 = ? identify 30 is 3 more 10’s child says “60 70 80” to find sum. 
Add a single digit number to a multiple of ten  not crossing into the next ten.  Children will use their place value knowledge and to begin place value charts as shown in the second picture to add a single digit to a multiple of 10.

Add 4 addends  2 multiples of 10 and 2 single digit numbers  Children will use their knowledge of adding multiples of 10 to support this stage of learning. Children will recognise and add the multiples of 10 and then the single digit numbers, before finally adding together.

Add two 2digit numbers not crossing the ten.  Children will add two 2digit numbers where the ones do not total more than 10. They will explore this using math equipment such as diennes. The children will be taught the stem sentences below:
First I partition both numbers. Then I add the tens. Then I add the ones. Then I combine all of the tens and all of the ones 
Adding two 2digit numbers which do cross the ten  Children will now explore the addition of two 2digit numbers where the ones total more than 10. This will once again be supported initially by using tens and ones equipment, moving onto numbers lines
