How we teach mathematics spotlight on addition and subtraction.

Addition and subtraction progression from EYFS to Year 6

EYFS A key priority in Early Years is to ensure the children have a strong sense of number and place value. The Early Years team teach each digit (0-9) in isolation for 2 full weeks – learning everything there is to know about the digit!

EYFS + Addition Charlie has 5 apples and Lola has 3 apples. How many apples do they have altogether? 5 + 3 = Charlie Lola Charlie Lola Charlie Lola + 5

EYFS Subtraction (as take away/reduction) ? eaten apples to begin with Lola has 8 apples to begin with. She eats 3 apples. How many apples does she have left? apples to begin with ? eaten apples to begin with ? eaten

Year 1 In Year 1, children progress to addition and subtraction of one and two digit numbers up to and including 20 using much the same methods as in early years. The use of base 10, tens frames and counters and numicon enables the children to develop a deep understanding of 2 digit numbers.

Year 1 Subtraction Children in Year 1 also begin to understand subtraction as partitioning and find the difference as well as take away/reduction. Partitioning Find the difference Charlie has 8 apples. Three are green. Charlie has 8 apples. Lola has 3. The rest are red. How many are red? How many more does Charlie have than Lola? Charlie red green Lola ? ? 3 8 3

Year 1 Children also begin to learn that the equals sign means equal to or equivalent and explore the concept that both sides of the equals sign should balance by answering questions where the equals sign comes before the calculation or in-between two different calculations. 4 + 1 = 3 + 2 5 = 3 + 2 2 = 6 - ?

Year 1 Children begin to represent their understanding using their own bar or part-part-whole model which is helpful for moving on to problem solving and reasoning questions involving addition and subtraction. 12 ? ? 12 5 5 12 17 17 12 ? ?

Year 2 In Year 2, children progress to more formal written methods of addition and Subtraction as they are expected to add and subtract two 2-digit numbers. Children begin by using concrete objects to ensure a deep understanding of the method. Partitioning Through this step, children are introduced to the concept of exchanging for the first time.

Year 2 Children begin to set out their concrete objects in the same style as the formal written method of column addition. Expanded column method column method Children are also taught how to use a number line and a blank number line to solve 2 digit addition problems e.g.. 59 + 26 = or 43 + 33 = Tens Ones + +10 +6

Year 2 The progression for subtraction in Year 2 is very similar e.g. 56 – 24 = Expanded column method Column method

Year 2 As with addition, the children will come across the need to exchange in subtraction for the first time. e.g.. 52 – 18 = now we can subtract 18 Expanded column method Column method

Year 2 As in Year 2, children are encouraged to represent their understanding using their own bar or part-part-whole model which is helpful for moving on to problem solving and reasoning questions involving addition and subtraction. A missing whole = addition A missing part = subtraction 46 ? ? 46 27 27 46 73 73 46 ? ?

Year 2 Problem solving and reasoning: Have a go at drawing a bar or part-part-whole model for these Year 2 expected standard addition and subtraction questions.

Year 2 Problem solving and reasoning: Have a go at drawing a bar or part-part-whole model for these Year 2 expected standard addition and subtraction questions. 27 5 6 There are 16 cakes left.

Year 3 In Year 3, children consolidate their understanding of the column method for addition and subtraction and progress to using this method to add and subtract numbers with up to 3-digits Addition e.g.. 538 + 247 =

Year 3 Subtraction e.g.752 – 318 = Or 923 – 564 = (more than one exchange is needed)

Year 3 Children are presented with a variety of subtraction questions including some which are take away/reduction, some which are partitioning and some which are find the difference. They are taught to recognise that these are all subtraction and the column method will work for all of these types of question however they are encouraged to use the most efficient method. For some questions, where the numbers are close together, it may be more efficient to find the different using a mental method or a blank number line. Children are also taught to estimate their answer and then check it using the inverse e.g.. 253 + 127 = I know that 250 + 100 is 350 so my answer should be slightly more than 350 . 380 – 127 = 253 therefore my answer is correct.

Year 3 Problem solving and reasoning: Have a go at solving these Year 3 expected standard questions. The children are encouraged to draw a bar or part-part-whole model to help them to decide which method is required to solve the problem.

Year 3 Problem solving and reasoning: Have a go at solving these Year 3 expected standard questions. The children are encouraged to draw a bar or part-part-whole model to help them to decide which method is required to solve the problem. There are 54 chocolates left in the box Ken buys 192 chocolates altogether

Year 4 In Year 4, children consolidate their understanding of the column method for addition and subtraction and progress to using this method to add and subtract numbers with up to 4-digits. Children also begin to use this method for numbers with up to 2 decimal places. For example: And for addition problems with more than 2 numbers and numbers with different numbers of digits, for example:

Year 4 Problem solving and reasoning: Have a go at solving these Year 4 expected standard questions. The children are encouraged to draw a bar or part-part-whole model to help them to decide which method is required to solve the problem.

Year 4 Problem solving and reasoning: Have a go at solving these Year 4 expected standard questions. The children are encouraged to draw a bar or part-part-whole model to help them to decide which method is required to solve the problem. He used 43 cubes He has 24 cubes left now. The complete football kit costs £18.85

Year 5 and 6 In Years 5 and 6, children consolidate their understanding of the column method for addition and subtraction and progress to using this method to add and subtract numbers with more than 4 digits and up to 3 decimal places. Children are also expected to consolidate their understanding of addition and subtraction of more than 2 numbers and when the numbers have different numbers of digits. Additionally, children are expected to add and subtract increasingly large numbers using mental methods. The emphasis being on using the most efficient method to solve the problem.

Year 5 Problem solving and reasoning: Have a go at solving these Year 5 expected standard questions. The children are encouraged to draw a bar or part-part-whole model to help them to decide which method is required to solve the problem.

Year 5 Problem solving and reasoning: Have a go at solving these Year 5 expected standard questions. The children are encouraged to draw a bar or part-part-whole model to help them to decide which method is required to solve the problem. There were 1,048 toy cars left at the end of June. Mount Everest is 1,609m higher than the combined height of the other mountains.

Year 6 Problem solving and reasoning: Have a go at solving these Year 6 expected standard questions. The children are encouraged to draw a bar or part-part-whole model to help them to decide which method is required to solve the problem.

Year 6 Problem solving and reasoning: Have a go at solving these Year 6 expected standard questions. The children are encouraged to draw a bar or part-part-whole model to help them to decide which method is required to solve the problem. 6 5 Altogether they collect £33.75 An iced cake costs 30p