Progression through the teaching of addition and subtraction

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1 Progression through the teaching of addition and subtraction

2 Maths has changed! The maths work your child is doing at school may look very different to the kind of sums you remember. This is because children are encouraged to work mentally, where possible, using personal jottings to help support their thinking. Formal calculations are introduced from Year 3 onwards. Children are then encouraged to use these methods for calculations they cannot solve in their heads.

3 Parents Meeting on: Progression through Calculations When faced with a problem, we want children to ask themselves. Do I need jottings? Shall I use a pencil and paper method? Can I do it in my head? Do I need to use a calculator? Lancashire Mathematics Team

4 How would you solve these calculations? = = = = 27 5 = = =

5 Laying the foundations for addition o Partitioning and subtraction o Rounding o Compensating o Counting on and back o Bridging through 10s, 100s, 1000s boundaries o Addition and subtraction facts Lancashire Mathematics Team

6 Addition + THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE. Reception and Year 1 Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures.

7 A number line is just a picture of how we work out some calculations in our heads!

8 They use number lines and practical resources to support calculation and teachers demonstrate the use of the number line = Year 1 Children then begin to use number lines to support their own calculations using a numbered line to count on in ones = Bead strings or bead bars can be used to illustrate addition including bridging through ten by counting on 2 then counting on 3.

9 Year 2 Children will begin to use empty number lines themselves starting with the larger number and counting on. First counting on in tens and ones = Then helping children to become more efficient by adding the units in one jump (by using the known fact = 7) = Followed by adding the tens in one jump and the units in one jump.

10 Your turn! =

11 Year 3 Children will continue to use empty number lines with increasingly large numbers, including compensation where appropriate. Count on from the largest number irrespective of the order of the calculation =

12 Compensation = Year Children will begin to use informal pencil and paper methods (jottings) to support, record and explain mental methods building on existing mental strategies. Stage 1: Adding the most significant digits first, then moving to adding least significant digits ( ) 200 ( ) 11 (7 + 4) 140 (60 +80) (7 + 5) 352

13 Year 3 Moving to adding the least significant digits first in preparation for carrying (7 + 4) 12 (7+5) 80 ( ) 140 (60+80) (200+0) 352

14 Your turn! = (2 + 6) ( ) 118

15

16 Year 4 Children will in Year 4 be introduced to carrying above the line Using similar methods, children will: Add several numbers with different numbers of digits; Begin to add 2 or more 3-digit sums of money, with or without adjustment from pence to pounds; Know that the decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g p

17 Year 5 Following formal addition methods with carrying above the line being introduced at Year 4, children should at Year 5, extend the carrying method to numbers with at least four digits Using similar methods, children will: Children would use rounding to estimate the answer to the calculation. So is about , which is approximately Add several numbers with different numbers of digits; Begin to add two or more decimal fractions with up to three digits and the same number of decimal points Know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g 3.2m 280cm

18 Year 6 Children should extend the carrying method to numbers with any number of digits Using similar methods, children will: Add several numbers with different numbers of digits; Begin to add two or more decimal fractions with up to four digits and either one or two decimal places; Know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g

19 Add Plus Altogether Addition Total Count on Increase Sum Make Vocabulary.

20 Subtraction - THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE. Reception and Year 1 Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures etc.

21 There are five frogs. If 2 frogs jumped into the lake how many would be left?

22 Year 1 They use number lines and practical resources to support calculation. Teachers demonstrate the use of the number line. 6 3 = The number line should also be used to show that 6-3 means the difference between 6 and 3 or the difference between 3 and 6 and how many jumps they are apart

23 Year 1 Children then begin to use numbered lines to support their own calculations - using a numbered line to count back in ones = Bead strings or bead bars can be used to illustrate subtraction including bridging through ten by counting back 3 then counting back = 8

24 Year 2 Children will begin to use empty number lines to support calculations. Counting back First counting back in tens and ones =

25 Then helping children to become more efficient by subtracting the units in one jump (by using the known fact 7 3 = 4) = Year Subtracting the tens in one jump and the units in one jump

26 Your turn! =

27 Counting on If the numbers involved in the calculation are close together or near to multiples of 10, 100 etc, it can be more efficient to count on = Year =

28 Year 3 Children continue to use empty number lines with increasingly large numbers. Children are then taught this expanded method using partitioning. 89 = = 32 Initially, the children are taught using examples that do not need the children to exchange.

29 Year 3 From this the children move to exchanging; 71 = - 46 Step 1: Step 2: = 25 This would be recorded by the children as = 25

30 Your turn! = 47

31 Year 4 Partitioning and decomposition 754 = 86 Step Step (adjust from T to U) Step (adjust from H to T) = 668

32 This would be recorded by the children as: = 668 Year 4 As decomposition this would look like this:

33 Common calculation errors!

34 Year 4 Children should: Be able to subtract numbers with different numbers of digits; Using this method, children should also begin to find the difference between 2 3-digit sums of money, with or without adjustment from the pence to pounds; Know that decimal points should line up under each other. For example: 8.95 = leading to = Alternatively, children can set the amounts to whole numbers, i.e and convert to pounds after the calculation.

35 Year 4 Where the numbers are involved in the calculation are close together or near to multiples of 10, 100 etc. counting on using a number line should be used =

36 Year 5 The teaching of subtraction continues from Year 4 where an expanded method will have been introduced. This expanded method uses partitioning Step 1: 754 = Step 2: (adjusting from T to U) Step 3: (adjusting from H to T) = This would be recorded by the children as = 468

37 Year 5 Decomposition Children would use rounding to estimate the answer to the calculation. So is about , which is approximately 500. Children should: Be able to subtract numbers with different numbers of digits Begin to find the number between two decimal fractions with up to three digits and the same number of decimal places this could be in the context of money or measures Know that decimal points should line up under each other.

38 Year 5 Where the numbers are involved in the calculation are close together or near to multiples of 10, 100 etc. counting on using a number line should be used =

39 Year 6 Decomposition Now using 4 digit numbers and beyond. Children should: be able to subtract numbers with different numbers of digits; Be able to subtract two or more decimal fractions with up to three digits and either one or two decimal places; this could be in the context of money or measures know that decimal points should line up under each other.

40 Year 6 Where the numbers are involved in the calculation are close together or near to multiples of 10, 100 etc. counting on using a number line should be used =

41

42 Subtraction Vocabulary How many are left? Take (away) Difference between How many have gone? Decrease 1 less How many fewer is... than less How many are left over? Count back

43 Key messages Children need to develop skills such as counting, partitioning and recombining numbers They need to build an awareness of the number system, value of numbers and number relationships They need to recall facts such as halving and doubling, number bonds and multiplication facts From all of these they learn to construct strategies that they can apply in many different areas. The questions at the forefront of their minds: Can I do it in my head? If not which method will help me?

44 Thank you for attending our workshop on the progression through addition and subtraction.

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