 # Progression in written calculations Tuesday 20 th October.

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Progression in written calculations Tuesday 20 th October

Addition Practical activities and discussions Finding one more than a number from 1 – 10 Using vocabulary associated with addition Use of a number line Begin to use the + and = sign to record mental calculations Know by heart all number bonds to 10 and within 10 Use knowledge to know that addition can be done in any order to do mental calculations more efficiently

Addition Adding 3 single digit number mentally Know by heart all number bonds to 20 and within 20 Use + and = to record mental calculations use a number line to make informal calculations Use a number line to make informal jottings Use partitioning to reflect mental methods 45 +78 = 40 + 70 + 5 + 8

Addition Vertical format least significant digit first extended to bigger numbers 368 + 493 11 150 700 861 Use of a number line to check

Addition Compact layout, starting to involve carrying 546 472 + 253 +372 799 844 1 Extending to decimals Compact addition using carrying for Th, H, T, U and decimals

Subtraction Practical activities and discussions Finding one less than a number from 1 – 10 Begin to relate subtraction to ‘taking away’ Use a number line to count on and back Begin to understand that subtraction is ‘finding the difference’ Begin to use the – and = sign to record mental calculation Know by heart all subtraction facts to 10

Subtraction Know by heart all subtraction facts to 20 Partition numbers (no crossing boundaries) Use informal pencil and paper methods (jottings) Use a number line to record complementary addition eg 84 – 56 = +4 +20 +4 ---------------------------------------------- 56 60 80 84

Subtraction Vertical expanded method 563 – 241 = 500 + 60 + 3 - 200 + 40 + 1 300 + 20 + 2 373 – 125 = 60 13 300 + 70 + 3 - 100 + 20 + 5 200 + 40 + 8 Use of a number line to check

Subtraction Compact method – decomposition including larger numbers and decimals 6695 2584 - 4111 6 8 7293 3426 - 3867

Multiplication Practical activities to gain experience of doubling Become familiar with appropriate language Use of arrays Know by heart addition doubles to at least 10 Know by heart x2, x10 multiplication facts

Multiplication Understand multiplication as repeated addition Know by heart multiplication facts up to x10 Use a number line to show repeated addition

Multiplication Mental methods using partitioning 38 x 7 = ( 30 x 7 ) + ( 8 x 7 ) = 210 + 56 = 266 Introduce the grid method 38 x 7 = 266 308Total 721056266

Multiplication Extend the grid method to larger numbers 56 x 27 = 506Total 2010001201120 735042392 1512

Multiplication Extend the grid method to even larger numbers and decimals 23.5 x 12 = Compact vertical multiplication 38 x 7 266 2030.5Total 10200305235 2406147 282

Division Practical activities to gain experience of sharing and to become familiar with the appropriate language Understand division as grouping, repeated subtraction or sharing and record informally including calculations with remainder eg How many 4s in 12? How many are left over if I share 13 between 4?

Division Use practical informal methods to divide 2 digit numbers. Round remainders up and down eg 14 ÷ 4 = ---------------------------------------------- 0 4 8 12 14

Division Develop and refine written method eg 98 ÷ 6 = 10 x 6 6 x 6 r2 or 1/3 ---------------------------------------------- 0 60 96 98 Refine and use efficient written methods using multiples of 10 and remainders eg 178 ÷ 8 = 20 x 8 2 x 8 r2 or ¼ ---------------------------------------------- 0 160 176 178

Division Use a standard written method: Long division 168 4 ) 672 400 – 272 240 – 32 Compact short division 0 4 7 r 2 or 2/5 5 ) 2 2 3 3 7