Progression in written calculations

Tuesday 20th 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 additioneg 84 – 56 = +4 +20 +4 ----------------------------------------------56 60 80 84

Subtraction

Subtraction

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

30 8 Total

7 210 56 266

Multiplication

• Extend the grid method to larger numbers 56 x 27 =

50 6 Total

20 1000 120 1120

7 350 42 392

1512

Multiplication• Extend the grid method to even larger numbers

and decimals 23.5 x 12 =

• Compact vertical multiplication 38 x 7 266

20 3 0.5 Total

10 200 30 5 235

2 40 6 1 47

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

DivisionDevelop and refine written methodeg 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