Progression in written calculations

1. Progression in written calculations Tuesday 20th October

2. 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

3. 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

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

5. 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

6. 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

7. 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

8. 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

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

10. 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

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

12. 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

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

14. Multiplication • Extend the grid method to even larger numbers and decimals 23.5 x 12 = • Compact vertical multiplication 38 x 7 266

15. 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 egHow many 4s in 12? • How many are left over if I share 13 between 4?

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

17. 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

18. 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 ) 22337