1. Numeracy Calculation Strategies & Conjecturing and Convincing

2. Purpose of the evening:  To explore what calculation strategies are taught as part of the National Numeracy Strategy;  To explore the Mathematical ‘power’ of conjecturing and convincing to enable children to ‘reason’ more about mathematics.

3. The National Numeracy Project 1996 ~ Concerns:  Expectations were too low. Poor foundation skills in arithmetic, particularly mental arithmetic.  Dominance of published schemes with little direct teaching or discussion.  Over emphasis on standard written methods at the expense of mental methods.

4. The National Numeracy Project Research:  Emphasis on mental methods;  Use of oral work - children were encouraged to talk about their work;  Direct and interactive teaching;  Standard written methods not introduced too soon.

5. The Primary National Strategy Key features:  Consistent planning and teaching using the Framework;  A daily, dedicated mathematics lesson for all children;  A high proportion of lessons focussing on numeracy skills;  Greater emphasis on whole-class teaching and participation;  Controlled, manageable differentiation;  An emphasis on interactive oral and mental work;  Regular exercises and activities for children to complete;  Advice, support and training available for schools.

6. A typical daily mathematics lesson Oral and mental starter:  Whole class;  Oral and mental work to rehearse and sharpen skills;  About 5 to 10 minutes.

7. A typical daily mathematics lesson Main teaching and pupil activities:  Whole class / groups / pairs / individuals;  Clear objectives shared with the children;  Direct teaching input;  Practical and / or written work for children;  Differentiated activities with focused teaching;  Continued interaction and intervention;  Misconceptions identified;  About 30 to 40 minutes.

8. A typical daily mathematics lesson Plenary:  Whole class;  Feedback from children;  Summary of key ideas and what to remember;  Pupil self assessment  Links made to other work and possible next steps;  Work to be done at home;  About 10 minutes.

9. Mental Calculation Strategies ~ Addition and Subtraction  Count all  Count on from first number  Count on from largest number  Step counting  Use known facts or skills  Derived facts  2 digit numbers

10. Mental Calculation Strategies ~ Multiplication and Division  Use the relationship between multiplication and division  Multiply / divide by 2 as double / halve  Number trios  Multiply / divide by 10  Use doubling / halving to build on known number facts  4 x tables as double, double, 8 x table as double, double, double  Use related facts  Partition 2 digit numbers  Multiply / divide by 100  Use factors

11. Written Calculation Strategies ~ Addition and Subtraction Find the total of 32 and 45 32 + 40 +5 7277 Empty Number lines 32 + 45 = 77

12. Written Calculation Strategies ~ Addition and Subtraction Find the difference between 63 and 37 37 + 20 +3 576360 +3 37 + 20 +6 5763 Empty Number lines 63 - 37 = 26

13. Written Calculation Strategies ~ Addition and Subtraction Find the difference between 63 and 37 23 - 40 +3 6326 Empty Number lines 63 - 37 = 26

14. Written Calculation Strategies ~ Addition Expanded method Find the total of 625 and 48 625 + 48 13 60 600 673

15. Written Calculation Strategies ~ Addition Expanded method Find the total of 378 and 94 378 + 94 12 160 300 472 Contracted method 378 + 94 472 1 1

16. Written Calculation Strategies ~ Subtraction Expanded method Find the difference between 578 and 154 500 + 70 + 8 - 100 + 50 + 4 400 + 20 + 4 = 424

17. Written Calculation Strategies ~ Subtraction Expanded method Find the difference between 475 and 127 400 + 70 + 5 - 100 + 20 + 7 400 + 60 + 15 - 100 + 20 + 7 300 + 40 + 8 475 - 127 = 348

18. Written Calculation Strategies ~ Subtraction Expanded method Find the difference between 632 and 74 600 + 30 + 2 - 70 + 4 600 + 20 + 12 - 70 + 4 632 - 74 = 558 500 + 120 + 12 - 70 + 4 500 + 50 + 8

19. Written Calculation Strategies ~ Subtraction Expanded method Find the difference between 372 and 54 300 + 70 + 2 - 50 + 4 372 - 54 = 318 300 + 70 + 2 - 50 + 4 300 +10 + 8 60 12 372 - 54 318 6 12 Contracted method

20. What is the difference between 183 and 68? There should be 384 children at school, but there are only 266 present. How many children are absent? Find the total of 278 and 164. Find the sum of two hundred and nineteen and three hundred and seventy two. 384 - 266 = 118278 + 164 = 442 183 - 68 = 115219 + 372 = 591

21. Written Calculation Strategies ~ Multiplication Grid method Calculate 75 x 6 x 70 5 6420 30= 450

22. Written Calculation Strategies ~ Multiplication Grid method Calculate 435 x 7 x 400305 7280021035= 3045

23. Written Calculation Strategies ~ Multiplication Grid method Calculate 352 x 27 300502 6000100040 x 20 7 210035014 7040 2464 + 9504

24. A gardener wishes to plant 7 rows of bulbs with 45 in each row. How many bulbs must the gardener order? A plot of ground has 23 trees each with 16 apples. How many apples altogether? A matchbox holds 48 matches. How many matches in 135 boxes? From Monday to Friday the milkman delivered 268 bottles of milk daily. How many was that altogether? 7 x 45 = 31523 x 16 = 368 48 x 135 = 64805 x 268 = 1340

25. Written Calculation Strategies ~ Division Chunking Calculate 455  7 10 x 7 = 70 100 x 7 = 700 50 x 7 = 350 60 x 7 = 420 70 x 7 = 490 455 - 420 60 x 7 35 - 35 5 x 7 0 455  7 = 65

26. Written Calculation Strategies ~ Division Chunking Try 264  4 10 x 4 = 40 100 x 4 = 400 50 x 4 = 200 60 x 4 = 240 70 x 4 = 280 80 x 4 = 320 264 - 240 60 x 4 24 - 24 6 x 4 0 264  4 = 66

27. Written Calculation Strategies ~ Division Chunking ~ with remainders Calculate 353  8 10 x 8 = 80 20 x 8 = 160 30 x 8 = 240 40 x 8 = 320 50 x 8 = 400 353 - 320 40 x 8 33 - 32 4 x 8 1 353  8 = 44 r 1 353  8 = 44 1 / 8

28. Written Calculation Strategies ~ Division Chunking ~ with remainders Try 285  6 10 x 6 = 60 20 x 6 = 120 30 x 6 = 180 40 x 6 = 240 50 x 6 = 300 285 - 240 40 x 6 45 - 42 7 x 6 3 285  6 = 47 r 3 285  6 = 47 3 / 6 285  6 = 47 1 / 2

29. It has been arranged for 6 buses to take 330 pupils on a school outing. How many will there be to each bus? A shelf holds 870 bottles of coke, packed in boxes of 6. How many boxes does the shelf hold? A packer has 9 crates into which 432 apples need to be packed. How many should the packer put in each crate? If 144 chicks are packed in boxes of eight, how many boxes would I need? 330  6 = 55870  6 = 145 432  9 = 48144  8 = 18

30. Imagining And Expressing

31. Imagining And Expressing Specialising and Generalising

32. Imagining And Expressing Specialising and Generalising Organising and Classifying

33. Imagining And Expressing Conjecturing and Convincing Specialising and Generalising Organising and Classifying

34. Circle Times Conjecturing and Convincing 0 1 2 3 4 5 6 7 8 9 0 x 2 = 0 1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10

35. Circle Times Conjecturing and Convincing 0 1 2 3 4 5 6 7 8 9 0 x 4 = 0 1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20

36. Circle Times Conjecturing and Convincing 0 1 2 3 4 5 6 7 8 9

37. Circle Times Conjecturing and Convincing 0 1 2 3 4 5 6 7 8 9

38.   What are the patterns?   Why are these patterns appearing?   Convince yourself   Convince a partner…

39. Conjecturing and Convincing 2, 8, 12 3, 7 4, 6 1, 9, 11

40. Pirton School Website http://www.pirtonschool.org.uk