The document contains a series of doubling and halving calculations with numbers in categories ranging from basic facts to more complex multi-digit numbers. It includes calculations like 1 x 16, 2 x 8, 4 x 4 which double and halve basic numbers and also calculations like 8 x 32, 4 x 64, 2 x 168 which double and halve multi-digit numbers. It has sections for doubling and halving 1 digit and 2 digit numbers, 2 digit numbers, and also explores tripling, quadrupling, thirding and quartering numbers. The purpose is to investigate patterns that emerge from performing these types of calculations.

1. Doubling and
Halving

2. CATEGORY 1
Doubling and Halving with basic facts.

3. 1 x 16
2 x 8
4 x 4
8 x 2
16 x 1

4. 1 x 36
2 x 18
4 x 9

5. 1 x 20
2 x 10
4 x 5

6. 1 x 24
2 x 12
4 x 6
8 x 3

7. 1 x 48
2 x 24
4 x 12
8 x 6
16 x 3

8. 1 x 40
2 x 20
4 x 10
8 x 5

9. 1 x 12
2 x 6
4 x 3

10. 1 x 32
2 x 16
4 x 8
8 x 4
16 x 2
32 x 1

11. 1 x 56
2 x 28
4 x 14
8 x 7

12. CATEGORY 2
Doubling and Halving with 1 x 2-digit and 1 x 3-digit numbers.

13. 8 x 16
4 x 32
2 x 64

14. 8 x 32
4 x 64
2 x 168

15. 36 x 5
18 x 10
9 x 20

16. 8 x 125
4 x 250
2 x 500

17. 84 x 5
42 x 10
21 x 20

18. 35 x 8
70 x 4
140 x 2

19. 125 x 8
250 x 4
500 x 2

20. 345 x 8
690 x 4
1380 x 2

21. 8 x 29
4 x 58
2 x 116

22. CATEGORY 3
Doubling and Halving with 2 x 2-digit numbers.

23. 3 x 60
6 x 30
12 x 15

24. 9 x 56
18 x 28
36 x 14

25. 2 x 280
4 x 140
8 x 70
16 x 35

26. 104 x 3
52 x 6
26 x 12

27. 4 x 120
8 x 60
32 x 15

28. 100 x 4
50 x 8
25 x 16

29. 112 x 2
56 x 4
28 x 8
14 x 16

30. 360 x 3
180 x 6
90 x 12
45 x 24

31. 2 x 1440
4 x 720
8 x 360
16 x 180
32 x 90
64 x 45

32. CATEGORY 4
For investigation of what happens when you third or triple or
quarter and quadruple numbers.

33. 9 x 12
3 x 36
1 x 108

34. 27 x 15
9 x 45
3 x 135
1 x 405

35. 36 x 18
72 x 9
216 x 3
648 x 1

36. 15 x 16
60 x 4
240 x 1

37. 25 x 48
100 x 12
400 x 3
1200 x 1

38. 64 x 35
16 x 140
4 x 560
1 x 2240

39. 18 x 12
9 x 24
4.5 x 36
2.25 x 72

40. 6 x 12
3 x 24
1.5 x 48

41. 6 x 24
3 x 48
1.5 x 96