1. Multiplying
Negative
Numbers
© T Madas

2. © T Madas

3. © T Madas

4. 5 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5
© T Madas

5. The 2 times table Follow the pattern4 8 3 6
The 2 times table 2 4 1 2 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2
Follow the pattern -2 -4 -3 -6 -4 -8 -5
-10
© T Madas

6. The 3 times table Follow the pattern4 8 12 3 6 9
The 3 times table 2 4 6 1 2 3 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3
Follow the pattern -2 -4 -6 -3 -6 -9 -4 -8
-12 -5
-10
-15
© T Madas

7. The 4 times table Follow the pattern8 12 16 3 6 9 12
The 4 times table 2 4 6 8 1 2 3 4 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4
Follow the pattern -2 -4 -6 -8 -3 -6 -9
-12 -4 -8
-12
-16 -5
-10
-15
-20
© T Madas

8. 4 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10
So far 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

9. 4 3 2 0 times table 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 84 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10
0 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

10. 0 times table Follow the pattern4 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10
0 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5
Follow the pattern -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

11. 4 3 2 1 times table 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 84 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10
1 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

12. 1 times table Follow the pattern4 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10
1 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10
Follow the pattern -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

13. 4 3 2 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 84 8 12 16 20 3 3 6 9 12 15
2 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

14. 2 times table Follow the pattern4 4 8 12 16 20 3 3 6 9 12 15
2 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10
Follow the pattern -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

15. 4 3 3 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 84 8 12 16 20 3 3 6 9 12 15
3 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

16. 3 times table Follow the pattern4 4 8 12 16 20 3 3 6 9 12 15
3 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10
Follow the pattern -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

17. 4 3 4 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 84 8 12 16 20 3 3 6 9 12 15
4 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

18. 4 times table Follow the pattern4 8 12 16 20 3 3 6 9 12 15
4 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10
Follow the pattern -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

19. 4 3 5 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 84 8 12 16 20 3 3 6 9 12 15
5 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

20. 5 times table Follow the pattern4 4 8 12 16 20 3 3 6 9 12 15
5 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10
Follow the pattern -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

21. So far we continued the patterns vertically 4 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5
So far we continued the patterns vertically
Can we see any patterns horizontally? -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

22. 4 3 2 1 2 times table -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 84 8 12 16 20 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 1 1 2 3 4 5
2 times table -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

23. 4 3 2 3 times table 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 84 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10
3 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

24. 4 3 4 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2
4 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

25. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

26. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

27. We filled ¾ of our table 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3
-24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10
We filled ¾ of our table
We can fill the bottom left corner by following the patterns vertically or horizontally -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

28. Horizontally 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5
Horizontally -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 -3 -3 -6 -9
-12
-15 -4 -4 -8
-12
-16
-20 -5 -5
-10
-15
-20
-25
© T Madas

29. Vertically 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 -24 -20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1
Vertically 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 6 -3 -3 -6 -9
-12
-15 8 -4 -4 -8
-12
-16
-20 10 -5 -5
-10
-15
-20
-25
© T Madas

30. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 9 6 -3 -3 -6 -9
-12
-15 12 8 -4 -4 -8
-12
-16
-20 15 10 -5 -5
-10
-15
-20
-25
© T Madas

31. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 12 9 6 -3 -3 -6 -9
-12
-15 16 12 8 -4 -4 -8
-12
-16
-20 20 15 10 -5 -5
-10
-15
-20
-25
© T Madas

32. We can try a few horizontal patterns again
-24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5
We can try a few horizontal patterns again -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 12 9 6 -3 -3 -6 -9
-12
-15 16 12 8 -4 -4 -8
-12
-16
-20 20 15 10 -5 -5
-10
-15
-20
-25
© T Madas

33. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 18 15 12 9 6 3 -3 -3 -6 -9
-12
-15 16 12 8 -4 -4 -8
-12
-16
-20 20 15 10 -5 -5
-10
-15
-20
-25
© T Madas

34. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 18 15 12 9 6 3 -3 -3 -6 -9
-12
-15 24 20 16 12 8 4 -4 -4 -8
-12
-16
-20 20 15 10 -5 -5
-10
-15
-20
-25
© T Madas

35. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 18 15 12 9 6 3 -3 -3 -6 -9
-12
-15 24 20 16 12 8 4 -4 -4 -8
-12
-16
-20 30 25 20 15 10 5 -5 -5
-10
-15
-20
-25
© T Madas

36. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 5 4 3 2 1 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 18 15 12 9 6 3 -3 -3 -6 -9
-12
-15 24 20 16 12 8 4 -4 -4 -8
-12
-16
-20 30 25 20 15 10 5 -5 -5
-10
-15
-20
-25
© T Madas

37. -24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 5 4 3 2 1 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 18 15 12 9 6 3 -3 -3 -6 -9
-12
-15 24 20 16 12 8 4 -4 -4 -8
-12
-16
-20 30 25 20 15 10 5 -5 -5
-10
-15
-20
-25
© T Madas

38. Let’s use this table
© T Madas

39. And that is maths’ magic 1
-24
-20
-16
-12 -8 -4 4 4 8 12 16 20
-18
-15
-12 -8 -6 -3 3 3 6 9 12 15
-12
-10 -8 -6 -4 -2 2 2 4 6 8 10
And that is maths’ magic -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 5 4 3 2 1 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8
-10 18 15 12 9 6 3 -3 -3 -6 -9
-12
-15 24 20 16 12 8 4 -4 -4 -8
-12
-16
-20 30 25 20 15 10 5 -5 -5
-10
-15
-20
-25
© T Madas

40. It was hard work making all these slides…
I must start getting out more
© T Madas

41. Negative
Numbers
Formal
Proofs
© T Madas

42. © T Madas

43. © T Madas

44. © T Madas

45. © T Madas