Working with integers is a major area of pain where students usually start mugging up algebra and that's the beginning of the end of logical thinking. This presentation aims at explaining graphically the addition and subtraction of integers.

1. Addition & SubtractionAddition & Subtraction
of Integers

2. - 4 + 6

3. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +

4. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here

5. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
+

6. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
+ means GO RIGHT

7. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
+ means GO RIGHT
6 steps

8. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
1
+ means GO RIGHT
6 steps

9. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
2
+ means GO RIGHT
6 steps

10. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
3
+ means GO RIGHT
6 steps

11. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
4
+ means GO RIGHT
6 steps

12. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
5
+ means GO RIGHT
6 steps

13. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
6
+ means GO RIGHT
6 steps

14. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
6
+ means GO RIGHT
6 steps
- 4 + 6 = 2

15. - 4 + 6
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
6
+ means GO RIGHT
6 steps
- 4 + 6 = +2

16. Another Problem

17. - 2 - 3

18. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +

19. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here

20. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
–

21. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
– means GO LEFT

22. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
– means GO LEFT
3 steps

23. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
1
means GO LEFT
3 steps
–

24. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
2
means GO LEFT
3 steps
–

25. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
3
means GO LEFT
3 steps
–

26. - 2 - 3
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
3
means GO LEFT
3 steps
–
- 2 - 3 = - 5

27. Another Problem

28. - 5 + 2

29. - 5 + 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +

30. - 5 + 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here

31. - 5 + 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
+

32. - 5 + 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
+ means GO RIGHT

33. - 5 + 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
start here
+ means GO RIGHT
2 steps

34. - 5 + 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
1
+ means GO RIGHT
2 steps

35. - 5 + 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
2
+ means GO RIGHT
2 steps

36. - 5 + 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
2
+ means GO RIGHT
2 steps
- 5 + 2 = - 3