The document provides step-by-step instructions for subtracting integers using a number line. It explains that to solve 5 - 3, you start at 5 on the number line, turn around since it's a subtraction problem, and count back 3 steps to reach the answer of 2. Similarly, it works through solving 6 - 10 step-by-step, starting at 6 and counting back 10 steps to reach the answer of -4. The key steps are to start at the first number, turn if it's a subtraction problem, and count back the number of steps in the second number.

1. 9-4 Subtracting
Integers
Math Notes
Number Sense 2.1

2. + -
Find 5 - 3

3. + -
Find 5 - 3
Think of walking on a number line.

4. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)

5. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10

6. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10

7. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 5 steps for positive 5.

8. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 5 steps for positive 5.

9. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 5 steps for positive 5.
STEP 2: The “-” sign means turn around.

10. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 5 steps for positive 5.
STEP 2: The “-” sign means turn around.

11. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 5 steps for positive 5.
STEP 2: The “-” sign means turn around.
STEP 2: Walk backward 3 steps for negative 3.

12. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 5 steps for positive 5.
STEP 2: The “-” sign means turn around.
STEP 2: Walk backward 3 steps for negative 3.

13. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 5 steps for positive 5.
STEP 2: The “-” sign means turn around.
STEP 2: Walk backward 3 steps for negative 3.

14. + -
Find 5 - 3
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 5 steps for positive 5.
STEP 2: The “-” sign means turn around.
STEP 2: Walk backward 3 steps for negative 3.
You end up at +8

15. Something to keep in mind, if you
choose to draw it out...

16. Something to keep in mind, if you
choose to draw it out...
You might have to “borrow.”

17. Something to keep in mind, if you
choose to draw it out...
You might have to “borrow.”
Borrow “zero,” “nothing” - Huh?

18. Something to keep in mind, if you
choose to draw it out...
You might have to “borrow.”
Borrow “zero,” “nothing” - Huh?
Remember a + and - cancel each other
out leaving “nothing” or “zero.”

19. +
Something to keep in mind, if you
- choose to draw it out...
You might have to “borrow.” +
-
Borrow “zero,” “nothing” - Huh?
+
Remember a + and - cancel each other
+
-
-
out leaving “nothing” or “zero.”
They float invisibly waiting for you to use
+ ++
them.
- + + -
+ - - + -
- -

20. + -
Find 5 - 3

21. + -
Find 5 - 3
STEP 1: Draw five positives

22. + -
Find 5 - 3
+++++
STEP 1: Draw five positives

23. + -
Find 5 - 3
+++++
STEP 1: Draw five positives
FYI: The “-” means subtract, take away...
Can you take away 3 negatives?

24. +
- Find 5 - 3+ -
+
-
+++++
STEP 1: Draw five positives
+
- +
-
+
FYI: The “-” means subtract, take away...
-
Can you take away 3 negatives?
STEP 2: This is when you “borrow” some +
-

25. +
- Find 5 - 3+ -
+
-
+++++
STEP 1: Draw five positives
+
- +
-
+
FYI: The “-” means subtract, take away...
-
Can you take away 3 negatives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
negatives are you supposed to take away? 3

26. Find 5 - 3+ -
+
-
+++++
STEP 1: Draw five positives
+
- + +
- -
+
FYI: The “-” means subtract, take away...
-
Can you take away 3 negatives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
negatives are you supposed to take away? 3

27. Find 5 - 3+ -
+
-
+++++
STEP 1: Draw five positives
+
- + + +
- -
FYI: The “-” means subtract, take away...
-
Can you take away 3 negatives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
negatives are you supposed to take away? 3

28. Find 5 - 3+ -
+
-
+ + + +++
STEP 1: Draw five positives
+
- + + -
- -
FYI: The “-” means subtract, take away...
Can you take away 3 negatives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
negatives are you supposed to take away? 3

29. Find 5 - 3+ -
+
-
+ + + +++
STEP 1: Draw five positives
+
- + + -
- -
FYI: The “-” means subtract, take away...
Can you take away 3 negatives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
negatives are you supposed to take away? 3
STEP 3: NOW, take away 3 negatives. How
many positives are left?

30. Find 5 - 3+ -
+
-
+ + + +++
STEP 1: Draw five positives
+
- + +
FYI: The “-” means subtract, take away...
Can you take away 3 negatives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
negatives are you supposed to take away? 3
STEP 3: NOW, take away 3 negatives. How
many positives are left?

31. Find 5 - 3+ -
+
-
+ + + +++
STEP 1: Draw five positives
+
- + +
FYI: The “-” means subtract, take away...
Can you take away 3 negatives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
negatives are you supposed to take away? 3
STEP 3: NOW, take away 3 negatives. How
many positives are left? 8
+

32. + +
Find 6 - 10

33. + +
Find 6 - 10
Think of walking on a number line.

34. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)

35. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10

36. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10

37. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 6 steps for positive 6.

38. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 6 steps for positive 6.

39. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 6 steps for positive 6.
STEP 2: The “-” sign means turn around.

40. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 6 steps for positive 6.
STEP 2: The “-” sign means turn around.

41. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 6 steps for positive 6.
STEP 2: The “-” sign means turn around.
STEP 2: Walk forward 10 steps for positive 10.

42. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 6 steps for positive 6.
STEP 2: The “-” sign means turn around.
STEP 2: Walk forward 10 steps for positive 10.

43. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 6 steps for positive 6.
STEP 2: The “-” sign means turn around.
STEP 2: Walk forward 10 steps for positive 10.

44. + +
Find 6 - 10
Think of walking on a number line.
You are ALWAYS facing right and starting at zero (0)
- 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 + 10
STEP 1: Walk forward 6 steps for positive 6.
STEP 2: The “-” sign means turn around.
STEP 2: Walk forward 10 steps for positive 10.
You end up at -4

45. + +
Find 6 - 10

46. + +
Find 6 - 10
STEP 1: Draw six positives

47. + +
Find 6 - 10
++ + +++
STEP 1: Draw six positives

48. + +
Find 6 - 10
++ + +++
STEP 1: Draw six positives
FYI: The “-” means subtract, take away...
Can you take away 10 positives?

49. +
- Find 6 - 10 +
-
+ +
++ + +++
STEP 1: Draw six positives
+
- +
-
+
FYI: The “-” means subtract, take away...
-
Can you take away 10 positives?
+
-
STEP 2: This is when you “borrow” some

50. +
- Find 6 - 10 +
-
+ +
++ + +++
STEP 1: Draw six positives
+
- +
-
+
FYI: The “-” means subtract, take away...
-
Can you take away 10 positives?
+
-
STEP 2: This is when you “borrow” some
FYI: How many do you “borrow?” How many
positives are you supposed to take away? 10, you
need 4 more.

51. + +
Find 6 - 10
+ + + ++ +
+ +
STEP 1: Draw six positives
+
- + + - -
- -
FYI: The “-” means subtract, take away...
Can you take away 10 positives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
positives are you supposed to take away? 10, you
need 4 more.

52. + +
Find 6 - 10
+ + + ++ +
+ +
STEP 1: Draw six positives
+
- + + - -
- -
FYI: The “-” means subtract, take away...
Can you take away 10 positives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
positives are you supposed to take away? 10, you
need 4 more.
STEP 3: NOW, take away 10 positives. What
are left with?

53. + +
Find 6 - 10
STEP 1: Draw six positives
+
- - - - -
FYI: The “-” means subtract, take away...
Can you take away 10 positives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
positives are you supposed to take away? 10, you
need 4 more.
STEP 3: NOW, take away 10 positives. What
are left with?

54. + +
Find 6 - 10
STEP 1: Draw six positives
+
- - - - -
FYI: The “-” means subtract, take away...
Can you take away 10 positives?
STEP 2: This is when you “borrow” some +
-
FYI: How many do you “borrow?” How many
positives are you supposed to take away? 10, you
need 4 more.
STEP 3: NOW, take away 10 positives. What
are left with? 4
-