We will use hops on a number line to model subtraction of positive and negative numbers. When subtracting a positive number we move to the left on the number line. When subtracting a negative number we move to the right on the number line. Why is this? Read on... 
Example 1: Simplify 5 – 2 To model this problem we use two hops. The first hop is 5 units to the right. Then hop 2 units to the left. Since we end up on 3, the answer is 3. 5 – 2 = 3 
Example 5: Simplify (3) – 2 To model this problem we begin with 3 hops to the left. Subtracting positive 2 means to hops to the left. Since we end up on 5, the answer is 5. (3) – 2 = 5 
Example 2: Simplify 5 – 8 To model this expression begin by hopping 5 units to the right. Then go 8 units to the left, landing at 3. 5 – 8 = (3) 
Example 6: Simplify (3) – 8 This expression is model by a hop 3 units to the left, followed by another hop to the left of 8 units. (3) – 8 = 11 
Example 3: Simplify 5 – (2) If subtracting a positive means a move to the left on a number line, then subtracting a negative means a move towards the right. To model this problem, we hop 5 units to the right. The second hop is 2 units to the right (please see note below). Since we end up on 7, the answer is 7. 5 – (2) = 7 
Example 7: Simplify (3) – (2) Just as in Example 3 above, subtracting 2 means moving to the right. So the number line with show two hops: the first is a hop 3 spaces to the left and the second hop 2 spaces to the right. The result is 1. (3) – (2) = 1 
Example 4: Simplify 5 – (8) To model this problem, go 5 units to the right, and then 8 more units to the right. Since we end up at 13, the answer is 13. 5 – (8) = 13 
Example 8: Simplify (3) – (8) This expression is modeled by hopping 3 units to the left and then 8 units to the right. This lands at 5. (3) – (8) = +5 
In the example 5 – (2) we saw that it was modeled with a 5 unithop to the right and then a 2 unithop to the right. How can we be certain that subtracting (2) represents a hop to the right?
Let's look at this table of problems and look for a pattern.
5 – 3 = 2 
As the second number goes down, the difference gets larger. The pattern verifies that 5 – (2) is equal to 7. This means subtracting (2) is accurately represented by a hop to the right. 

5 – 2 = 3 

5 – 1 = 4 

5 – 0 = 5 

5 – (1) = 6 

5 – (2) = 7 

5 +– (3) = 8 
Important understandings 

Question 1 Simplify: (7) – (10)

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Question 2 Simplify: (4) – (9)

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Question 3 Simplify: (3) – (5)

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