GOAL: I can subtract positive and negative numbers without using a calculator 
Learning Standards 
Common Core Standard: 7.EE.1 
Resources    GREEN BOOK Reference: Pages: 70 ─ 73 Practice on page 73,
#1533 odds.
 RED BOOK Reference: Pages: 73 ─ 77
Practice on page 76, #1727 odds. 
BLACK BOOK Reference: Pages: 30 ─ 34
Practice on page 34, #3039 odds. 
Lesson Vocabulary 

Integer 
Positive and negative numbers that are not fractions and do not have decimals. 

Strategies and Content Practice 
Begin
(prepare) 
What do you recall about adding positive numbers? What makes adding positive and negative or negative and negative numbers different? 
Engage 
When it comes to subtracting integers, what are we really doing? Well, I'm sure you're familiar with subtraction. But what are integers? From the vocabulary above, you read that integers are simply positive and negative numbers that do not have decimals or fractions. Of course, zero is also on their team. If you can master subtraction with integers, you can do the same with decimals and fractions. Let's get started.
The first thing we have to remember in order to subtract positive and negative numbers is the rhyming rule for addition. Why (you might ask) do I need to know the rhyming rule for addition if I'm trying to subtract? Good question. Here's my good answer: In this method, I show you how to trick the subtraction problem back into an addition problem. Once the subtraction problem is tricked back into an addition problem, then you use the addition rhyming rule on it and you have your answer. Isn't that cleaver?
So, here's the addition rhyming rule we learned under the Adding Integers section. The rhyme sounds like "Row, Row, Row Your Boat".
Same Signs, Add and Keep
Different Signs, Subtract
Keep the Sign of the Bigger Number
Then You'll Be Exact.
Notice that I color coded the rhyme. That means you will either do the blue instructions or both the red instructions.
Now that your brain is refreshed with the addition rhyming rule, let's take a look the trick for changing a subtraction problem into an addition problem. The trick is called Leave, Change, Opposite. It works like this... Any time you have a subtraction problem that's not super simple (like 10 ─ 6 = 4) then you can change the subtraction problem into an addition problem by going over it with Leave, Change, Opposite. Here are some examples.
8 ─ 12 = ?
Leave Change Opposite
8 + (12) = ?
Leave the first number alone, Change subtraction to addition, Opposite, take the opposite of the second number.
So now all you have to do is add 8 to (12). Recall from our addition rhyming rule, when we have numbers with different signs, we ignore their signs and subtract the smaller number from the bigger number. So...
12 ─ 8 = 4
Now don't forget that the "different signs subtract" instruction has a second line... "keep the sign of the bigger number". So for this example, the answer 4, keeps the sign of the bigger number (12) to make it...
(4)
Ta Dah! That's it.

Assess
(formative) 
After example problems and videos, try to solve the Practice Worksheets above. The answers to the practices are on the last page so you can check how well you are doing.
Please see me for more help if you are having difficulty with the practices. 
