1.  7.NS.1 Subtracting Integers

2. Just like with addition of integers, there are different ways of looking at subtraction of integers. We’ll look at these three.  Number lines  Simulation with Counters  Addition of the Opposite

3. 136 °F −128 °F 128 units from zero 136 units from zero So they are 264 units away from each other

4.  Subtraction means the difference between two numbers.  On the number line this can be interpreted as the distance between these two numbers.  With our temperatures we saw that the two values were 264 units apart.  So when we write it out we get 136 - -128 = 264

5. The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level. The lowest elevation is Death Valley, which is 282 feet below sea level. What is the difference between these two elevations?  The math equation would look like this: 20320 - - 282 =  Let’s look at a vertical number line.  We can see that from Death Valley we would have to climb 282 feet to get to zero, then climb another 20320 feet to get to the top of the mountain.  So, we have climbed a total of 20602 feet. This is the difference between the two elevations.

6. -8 - -3  Begin with eight negative counters.  When we look at subtraction as “taking away”, this problem is easy. We just “take away” three negative counters and were left with five negative counters.  Therefore, -8 - -3 = -5

7.  This one starts the same way, with seven negative counters.  This time we are supposed to “take away” five positive counters, but the problem is we don’t have any positive counters.  We can add zero to any expression without changing the value, so the way we solve this difficulty is adding zero pairs until we have enough positive counters to take away five.  Once we take away the five positive counters we are left with twelve negatives.  So -7 - 5 = -12 -7 - 5

8.  This time we start with three positive counters.  We are now supposed to “take away” four negatives, but since we don’t have any negatives we need to add four zero pairs.  Now we can take away the four negatives.  So for our answer we get: 3 - -4 = 7

9.  Again there are many different ways of looking at subtraction, but the easiest is to change it to an equivalent addition problem.  This is because subtraction is the same as adding the opposite of the second number.  Let’s look at all the problems we did with number lines and counters and compare the answers we found with those methods with the Addition of the Opposite method.

10. Number Line  The low temperature is 128 units from zero  The high temperature is another 136 units from zero.  Altogether, the difference between the two values is 264 degrees. Add the opposite  To find the difference between two numbers we subtract the smaller from the larger  136 - -128 =  First we change the subtraction to addition and then change the sign of the value that follows.  136 + +128 =  Now we see we have a simple addition problem.  136 + +128 = 264

11. Counters  Start with eight negatives.  Take away three negatives and we’re left with five negatives. Add the opposite  First we change the subtraction to addition and then change the sign of the value that follows.  -8 + +3 =  Now we can see that if we owe eight units and we have three, we use the three and still owe five.  -8 + +3 = - 5

12. Counters  Start with seven negatives.  To take away five positives we must first at five zero pairs.  Once we take away these five positives we see that we are left with twelve negatives Add the opposite  First we change the subtraction to addition and then change the sign of the value that follows  -7 + - 5 =  Now we see that we owe seven units and we owe five more units.  So altogether we owe twelve units.  -7 + - 5 = -12 The same answer with fewer steps

13. Asssignment