Subtracting Integers Using Counters

For this week, I decided to move away from fractions and decimals.  I think I have a better handle on the topic after working on it for four weeks.  

During our class last week, I was intrigued by the idea of using chip counters for adding and subtracting integers.   This was something I had never been exposed to, and I found it a little confusing.  I wanted to dig deeper into the topic so I could better understand the process. 

I wanted to see more examples of how it is done, so I found a video at LearnZillion.com that I found very helpful. 

I was able to conceptualize the adding with counters, however, I found the subtraction confusing because of the addition of the zero pairs.  Now I understand that no matter how many zero pairs you add, you do not change the value of the original number.  And you need to add those zero pairs when you need to subtract and you do not have enough counters to do so once you lay out the original problem.  

I will try to explain the problem -2 - (-4).  You would start by laying out two negative counters to represent -2.  

    

Now you need to take away 4 negative counters, but you do not have enough to do so.  Therefore, you have to add two zero pairs.  

    

    

  

Now, you have enough to take away the 4 negative counters, which leaves you with 2 positive counters left. 

  

Making the answer: -2 - (-4) = 2.

I am glad that I spent some extra time reviewing this, I think that it really helped me understand the process.  I think this will be helpful when explaining addition and subtraction of integers to my future students!