Explaining Integers and Integer Operations

One of the easiest but hardest topics to master for 5th and 6th graders is Integer Operations. It's the concept of a negative number that seems to be foreign for them.  And it's no wonder. What is a negative number?  How would you explain it?

Some of the explanations we've heard are in the following list:

(1)  "It's a number that's less than zero." - Let's think about what this means for a 5tth/6th grader.  Less than zero?  What?  Doesn't zero mean nothing?  What is less than nothing?  How does that make sense?  

(2)  "Well, there's a number line...." - Yes, there is a number line but how is that suddenly the numbers doubled?  Does a student just accept that out of nowhere, all these numbers appeared on the other side of zero?  

(3) "It's the set of counting numbers plus negative numbers."  Just words.  Where does it fit in?  Have you seen the Venn Diagram?  Again, what is a negative number?

(4) "No one ever explained it to me." That's definitely not acceptable.  You've been working with Integers and no one ever explained what they were?  Isn't that just scary?

Shouldn't there be a better way to explain negative numbers?  Wouldn't it be great to have tangible and creative ways to show what negative numbers mean?

When talking to our staff, we've come up with some creative ways to explain negative numbers.

(1) Let's use money.  Have you ever owed anyone money?  Owing money means you don't have the funds at the time to pay a person or a store.  Think about this.  You go to the Candy Store and there's this huge chocolate bunny you need in your life and it's $7.  In your pocket, you only have $3.  Can you buy that bunny? No.. because you don't have enough money. So, you are SHORT $4 or -4.

(2) Let's say you are walking along a flat sidewalk and everything is going great.  You are effectively walking on zero slope, totally flat.  Looking at the beautiful sky above, you don't notice there is a huge hole in the sidewalk and you fall into a deep hole.  Where are you now?  How would you describe how deep the hole is if you below the sidewalk?

(3) Very simply put, a negative number is the ABSENCE of VALUE.  You don't have it so it's a negative.

We're sharing this so that you can see what works in our Center.