As a parent or teacher, have you ever had to explain and re-explain Adding and Subtracting Integers?

Why do two negatives make a positive… are two methods that are clear for the students to understand. Let’s consider the following two examples.

Example 1: 5 – 4

Example 2: 5 – (-4)

Conceptualizing Example 1 is fairly straight forward… we can think of 5 as let’s say, we have 5 dollars, and then -4 represents losing 4 dollars, so all in all we have 1 dollar left, hence the answer of 1. Many students find it useful to use a number line to visualize this as well. When negative we go left on the number line. So staring at 5 on the number line, we then go LEFT another 4 units and end up at 1.

Image result for number line

However, Example 2 looks similar BUT is totally different!

There are two methods that I have found to be useful to explain the meaning behind the deep understanding of 5-(-4). The first method is to create a logical chain of mathematical processes.

Method 1

If we start with 5 and subtract 3, this is represented as 5-3, on the number line we can see the answer is 2

Then we subtract 2, so 5-2 = 3

Next we subtract 1, so 5-1 = 4

Next we subtract 0, so 5-0 = 5

When we look at the PATTERN, we can see that for the final answer we are increasing by ONE unit... so following the pattern

5-(-1) the result would be one more than 5,

so the solution would be 5-(-1)=6

Then we ask, what prcess is happening to arrive at 5-(-1) = 6? The simplified form would be 5+1=6

So it follows that:

5-(-2) = 7

5-(-3) = 8

5-(-4) = 9

The process of following the pattern leads us to conclude that:

a -(-b)= a+b.

Method 2

This method was explained to me by Dr. Barrie Bennett, my M.Ed. professor at the University of Toronto, Canada. He exaplained it this way….

If a postitive represents you liking something and a negative represents you hating something….

+(+4) represents you like to like so like overall you LIKE so, +4

+(-4) represents you like to hate so you overall you hate so, -4

-(-4) represents you hate to hate so overall you LIKE so, +4

This was a great way to relate the integers to a personal method the students could use! Thank you Dr. Barrie Bennett!

After the chlid understands the concept, it’s time to practice. There are many practice sheets online, the fact is that students need to reinforce ideas once they are learned. If you are looking for a fun game that the whole family or class can play, here is a FREE game on Integers.



Do you have other ways to teach why a subtracting a negative is a postive? We’d love for you to share!

Thanks for visiting our Math blog!


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