Often, middle and high school teachers find themselves trying to teach a skill, only to find that their students have still not mastered Adding Integers. Here are 3 different methods to teach this foundational skill.
Counter Chips
Counter chips have two sides, one side is red and the other is yellow (sometimes it’s another color). Normally, we choose red to represent a negative integer, and yellow to represent a positive integer.
Typically, you should begin by having your students think about real world examples of positive and negative integer. For example
- Earning money versus having debt
- Above sea level versus below sea level
- Gaining and loosing yards in football
Next you want to teach your students that a positive one and a negative one combine to equal zero (they cancel each other out). You can use your real world examples to illustrate this point.
For example, if you owe someone $1 (meaning you have -1 dollars), and then you gain $1 (a positive one) you would use that money to pay off your debt, and the result would be that you had 0 dollars.
Then, model this example using counter chips.
Finally, have your students model addition problems using the counter chips. You should begin with adding integers of the same sign.
After you have modeled a few problems with the same integers. You must proceed to the more difficult task of adding integers with the different signs. Remind your students that a positive and negative integer cancel each other out.
First have your students model the problem.
Then show the students how to solve by having students make one positive counter chip and one negative counter chip cancel out.
Have your students model several other problems. Making sure to first build the problem before solving.
Afterwards, put the examples onto the board, of all the problems that you have done, and have the students see if they can discover the rule for adding integers with opposite signs.
Number Lines
It is worth the time to teach your students how to properly number the number line, as they often don’t know the correct order.
Have your students fill in the dashes between -10 and -5, and between -5 and 0, etc. Then remove the -5 and have the students fill in all the dashes. Finally, have your students draw their own number line numbered -10 to 10, or -20 to 20 going by 5’s.
Don’t assume that all your students know how to setup the number line, spend the time to reinforce this skill, as it will help them understand negative numbers, and thus increase their number sense.
To teach this skill, ask students how they would get from 0 to 5. Or from 0 to -5.
The goal is to get them to realize that you move to the right for positive, and to the left for negative.
Then begin teaching how to use the number line for addition problems by modeling problems that they already know how to do. So first show them how to add positive integers on the number line:
Then model the similar skill of adding negative integers:
Finally, model how to add integers with opposite signs on the number line:
Again, have the students practice multiple examples, each time modeling on the number line. Then, put the examples on the board, and help students ‘discover’ the rules to adding integers with the same and opposite signs.
The Absolute Value Rules
Some people work better when the rules are simply explained to them, and then examples are given. So give a brief tutorial or refresher on absolute values and then teach students the rules for adding integers:
To add integers with the SAME SIGN, add their absolute values
If both integers are:
positive, the answer is positive
negative, the answer is negative
To add integers with DIFFERENT SIGNS
subtract their absolute values
The answer will have the same sign as the LARGER integer
Same Sign Examples:
-4 + (-3) = -7 4 + 3 = 7
Opposite Sign Examples
-4 + 3 = -1 4 + (-3) = 1
Give lots of practice on all of the above and be sure to give immediate feedback so students immediately recognize when they are making a mistake.
Want More Great Resources on Integers?
Read these articles on helping your students master integer skills.
And check out our reteach worksheets and station resource pack below
Our Station Resource Pack for Adding Integers
(click image to learn more)
