Adding integers with different signs using models

Adding Integers with different signs

Banner math integers.gif


Student will be able to...

  1. Develop real life situations involving integers
  2. Understand how to use models to addd integer
  3. Evaluate addition problems using mental math


  • Let’s recall the definition for integers. Try to think of some examples in your head...
  • Definition: The set of whole numbers and their opposites.
  • Well, In case you forgot what whole numbers is...
    • Whole Numbers: The set of all counting (1, 2, 3, 4, ....) and zero.
  • So, can you think of three examples of an integer?
    • Here are some examples: -45, -11, -2, 0, 19, 100, 3,576...

Real Life Application

  • Integers can be found everywhere around you.
    • Can you think of any examples in which you see integers on a day to day basis? Write down at least three places that integers are used.
  • Some examples:
    • Football game (negative yards)
    • Bank (owing money/in debt)
    • Temperature

Using Models

In mathematics, we like to use models (or representations) to explain a specific topic. Please visit Jamie Woodcock’s page: Models: an Instructional Tool to learn more about models.

In this lesson, we will use “integer tiles to represent integers.” You can make (or find) your very own integer tiles in your house. If you have two different color poker chips, this will work great! If not, use two different colored construction paper. Cut up small squares that are approximately the same size. You should cut at least 15 squares for each color.

For our purposes, we are going to use red “tiles” for negative numbers and white “tiles” for positive numbers. (If using different color, denote one color for negative and one for positive!)

Let’s Add! (Adding integers with different signs)

Now that we understand what integers are and what models are, lets use the models to add integers.

So, if we wanted to add the two integers -7 + 5, how would we represent this using tiles?

Let’s put 7 red tiles and 5 white tiles next to each other to represent this problem.

-7 + 5 tiles.jpg


Can you think of a way to add these numbers? Share your ideas on how you might add your numbers here

One way to look at the models, is to see that a 1 positive tile and 1 negative tile, cancel each other out. Think about it this way, if you have $1 in your pocket, but buy a Gatorade for $1, how much money are you left with? The answer is zero!

This is what we call, “zero pairs.” Make as many zero pairs as you can and then count up what is left! Don’t forget to look at the color of the tile! This will tell us if our answer is positive or negative.

Now, we can add...

-7 + 5 =0 tiles.jpg

-7 + 5 = 2 red tiles = -2

Final answer: -2

  • Challenge:
    • Can you create a real life scenario that represents the integer expression -7 + 5?
    • Mental Math: Can you mentally visualize the problem -3 + 2 in your head? Try to arrange the tiles mentally and find a solution!

Click here to write your example

Now lets do some practice with adding integers using our models with different signs...


  • 1. -8 + 9
  • 2. 10 + -5
  • 3. 4 + -11
  • 4. -6 + 3
  • 5. -15 + 15
  • 6. Word problem: The low temperature for the day in Alaska was -8°F. What was the high temperature for the day if the temperature rose 15°F ? Can you write an integer expression to solve this?

Click here for answers for # 1-6.

Writing: Ask one question you have from the lesson today.