Math = Love: Teaching Integer Operations with the Integer Operations Work Mat, Colored Counters, and Number Line

Saturday, August 25, 2012

Teaching Integer Operations with the Integer Operations Work Mat, Colored Counters, and Number Line

I'm so excited about my Algebra 1 class next week.  We're starting integer operations.  And, I just can't wait to teach my students how to add, subtract, multiply, and divide integers.

I'm going to cover integer operations in more depth and more slowly than most Algebra 1 teachers would, but it's something I know I have to do.  My students don't have a strong pre-algebra foundation to build on.

The ability to successfully add/subtract/multiply/divide integers is going to be crucial for their future success at solving equations and graphing.  If my students do not master these basics, they will not be able to solve equations, even if they understand the concept of solving an equation.  When they subtract three from both sides of the equation or multiply both sides by negative five, that needs to be done correctly, or their answer will be incorrect.

My Algebra 2 students never mastered integer operations.  Yesterday, I reviewed how to combine like terms, and the majority of their mistakes could be traced back to not knowing how to add, subtract, or multiply integers.  My Math Analysis students have been struggling with the concept that subtracting a negative is the same as adding a positive.

I don't want my Algebra 1 students to struggle in the future, so I want to make sure that they fully grasp how to do integer operations.  To achieve this goal, I plan on presenting adding and subtracting integers in 3 different ways.

1. Using colored counters
2. Using the number line
3. Using generalized rules

The other day, I was looking for a game to review exponent rules in my Math Analysis class.  While on Maria Andersen's blog looking at her Exponent Block Game, I found a video of her explaining how to use colored counters.  I already knew that I was going to use colored counters to introduce the concept of adding and subtracting integers.  My pre-algebra teacher taught us that way.  I'd already even ordered bingo chips from Amazon to use as counters.  

However, I watched her video for some inspiration.  And, she used the concept of a "Sea of Zeros."  After I saw it explained this way, I knew I had to use it.

To keep my students organized and engaged, I made a document with a box to place the chips, a box to keep the Sea of Zeros, and a number line.  I want my students to see that you will get the same answer whether you use the chips or a number line.

I printed off 24 copies of the document and laminated them.  Now, they will hold up to multiple classes using them.  And, my students can write on them with their dry erase markers.  This will be especially useful for the number line.

So, I haven't actually taught this lesson yet, but I wanted to share it with the mathtwitterblogosphere.  I'm hoping that by introducing it with manipulatives, my students will discover pattern for themselves.  I'm so excited for Tuesday and Wednesday!

Here's some pictures of my Integer Operations Work Mat in action!

I've included my file if you would like to download it and use it in your own class.


  1. I LOVED teaching integer rules with counters! I think the visual representation clicks so well for students. I had a math coach explain addition with opposite signs as "which has more, how many more?" I still use that idea to this day (in fact, I just used it yesterday). The other manipulative I used was elbow macaroni, ( was negative and ) was positive... when they join () it makes a zero! I love your sea of zeros by the way!

  2. Oh my goodness, you just marked something off my list! I'm teaching this in a few weeks and I had planned it out to do. I love the "Sea of Zeroes" and can't wait to introduce that to my 7th & 8th grade math students! :)

  3. Excellent post! I will be using this representation when I get to Integers with my 7th graders this year.

  4. Thanks so much. I love your approach with integers. The concrete visuals will be very helpful with my students. Thanks again for sharing your ideas.

  5. I love this mat, especially the sea of zeros. I use elbow macaroni too which I colored red and green.

    1. The elbow macaroni is a brilliant idea. Thanks for sharing!

  6. I know this is an old post but I hope that you are still here to respond. What do you for subtraction of negative numbers?? Add the opposite and then Sea of Zeros?? I am teaching 8th grade and they are horrible at this. I want to go back and reteach it! Help!!

    1. We add zero pairs until we have enough to subtract that amount of negatives.

  7. Have you used this same idea when dealing with multiplication and division of signed integers?

  8. Thanks so much! I just used this with a student who learns visually and she mastered adding integers in 20 minutes! This will be a method I use again :)

  9. Hi Sarah!
    For some reason I cannot find the link for this file. I am not sure if it is my computer or not but was wondering if you could send it to me. I am teaching a transition class like you this year for kids not quite ready for algebra 1. I think this will be a great resource for this class.