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3/3/2018 13 Comments

Teaching Adding & Subtracting Integers

How to Teach Integer Addition and Subtraction Through Hands-On Exploration

adding and subtracting integers - a guided investigation approach
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​Teaching your students to add and subtract integers can be tricky.  The concept of zero pairs does not come easily to many students, so it really helps to have awesome, engaging lessons prepared when introducing this topic!
 
The hands-on method described here is great for the first introduction to integer operations, but is also a great re-teaching strategy for those 10th graders who still are frustrated with integers.

It can take being exposed to integers over and over for years before some students really gain confidence.

Try this lesson for ANY level of students and approach it as if they have never seen integer addition or subtraction before (whether they have or not!)


To improve your students’ understanding, I have two major recommendations:
  1. Provide manipulatives to teach zero pairs
  2. Incorporate inquiry when introducing this concept
 
Teaching Zero Pairs with Manipulatives
 
To help students grasp the concept of zero pairs, I think manipulatives are essential.  If you’re new to this method check out the videos below.  Manipulatives can turn an abstract concept into something students can touch and see clearly.
 
You choose any manipulatives of your choice to represent positive and negative numbers, but I love using tile spacers!  You can buy a bag of 100 from the hardware store for under $2.00.  Cut half of them to be minus signs, and give each pair of students ten "positive" pieces and ten "negative" pieces.
how to teach integers with a hands-on approach - manipulatives for negative numbers
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​If you want to use something readily available, try using manipulatives in two colors - any little counting teddy bears or even cut up paper squares will work
 
Watch the video below to see how to set your class up to discover the rules for integer addition and subtraction.  Then, download the charts below for your students to use for the activity.  (Working in pairs is best for this lesson!)
 
As you can see in the video, using manipulatives to represent integers and zero pairs help to break down a complicated concept.   Once you set your students up this way, they’ll have the groundwork to explore and test different cases (see downloadable worksheets below).  
free lesson on adding and subtracting integers
free lesson download - developing rules for integer addition and subtraction
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Inquiry
 
When you use an inquiry-based approach in your classroom, students discover mathematical properties for themselves.  They investigate and explore, instead of sitting and listening to you presenting a lecture.  They can discover the concept themselves, helping them to internalize the new information.
 
Inquiry helps students develop independent problem-solving skills, deepen their understanding about a specific topic, gain new math confidence, and more! Click here to read more about the benefits of Inquiry Lessons and how to use them.
how to teach adding and subtracting integers
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​After I use manipulatives to teach the concept of using zero pairs to add and subtract integers, I have my students get to work on developing rules for this method.  Tell your students that we would not want to use this strategy for numbers in the hundreds.  Then, ask your students, “Why not?”
 
Explain that is going to be their job to write the rules for adding and subtracting integers;  we need rules that ALWAYS work.  I like to have my student write rules in "If ___, then ___" format.
adding and subtracting integers - a free hands-on lesson with video and worksheet download
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​Click here to download the free worksheets to guide your students through this task in pairs or in small groups.
 
 
Hopefully, my two favorite methods for teaching students to add and subtract integers resonate with your students and they learn this concept in a breeze!  Do you have any tips on teaching adding and subtracting integers?  Let us know in the comments below!
 
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More Inquiry-Based Explorations:

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13 Comments
Tricia
9/3/2018 10:56:45 pm

I love this method! Last year was my first year teaching middle school math, and I didn't do a great job explaining adding integers. I will be using this when teaching my new 7th graders this year. Thank you.

Reply
Math Giraffe link
9/4/2018 06:54:22 pm

Hi Tricia,
Thanks so much for commenting! I am so glad you can use this :)
Have an awesome second year! I hope everything goes great for you.
Integers are a sticking point and a struggle, so that is really common -- no matter what it takes a lot of re-teaching and a variety of tricks and methods up your sleeves for this topic :)
Enjoy!
-Brigid

Reply
hwoodard
2/16/2022 12:53:27 pm

Where do I buy the positive/ negative manipulatives?

Reply
Amy
2/16/2022 08:30:58 pm

The ones she's using are tile spacers that you get at both Home Depot and Lowe's. I have orange ones that are the "plus" and then got the same size in white where I cut off the "wings" to make the negatives.

You can also buy Algebra Tiles. Do a web search for "Algebra Tiles" and they should come right up.

Hope this helps.

Kayla
9/24/2018 03:55:55 pm

Do you have a video fro multiplying and dividing integers using this method?

Reply
Math Giraffe link
9/25/2018 08:26:03 am

Hi Kayla,
Thanks for asking! No, I don't, but it can be modeled.
It's just trickier. I have not done it with students unless they ask.
There are probably videos out there on how to model multiplication and division this way though.
It's a bit more complicated than the adding and subtracting. :)
Have a great week,
-Brigid

Reply
Lisa
10/14/2018 04:29:41 pm

I just taught this and the students loved using the manipulatives.

I have an unrelated question. How did you shoot this video? Did you use a camera or cell phone? How did you set it up?

I want to start making videos for my class and have no idea how to start.

Thanks

Reply
Math Giraffe link
10/15/2018 12:58:22 pm

Hi Lisa,
Thanks! I am so glad it worked well for your class.
I just use my iphone.
I have a foldable lap desk / standing desk thing (made of metal and with hinged legs for different options of height).
I just stand it over the area I want to show, almost like using an elmo projector.
Then I can press record and have it sit overtop while I use both hands. Pretty simple! :)
I am sure there are fancier ways, but I just use what I've got. Happy fall! Thanks for asking.
-Brigid

Reply
connie
3/2/2019 06:31:09 pm

Hi, thank you for this video. I have a question about the negative minus negative problems. Is there a reason you don't change it to a plus, negative so they can just add more negatives instead of adding a zero pair? Thank you.

Reply
Math Giraffe link
3/3/2019 09:53:12 am

Hi Connie,
Mainly just for building understanding. It helps to see the "WHY" behind each type of problem. I do show them how to change it, but then explore the concept in both formats so they can build that deeper knowledge and see the process both ways. Thanks for asking! Have a great week,
-Brigid

Reply
Amy
1/11/2020 03:39:36 pm

I've taught math a long time but just started with middle school this year. I've used Algebra Tiles but my packs don't have a lot of the individual "ones" in them plus they cost a bit more than heading over to Home Depot (actually we have quite a few around here, too). The one thing I'm going to take from the Algebra Tiles and use with this is to go buy some orange/red ones like you have and cut them up to be only the negative sign. What I like about the Algebra Tiles is that they use color for the positive/negative with red being for the negative. What I like about your method is that they are actual positive/negative signs. So, I can have the best of both worlds! Thanks for sharing this.

Reply
Math Giraffe link
1/14/2020 08:18:24 am

Hi Amy,
That sounds like the perfect way to get the best of each manipulative! :) Great plan.
I hope this works well for your students. Thanks so much for reading, and thanks for your comment!
Have a wonderful day,
-Brigid

Reply
Betsy Mays link
3/15/2021 07:57:17 pm

I love your examples of problems with manipulatives and creating zero pairs. I use pennies, heads are positive and tails are negatives. My students can then draw the problems if manipulatives aren't available.
I have also created 2 fun integer math games to help kids become proficient with this important standard. Absolute Zero and Hunch - check them out at gamesbyabsolutezero.com

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