Modeling Subtraction Algebraic Equations

If you happened to use the packet I made for modeling addition algebraic equations (which you can find here), leave a comment to tell me how it went!

Our next skill was to solve algebraic equations that were subtraction. For this lesson, you can use the positive and negative counters that I included in the packet here for addition algebraic equations, but I just had my students draw the models (if your students need them, I would use them).

I treat subtraction in algebraic equations the same as I do with integers. As an algebra teacher, I found myself having to basically rewire their brains because the prior year teacher just told them that if the problem was subtracting, they just had to add. WRONG! Complex equations don’t work that way. I always teach my students that there is a difference between operations and signs. A minus sign is not a negative sign. Teaching them that from the beginning helps them in the long run. I also teach my students that a negative sign means “the opposite of.”

So…..with that being said, I have them change the subtraction sign to an addition sign and change the sign of the number after that operation. For example, x – 4 = 10 would then become x + (-4) = 10. This is how you work with integers, and your students will eventually encounter integers in their equations. Just because they may not this year, they will next year. Now ask your students to model that either with their cup and counters (positive and negative counters) or have them draw the model. They should have a cup and four negative counters on the left and ten positive counters on the right. Explain to your students that you need the cup all by itself so that you can see exactly how many counters equal that cup. Ask them how they would get rid of those four negatives. Some will get it right away, while others will take longer. I give them a few minutes to guess and try to get it. They need to add four positives in order to make zero pairs. This they should remember from integers (if you have taught them integers). If you have not taught them integers, you should explain that a negative and a positive make a zero pair and zeros can be removed without changing the value. After they add four positives to the left side, their balance is no longer equal. They must add four positives to the other side.

Here is an example that you can print off as a guide if you need it. Modeling Subtraction Algebraic Equations PictureThe bottom picture is what I have my students draw. So….this is how I teach subtraction algebraic equations. After learning addition and subtraction algebraic equations, we did my Panda Pirate Find. My students LOVE this activity!!! It is such a joy to watch them wonder the room looking for the partners. EVERY one of my students participates and loves it. Here is a link to that activity. You can get it in my Teachers Pay Teachers store for only $2.50.

Panda Pirate Find for adding and subtracting equations picture


Let me know in the comments how this worked out for you!! Thanks for reading!!

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5 Responses to Modeling Subtraction Algebraic Equations

  1. Jessica says:

    So I’m guessing you teach integers before you teach equations. My problem is that I haven’t taught integers yet and when I do I won’t be teaching adding and subtracting them. Any ideas for that?

    • Andrea Kerr says:

      I would still teach them to solve subtraction equations by changing the subtraction sign to an addition sign and making the second number a negative. They should still be able to grasp the fact that a negative one and a positive one would make zero. That would be my suggestion. What grade to you teach? I know so many teachers just teach them to do the opposite operation, and that works when you don’t have integers. I always want them to understand the difference between a subtraction (operation) sign and a negative sign. It helps them so much when they start solving more complex equations. Thank you for your comment! Let me know what you decide. I would love to hear!

  2. Stephanie Norton-McDonald says:

    Your blog is seriously a life saver! I am a first year teacher in Nebraska and I look forward to receiving your emails regarding a new post! This year we have been doing mini lessons in solving equations in preparing for the state assessment. It has not been going well at all for me or my students. Next week we are starting the chapter in the book on solving equations and I am looking forward to incorporating everything you have to offer. Please keep up the good work! It is truly appreciated!!


  3. Erin says:

    I teach resource math classes and intervention math classes to 6th graders. I am constantly working and thinking about how to make math concrete. THANK YOU for this blog!!!! I have been on spring break this last week and have been stressed on how I was going to teach my kids to do subtraction equations AND make it make sense conceptually. Hopefully this week will go much better than it would’ve had I not found your blog!

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