Visualizing Combining Like Terms

We have been told to provide visual representations for everything we teach in math.  Unfortunately, the visual of us use tends to be pointing out the squared or cubed associated with the variable.  We assume students know the difference between them but if that is the only way they've seen the terms, they wouldn't know how to visualize them. Without a visualization, they won't see the differences between a squared or a plain x or a constant.  

I took a class this semester on teaching math either remotely or via a hybrid model.  In it she said graphs work as visualizations but what do you use to show the differences between x^2 and x's visually.  I had to think about it but realized I could have students use either algebra tiles or jam board to help them visualize why you cannot combine the two. 

I looked at Jamboard and it is possible to create the large squares, rectangles, or small squares in different colors so they have one color for positive and another for negative.  It would require setting up ahead of time and making copies for each student.  

Jamboard allows students to move pieces around so they can group the like terms and then count the final total for each group.  This can be done by students via distance learning as easily as ones in class.

On the other hand, an easier solution is to use an Algebra Tiles app or online version so students can make as many x^2 as they need in two different colors so they can easily identify positive and negative terms.  They can make as many of each as is needed and move them around  to work out problems.

In addition, this type of visualization can help connect the dots on why the terms in the second part has to change signs for each term following the subtraction sign.  It supports the explanation of subtracting from the original.  

I realize that both of the suggest apps rely on having a mobile device and possibly the internet but what about students who only have a phone with limited data or no internet access?  How do we allow them to do the same exploration as those who have the devices.  I don't have Algebra Tiles as part of my classroom supplies and if I did, I don't think I'd be allowed to loan them out.  Fortunately, there are templets available on the internet.  These can be used to copy tiles onto colored paper to make a physically based set.  There are templets here or here.

Since many teachers are both teaching virtually and have students who do not have internet or computer access, we may have to provide some sort of manipulative with instructions so that we meet the needs of all our students.  This version might require us to send home Algebra Tiles, a mat for them to work on and directions both written and visual.  If a student has a computer at home without internet, the teacher can send a thumb drive home with the video.  If the student does not have a computer, one can create a series of photos, print them out, and send them home.

I have to create two packets worth of work for the first two weeks after Christmas break and I have to figure out how to create the support materials since at least half my students do not have internet access so I'm figuring out how to do it.  Let me know what you think, I'd love to hear.  Have a great day.