Combining Like Terms

 

Combining like terms is one of those topics that students either get or struggle with. The standard way to teach it is to have students identify like terms, rearrange the terms so like terms are next to each other, simplify by combining like terms, and the remaining terms constitute your answers.  Sounds quite straight forward by it doesn't always work that way.

It doesn't always work that easily because some students have difficulty understanding the concept of like terms.  One way to help students identify like terms is to have them use circles, squares, triangles, diamonds, and other shapes. They would circle all terms that are constants, terms with x's are inside a square and x^2 are inside triangles.  This way they students can rewrite the terms so those in the circles are next to each other, squares, next to each other, and triangles gathered together.  

Another way is to use either physical or digital sticky notes in different colors.  Each color represents a type of terms such as constants, x's, or x^2's so write each term on the appropriate color so that when it is time to rearrange the terms, students can put terms on the same color notes together to make it easier to distinguish among terms.  

Then there is using base 10 blocks with the individual squares representing ones, the 10's become the x's, and the 100's represent the x^2's, so 2x^2 + 3x + 4 would be represented by 2 - 100 squares, 3 - 10 strips, and 4 - individual squares.  Once they've translated the terms into the base 10 blocks, the student can physically see which terms are alike and it makes it easier for them to combine like terms.  

Once students have been instructed in the concept of combining like terms, it is time to include a variety of activities to reinforce and practice this.  One activity is to whip out a game of combining like terms bingo.  Prepare a variety of cards with answers and pass the cards out to the students.  The other possibility is to like the answers on the board, hand out blank bingo cards, and have the students fill out their cards with the answers they've chosen from the board.  Always have more answers than squares so that students will not have all the same answers.  To start the game, have a container full of problems and draw one out.  Write it on the board and have students come the like terms.  When they have the answer, they check their cards to see if they have the answer.  When they are beginning, I always go over the problems so struggling students can see how to do it.  As they gain skill, I no longer of it or only do it for problems where many students struggle.

When students are more proficient at combining like terms, it is time to enjoy either jeopardy or Kahoot games.  For Jeopardy games, I like having students work in pairs and write the answer on a whiteboard so all the students who get the right answer will receive a score otherwise students who take a bit longer do not feel penalized.  

This is also the perfect item for students to do a scavenger hunt activity.  On a piece of paper, write down a problem and an answer but not the answer to the problem on this paper.  Write the answer down to another  problem.  On the next sheet, record the problem to the answer on the other paper, and write down the answer to a different paper.  Continue till you have 10 to 15 papers completed and post around the room.  Give each student an answer sheet so they can start at any paper.  They work the problem, and then search for the answer.  Once they find the correct answer, they do the problem on that page and search for the matching answer.  Continue until each students has worked all the way through the problems.

These are some ways for students to practice combining like terms.  Let me now what you think, I'd love to hear.  Have a great day.

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.