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.