Combining like terms (CLT) is fundamental to solving equations. Even if I include the distributive property during this lesson, I always give students at least 1 full period to process and practice before we move on to equations. Let’s be honest, it usually takes a few days of warm-ups before they start to fully get it. Just because I teach it doesn’t mean they get it…. right away, anyway.
CLT gives you an opportunity to build student understanding of a few things:
- Any variable with no coefficient has an invisible 1!
- Be consistent! Ask about it. Model it. Write it in yourself.
- Insist that the kids do too.
- Psst – this really helps with negative signs months later when we start rewriting standard form linear equations in slope-intercept form
- A term includes the positive or negative sign in FRONT of the number/variable!
- Too often they think the sign at the back is the one that counts…
- Also, there are far too many kids who subtract 5 from 17 on the left side of an equation by writing – in front of the 17, and then 5 in front of that. *facepalm*
There are so many ways to combine like terms:
- Use commutative property to rearrange terms so all like terms are together
- Stack all like terms vertically to add them
- etc, etc.
But my favorite (because it’s something I can consistently get kids to do until they develop a true understanding of terms) is to BOX TERMS and COMBINE!
A few tricks:
- Start with colored pencils. Pick one for each type of term.
- Use shapes to distinguish one term from another: boxes, circles, triangles underlining, squiggly underlining…. really, anything the kids want to use! They won’t always have colors readily available.
- Box the sign in front! Insist that they do too.
- Focus on one type of term at a time. In my example, I circled the c’s first, then wrote down their sum. I boxed the a’s next and wrote down their sum, etc.
- I don’t generally make kids re-copy the problem. The less “busy” work there is, the more they’re likely to be consistent in following the same process and show their work.
Psst… I’ll tell you a not-so-secret secret. And I know this is mathematical heresy to some of you out there… but I let kids use calculators if they need to. (Real calculators. Not the ones on their phones – it’s too easy for them to get distracted by social media and music.) Don’t hate me! Yes, there is a time and a place to practice math facts. You can build drills into your class as needed. But kids have been practicing basic math facts since elementary school. If they don’t get it now, it’s something they’ve struggled to master. As an Algebra teacher, I am trying to build algebraic understanding, and sometimes students need tools like calculators and times tables in order to access the algebraic side of their brains.
Good news, though! I find that students begin to strengthen their math facts as we practice simplifying expressions and solving equations throughout the year. Consistent practice means they begin to realize that – 5 * 1 will always be – 5.