Sixth Grade · Math · week 22

Combining like terms for equivalent expressions

Identify and combine like terms, and use the distributive property to generate equivalent expressions.

Two expressions are equivalent if they give the same value for every substitution, even though they look different. 2n + 3n and 5n are equivalent - they always compute to the same number.

"Like terms" have the exact same variable part - 4n and 7n are like terms, but 4n and 7n^2 are not. Combine like terms by adding or subtracting their coefficients, the numbers in front.

The distributive property also builds equivalent expressions: a(b + c) is always equivalent to ab + ac. Use it to expand parentheses before combining like terms.

📋 For the teacher
Teach it (10–15 min):
  • Use a physical sort - write terms on cards and group the "like" ones by matching variable part.
  • Always distribute BEFORE combining like terms when parentheses are present; order matters.
  • Test whether two expressions are equivalent by substituting the SAME number into both and comparing results.
  • Point out that only the coefficient changes when combining like terms - the variable part never changes (n + n = 2n, not 2n^2).
Talk about it:
  • What makes two terms "like terms"?
  • Why do you distribute before combining like terms?
  • How can substituting a number check whether two expressions are truly equivalent?

Mastery looks like: They combine like terms correctly and use the distributive property to simplify expressions with parentheses, and verify equivalence by substitution.

Common stumbles: Combining terms that are not actually alike; forgetting to distribute to every term inside the parentheses.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

FractionsSlice bars and circles into equal parts and compare them.try →AdditionSee groups combine — with counters, blocks, and the number line.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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