Sixth Grade · Math · week 21

Evaluating expressions by substitution

Evaluate algebraic expressions, including those with exponents and multiple variables, by substituting given values and following order of operations.

To evaluate an expression, replace each variable with its given value, then follow the order of operations: parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right (PEMDAS).

When a variable is replaced by a number, put the number in parentheses first, especially with negative values, so the substitution is clear before you calculate.

Expressions can have more than one variable, or include exponents like n^2 (n squared, meaning n × n). Substitute every variable before doing any arithmetic.

📋 For the teacher
Teach it (10–15 min):
  • Insist on the parentheses-substitution habit - replace the letter with (value) before calculating anything - it prevents sign errors.
  • Review PEMDAS as a refresher, with special attention to exponents coming before multiplication.
  • For two-variable expressions, substitute BOTH values before doing any arithmetic, rather than calculating with one at a time.
  • Have them double-check by re-substituting and recalculating if the first pass feels shaky.
Talk about it:
  • Why is it helpful to put a substituted value in parentheses?
  • In what order do you handle exponents versus multiplication?
  • How would the answer change if a variable's value were negative?

Mastery looks like: They correctly substitute given values into an expression, including exponents and multiple variables, and evaluate using order of operations.

Common stumbles: Multiplying before applying an exponent; forgetting parentheses around a negative substituted value and mishandling the sign.

See it visually

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

ExponentsRepeated multiplication and how fast powers grow.try →MultiplicationEqual groups and arrays make products finally click.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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