Seventh Grade · Math · week 14

Order of operations with negative numbers

Apply the order of operations accurately to expressions containing negative numbers, parentheses, and multiple operations.

Order of operations still runs the show: parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. Negative numbers do not change this order at all -- they just require extra care with signs at each step.

The safest habit is to rewrite every subtraction as "adding the opposite" before you start, so the whole problem becomes a chain of additions and multiplications with signed numbers, which are easier to track.

📋 For the teacher
Teach it (10–15 min):
  • Underline or circle whatever is inside parentheses first, every single time, before anything else happens.
  • Rewrite every subtraction as "plus the opposite" as a first step -- it removes a whole category of sign mistakes.
  • Go left to right for same-priority operations (like two multiplications in a row) rather than jumping around.
  • Check the final sign by asking "does this answer's sign make sense" as a fast gut check.
Talk about it:
  • Does having negative numbers change the order of operations rules?
  • Why is it helpful to rewrite subtraction as adding the opposite first?
  • What always happens first in an expression that has parentheses?

Mastery looks like: They correctly apply order of operations to multi-step expressions with negative numbers, tracking signs accurately at each step.

Common stumbles: Doing addition or subtraction before multiplication or division; mishandling a sign when parentheses are removed.

See it visually

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

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