🔢 MathGrade 4Lesson 13
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Apply Order of Operations

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Learning Objectives

  • 1State the order of operations: parentheses, multiplication and division, then addition and subtraction
  • 2Evaluate expressions with two or more operations using the correct order
  • 3Identify errors caused by applying operations in the wrong order
  • 4Write and solve expressions using parentheses to change the value
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Mini Lesson

When an expression contains more than one operation, the order in which you calculate matters. Mathematicians follow a set of rules — the order of operations — so that everyone gets the same answer. For Grade 4, the rule is: parentheses first, then multiplication and division left to right, then addition and subtraction left to right.

The Order of Operations Rule

  1. Parentheses first — calculate whatever is inside brackets before anything else.
  2. Multiplication and division next — work left to right.
  3. Addition and subtraction last — work left to right.

Without Parentheses

  • 3 + 4 × 2: multiply first → 4 × 2 = 8, then add → 3 + 8 = 11.
  • If you added first instead: 3 + 4 = 7, then 7 × 2 = 14 — that is wrong.
  • The correct answer is 11, not 14.

With Parentheses

  • (3 + 4) × 2: parentheses first → 3 + 4 = 7, then multiply → 7 × 2 = 14.
  • Parentheses change the value of the expression.
  • 3 + 4 × 2 = 11, but (3 + 4) × 2 = 14 — different results!

Real-Life Example

  • You buy 2 books at $5 each and 3 pens at $3 each.
  • Correct: 2 × $5 + 3 × $3 = $10 + $9 = $19.
  • Wrong: (2 + 3) × ($5 + $3) = 5 × $8 = $40 — this ignores the separate prices.
Wrong order vs correct order for 3 + 4 times 23 + 4 x 2Wrong: add first3 + 4 = 77 x 2 = 14= 14 (wrong)Correct: x first4 x 2 = 83 + 8 = 11= 11 (right)Multiply before you add!
Parentheses change the answerParentheses Change the Answer(3 + 4) x 2Step 1 (brackets first):3 + 4 = 7Step 2 (multiply):7 x 2 = 1414Without brackets: 3 + 4 x 24 x 2 = 8, then 3 + 8 = 11Same numbers, different answer: 11
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Tip: always scan the expression for parentheses first, then look for × and ÷ before doing any + or −.

Vocabulary
Order of operations
A set of rules that says which operation to do first in a math expressione.g. Order of operations: brackets, then × and ÷, then + and −.
Brackets
Parentheses that group operations to be done firste.g. Brackets in (2 + 3) × 4 mean add first.
Expression
A math statement made of numbers and operations, with no equals signe.g. 5 + 2 × 3 is an expression.
Evaluate
To work out the value of an expression by following the rules in ordere.g. Evaluate 5 + 2 × 3 = 11.
Operation
One of the four actions: add, subtract, multiply, or dividee.g. Multiplication is the operation done before addition.
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