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Second/Order Of Operations

Order of Operations: Writing Expressions from Words

Practice translating English phrases into mathematical expressions. Focuses on vocabulary like sum, difference, product, and quotient.
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Study Guide

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Practice Questions

  1. The sum of 8 and 2, multiplied by 5
    Show answer

    (8 + 2) x 5

  2. 10 less than the product of 6 and 4
    Show answer

    (6 x 4) - 10

  3. Double the difference of 12 and 7
    Show answer

    2 x (12 - 7)

  4. The quotient of 20 and 5, plus 3
    Show answer

    (20 ÷ 5) + 3

  5. 5 times the sum of 3 and 4
    Show answer

    5 x (3 + 4)

Teacher Resources
Teaching Notes

This is a crucial bridge step before full word problems. Ensure students understand that "less than" often flips the order (e.g., "5 less than 10" is 10-5, not 5-10).

Vocabulary
Translate: Change from one form to another.
Expression: Math problem with numbers and symbols.
Common Mistakes
  • Writing "5 - 10" for "5 less than 10".
  • Forgetting parentheses for "sum" or "difference" when multiplication follows.
  • Incorrect operation choice.
  • Misinterpreting 'less than' order.
  • Missing parentheses for grouping.
  • Ignoring implied order.
Differentiation
SupportProvide a vocabulary key (Sum = +, Difference = -, etc.).
ChallengeAsk them to write their own sentence for a given expression like (10-2)x5.
Discussion Questions
  • What words signal multiplication?
  • Why are parentheses important?
  • How is 'less than' different from 'subtracted from'?
  • Can two different phrases yield the same expression?
Extension Activities
  • Write expressions for stories.
  • Convert expressions to words.
  • Create complex sentences.
Parent Tip

Ask your child to write instructions for a simple task.

Learning Path
Skill Cluster

Algebraic Thinking & Operations

Estimated Time

15 minutes

Skills Practiced
Translating expressionsMath vocabulary