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Two-step word problems Knowledge-Based Study

Math · Number Sense & Operations · Math · Addition & Subtraction

Math topic explanations on Two-step word problems.

Study notes

  1. What Is a Two-Step Word Problem?

    A two-step word problem requires solving an unstated intermediate question before you can answer the main question. If you perform only one addition or subtraction, you have found only a partial result.

    The Four-Stage Strategy

    • Read and identify the target: Determine exactly what the final question asks for.
    • Find the hidden question: Ask yourself, "What number do I need first before I can find the final answer?"
    • Execute Step 1: Calculate the intermediate total or difference.
    • Execute Step 2: Use the result from Step 1 with the remaining information to solve the final question.

    Pattern 1: Add, Then Subtract

    In many real-life situations, quantities are combined into a single total before an amount is removed or compared.

    Worked Example

    A school library had 48 fiction books and 35 non-fiction books on display. By the end of the day, students borrowed 29 books in total. How many books remained on display?

    1. Identify the hidden question: How many books were on display altogether before any were borrowed?
    2. Step 1 (Add): Find the total starting books.
      48 + 35 = 83 books
    3. Step 2 (Subtract): Subtract the books that were borrowed.
      83 - 29 = 54 books

    Final Answer: 54 books remained on display.

    Pattern 2: Subtract, Then Subtract or Add

    Some problems track a quantity as it changes multiple times over time.

    Example: Two Consecutive Decreases

    A baker prepared 90 muffins in the morning. He sold 34 muffins to a café and 28 muffins to walk-in customers. How many muffins were left?

    Method A: Step-by-Step Subtraction
    • Step 1: Subtract the first group sold: 90 - 34 = 56 muffins remaining.
    • Step 2: Subtract the second group sold: 56 - 28 = 28 muffins remaining.
    Method B: Totaling the Reductions First
    • Step 1: Combine all muffins sold: 34 + 28 = 62 muffins sold.
    • Step 2: Subtract the total sold from the starting amount: 90 - 62 = 28 muffins remaining.

    Both methods yield the same correct result: 28 muffins.

    Common Mistakes to Avoid

    • Stopping after Step 1: A frequent error is writing down the intermediate answer as the final answer. Always reread the question to ensure you answered what was asked.
    • Choosing the wrong operation: Pay close attention to action keywords and relationships. Words like "fewer than" indicate a comparison (subtraction), while "in all" often signals addition.
    • Losing track of labels: Label each calculation with its unit (e.g., "muffins sold", "books left") so you know what each number represents.

    Verification Checklist

    Once you find your solution, check that your answer is reasonable. Estimate the numbers by rounding to the nearest ten to confirm your exact answer is close to your estimate.