Grade 6/Division
Mixed Four Operations Word Problems (877)
Students solve real-world stories that mix all four operations: addition, subtraction, multiplication, and division. Many problems have two steps, so students must decide which operation to use first and check that their answers make sense. All division situations are written so the answers are whole numbers, keeping the focus on choosing operations, not on remainders.
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Quick Tip
Some problems have two steps. Write the equation for each step, then circle your final answer.
Teacher Resources
Teaching Notes
Use these mixed-operation problems to help students slow down, read carefully, and plan their steps. Have them highlight or underline key words that show whether they should add, subtract, multiply, or divide. Encourage drawing quick sketches or bar models for tricky problems. Model thinking out loud: “First I will..., then I will...”. Emphasize checking if the final answer makes sense in the story.
Vocabulary
Mixed Operations: Using more than one math operation.
Order of Operations: Rules for solving problems with multiple steps.
Common Mistakes
- Solving only one step in a two-step problem and forgetting the second step
- Choosing the wrong operation because of a single keyword (like always subtracting with the word "left")
- Not reading the final question carefully and answering the wrong thing
- Ignoring units and writing bare numbers without labels
- Missing a step
- Choosing incorrect operation
- Calculation errors
- Misinterpreting keywords
Differentiation
SupportProvide graphic organizers that break problems into Step 1 and Step 2 with space for equations. Work through the first few together as a class. Allow students to use manipulatives or drawings to represent the situation. Offer sentence stems such as 'First I ____, then I ____ so the answer is ____ .'
ChallengeChallenge students to write their own two-step word problems that mix operations and exchange them with a partner to solve. Ask them to estimate answers before solving and check if their exact answer is reasonable. Extend some problems by asking “What if...?” follow-up questions that change one of the numbers.
Discussion Questions
- How did you decide which operation to use first in a two-step problem?
- What clues in the story told you that you should multiply or divide instead of add or subtract?
- Why is it important to check whether your answer makes sense in the real situation?
- How are division and multiplication connected in these problems?
- How do you decide which operation to use first?
- What clues help you find the operations?
- How can you check your answer?
- Can this problem be solved another way?
Extension Activities
- Have students sort problems by main operation or by one-step vs two-step and discuss their choices.
- Turn selected problems into short skits where students act out the story, then solve.
- Create math journals where students write about how they knew which operations to use.
- Use exit tickets where students invent a new mixed-operation problem similar to one from the worksheet.
Parent Tip
Help your child identify the math operations needed for everyday tasks.
Learning Path
Skill Cluster
Problem Solving & Operations
Estimated Time
25 minutes
Skills Practiced
addition subtraction within 1000multiplication facts to 12division facts to 12multi step word problems
Prerequisites
- Single-Step Word Problems (All Operations)
- Basic Multiplication and Division Facts
- Addition and Subtraction with Regrouping
Next Steps
- Multi-Step Word Problems (with Remainders)
- Word Problems with Fractions or Decimals
- Writing Expressions from Word Problems
- Multi-Step Word Problems with Remainders
- Solving Word Problems with Estimates
- Problem Solving with All Operations