Mastering Multi-Step Problems

---

Curriculum Area and Level

Common Core State Standards for Mathematics (Grade 4)

• CCSS.MATH.CONTENT.4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.

---

Lesson Objective

By the end of this 35-minute lesson, students will be able to:

1. Decode and solve multi-step word problems using addition, subtraction, and multiplication.
2. Determine the order of operations and apply logical reasoning to find correct solutions.

---

Materials Needed

• Whiteboard and markers
• Printed task cards with multi-step word problems (one per student)
• Math notebooks and pencils
• Small whiteboards for collaboration
• Colored counters (optional for visual learners)
• Timer

---

Lesson Outline

1. Introduction and Warm-Up (5 minutes)

Objective: Set the stage with easy mental math while introducing the concept of breaking down multi-step problems.

1. Write a quick single-step word problem on the board:
   “Sally has 5 apples. She buys 4 more. How many apples does Sally have now?”

   • Ask a student to solve it aloud (expected: addition).

2. Layer it with one more step:
   “Then, Sally gives 3 apples to her friend. How many does she have left?”

   • Celebrate answers and introduce the idea of multiple steps in a single problem.

3. Explain today’s focus:
   "Today, we’re detectives! We will solve problems step-by-step, deciding if we need to add, substract, or multiply, and make sure we double-check our answers!"

---

2. Guided Practice: Breaking Down Problems (10 minutes)

Objective: Model how to read, interpret, and solve multi-step word problems.

1. Write the following problem on the whiteboard:
   “Liz bakes 24 cookies. She packs them into 6 bags evenly and sells 3 of the bags. How many cookies does Liz have left?”

2. Walk through the problem step-by-step with the class:

   • Step 1: Identify key numbers and ask, “What is happening first?”
     (Divide 24 cookies into 6 bags: 24 ÷ 6 = 4 cookies per bag)
   • Step 2: Ask, “What happens next?”
     (3 bags are sold, calculate cookies in sold bags: 3 × 4 = 12 cookies sold)
   • Step 3: Final step:
     (Cookies remaining: 24 − 12 = 12 cookies left)
   • Write clear steps on the board to show the flow of logic.

3. Use color-coded circles (or counters) to visually model parts of the problem for support if needed.

4. Ask questions to reinforce understanding:

   • "How did we know we needed division first?"
   • "What would have changed if she sold 5 bags instead of 3?"

---

3. Student Independent Work (12 minutes)

Objective: Students solve multi-step problems on their own or in pairs using strategies taught.

1. Pass out task cards with differentiated multi-step word problems (tailored to varied skill levels within the group of 11 students).

   Examples:

   • Beginner Level: “A gardener plants 4 rows of flowers. Each row has 8 flowers. Then, 5 flowers wilt. How many flowers are left?”
     (Multiplication + Subtraction)
   • Intermediate Level: “Tim earns $15 per week helping at a store. He saves his earnings for 4 weeks and then spends $20 on a toy. How much money does he have left?” (Multiplication + Subtraction)
   • Advanced Level: “A baker bakes 48 muffins. He sells 3 dozen. Then, he bakes 24 more muffins. How many muffins does he have now?” (Division + Multiplication + Addition)

2. Let students work individually for the first 5 minutes, then pair up to discuss their solutions for the remaining time.

3. Encourage them to use notebooks to show written steps and label their operations clearly.

---

4. Collaborative Review and Real-World Fun (6 minutes)

Objective: Reinforce the learning and make connections to real-life situations.

1. Have students share their answers collaboratively on mini whiteboards. Each pair displays their calculated solution and explains their reasoning to the class.

   • Celebrate correct math logic.
   • Offer gentle guidance for errors (e.g., “What step might we have missed here?”).

2. Play “What Happens Next?”:

   • Present a word problem scenario on the board but stop midway through.
     Example: “Sarah buys 3 packs of gum. Each pack has 6 sticks of gum…”
   • Ask students:
     • “What operation is the first step?”
     • Pause and ask for predictions: “What could happen next to make this more of a multi-step problem?”

Students suggest possible scenarios (e.g., “She gives 5 sticks to her friends!”) and map out a plan to solve it.

---

5. Wrap-Up and Exit Ticket (2 minutes)

Objective: Summarize the learning and assess individual understanding.

1. Quick debrief on the board:

   • "What are the three steps to solving multi-step word problems?"
     • 1. Read the problem and underline key information.
     • 2. Decide which operations come first, second, etc.
     • 3. Solve step-by-step and check your work.

2. Hand out a 1-question Exit Ticket:

   • “A bus has 30 seats. 18 people get on. Then at the next stop, 7 more people get on. How many empty seats are left?”
     (Subtraction + Addition)

3. Collect the responses to gauge understanding and identify students to support further.

---

Differentiation Strategies

• For Advanced Learners:
  Provide more complex problems (e.g., involving three operations or larger numbers).
• For Struggling Learners:
  Offer visual aids like counters or break problems into smaller, scaffolded parts. Pair them with peers for support.
• For Kinesthetic Learners:
  Use movement-based activities, like acting out problems with physical items (e.g., chairs as seats on a bus).

---

Assessment

• Ongoing observation during independent work and collaborative review.
• Responses on the exit ticket to measure individual progress in solving multi-step problems.

---

Extension Activity (Optional)

Students create their OWN multi-step word problems based on a real-life scenario (e.g., shopping, cooking) and exchange them with a partner to solve.