Solving Division with Multiplication

Curriculum Area & Level

Subject: Mathematics
Grade: 3
Standard: McGraw-Hill Grade 3 Mathematics
Topic: Using Multiplication to Solve Division Equations

Lesson Duration

Total Time: 30 minutes
Class Size: 10 students

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Lesson Objectives

By the end of this lesson, students will:

1. Understand the relationship between multiplication and division.
2. Use multiplication to solve division equations.
3. Identify missing numbers in division equations by reversing operations.
4. Apply their knowledge to solve real-world division problems.

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Teaching Strategies

• Hands-on Learning: Using manipulatives for tactile understanding.
• Guided Discussion: Encouraging student explanations.
• Think-Pair-Share: Peer collaboration for problem-solving.
• Game-Based Learning: Reinforcing concepts through interactive activities.

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Teaching Materials & Resources

Materials Needed:

• Whiteboard & markers
• Multiplication & division flashcards
• Small counters (buttons, beads, or small cubes)
• Number line (printed or drawn)
• Student notebooks & pencils

Resources:

• McGraw-Hill Grade 3 Mathematics textbook
• Pre-made worksheets with multiplication and division problems
• Teacher-created word problems

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Warm-Up (5 minutes)

Activity: "Quick Think Multiplication"

1. Write a simple multiplication fact on the board (e.g., 4 × 3 = ?).
2. Ask students to answer quickly.
3. Repeat with different numbers.
4. Next, write a division fact related to one of the multiplication facts (e.g., 12 ÷ 4 = ?).
5. Ask students to identify the connection between multiplication and division.

Purpose: Prepares students for the main lesson by reinforcing fact families.

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Presentation (10 minutes)

Step 1: Introduction to Fact Families

• Write a multiplication and division fact family on the board:

  Example:

  • 4 × 3 = 12
  • 3 × 4 = 12
  • 12 ÷ 4 = 3
  • 12 ÷ 3 = 4

• Explain that division is the opposite of multiplication.

Step 2: Problem-Solving with Multiplication

• Show a division equation with a missing number:
  ? ÷ 5 = 6
• Ask students how multiplication can help.
• Have students rewrite the equation as a multiplication problem:
  ? = 5 × 6
• Solve together: ? = 30

Teacher Tip: Use counters or number lines to help students see the connection.

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Controlled Practice (5 minutes)

Activity: "Find the Mystery Number"

1. Write division equations on the board with missing dividends (e.g., ? ÷ 2 = 8).
2. Have students rewrite as multiplication (e.g., ? = 8 × 2).
3. Hand out small counters and let students group them to visualize.
4. Students work in pairs to solve the problem.
5. Discuss answers as a class.

Purpose: Builds confidence in using multiplication to solve division problems.

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Semi-Controlled/Free Practice (7 minutes)

Activity: Real-World Problem Solving

1. Divide students into small groups.
2. Give each group a word problem involving division (e.g., “Mrs. Lee bakes 24 cookies and divides them evenly among 6 students. How many cookies does each student get?”).
3. Have students model the problem with counters.
4. Guide them to write a multiplication sentence to help solve (e.g., 6 × ? = 24).
5. Groups present their solutions.

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Closure (3 minutes)

Reflection & Exit Ticket

1. Ask students to explain how multiplication helps with division.
2. Distribute a quick “Solve & Explain” exit ticket:
   • 36 ÷ 9 = ?
   • Write a multiplication sentence to check your answer.
3. Collect and review to assess understanding.

Final Thought: Remind students that multiplication and division are connected just like addition and subtraction.

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Assessment & Differentiation

Assessment:

• Exit tickets to check individual understanding.
• Observing student participation and explanations during activities.
• Quick oral questions throughout the lesson.

Differentiation:

• For struggling students: Provide additional support with counters and a number line.
• For advanced students: Challenge them with three-step word problems requiring both multiplication and division.

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Teacher’s Reflection:

• What went well?
• Were students able to grasp fact families?
• Did hands-on activities support understanding?
• Any adjustments for the next lesson?

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This lesson ensures an engaging and effective approach to helping third-grade students master using multiplication to solve division equations in accordance with McGraw-Hill standards.