Understanding area models for division (Grade 3 explanation)

🔢 Understanding Area Models for Division: A Teacher's Guide

This lesson plan provides a structured approach to teaching 3rd-grade students how to use area models for division. The area model is a visual representation that connects division to multiplication and helps students understand the concept of dividing a whole into equal groups.

🎯 Objectives

• 🧑‍🏫 Students will be able to represent division problems using area models.
• ➗ Students will be able to solve division problems using area models.
• 🤝 Students will be able to explain the relationship between division and multiplication using area models.

🧰 Materials

• 📃 Whiteboard or projector
• marker
• 🧱 Grid paper
• ✏️ Pencils
• ✂️ Scissors (optional)
• 🌈 Colored pencils or crayons
• ➕ Multiplication charts (optional)

Warm-up (5 minutes)

• 🗣️ Review multiplication facts. Ask students to quickly recall multiplication facts related to the numbers that will be used in the lesson (e.g., multiples of 2, 3, 4, 5).
• 🤝 Present simple division problems (e.g., 12 ÷ 3) and ask students to solve them using any method they know. Discuss their strategies briefly.

🧑‍🏫 Main Instruction (20 minutes)

1. Introducing the Area Model:
   • 🖼️Draw a rectangle on the board. Explain that the area of the rectangle represents the total number (dividend) that we are dividing.
   • 📏 Explain that one side of the rectangle represents the number of groups (divisor), and the other side represents the size of each group (quotient).
2. Example Problem: 15 ÷ 3
   • ✏️Write the problem on the board: $15 \div 3 = ?$
   • 🧱Draw a rectangle on grid paper representing 15 (e.g., 3 rows of 5 squares).
   • ❓Explain that we know one side of the rectangle is 3 (the divisor). Label that side.
   • ✍️Ask: "How many groups of 3 do we need to make 15?"
   • ✂️ Guide students to divide the rectangle into 3 equal rows (or columns). Each row (or column) will have 5 squares.
   • ✅ Explain that the other side of the rectangle is 5, which is the quotient. Therefore, $15 \div 3 = 5$
3. Another Example: 24 ÷ 4
   • ✍️ Write: $24 \div 4 = ?$
   • 🧱 Draw a rectangle on grid paper representing 24 (e.g., 4 rows of 6 squares).
   • ❓Explain we know one side is 4. Label that side.
   • ➗Guide students to divide rectangle into 4 equal rows (or columns). Each row (or column) will have 6 squares.
   • ✅ Explain that the other side of the rectangle is 6, which is the quotient. $24 \div 4 = 6$
4. Connecting to Multiplication
   • ➕ Emphasize that division is the inverse of multiplication.
   • 💡Show how $15 \div 3 = 5$ is related to $3 \times 5 = 15$.
   • 💬Use the area model to visually demonstrate this relationship.

📝 Assessment (10 minutes)

• ✍️Provide students with division problems and ask them to solve them using the area model on grid paper. Examples:
  • $12 \div 4 = ?$
  • $20 \div 5 = ?$
  • $16 \div 2 = ?$
  • $21 \div 3 = ?$
  • $28 \div 7 = ?$
  • $30 \div 6 = ?$
  • $36 \div 9 = ?$
• 🚶‍♀️Observe students as they work and provide assistance as needed.
• 🗣️Have students share their solutions and explain their area models.