4.NBT.5: Multi-Digit Multiplication

Visual Models for Multi-Digit Multiplication

1. Area Models

Area models are rectangular diagrams that help visualize multiplication as finding the area of a rectangle.

For example, to multiply 24 × 36:

• Draw a rectangle and divide it into sections (20 × 30, 20 × 6, 4 × 30, 4 × 6)
• Calculate each section: 20 × 30 = 600, 20 × 6 = 120, 4 × 30 = 120, 4 × 6 = 24
• Add all sections: 600 + 120 + 120 + 24 = 864

2. Arrays

Arrays show multiplication as rows and columns of objects. For smaller numbers, you can draw dots or use objects. For larger numbers, you can use grid paper and shade regions.

3. Expanded Form

Breaking numbers into expanded form can make multiplication more manageable:

For 36 × 24:

• 36 = 30 + 6
• 24 = 20 + 4
• 36 × 24 = (30 + 6) × (20 + 4)
• = (30 × 20) + (30 × 4) + (6 × 20) + (6 × 4)
• = 600 + 120 + 120 + 24
• = 864

Everyday Applications

1. Shopping Calculations

Calculate the total cost of multiple items. For example, if one book costs $12, how much would 24 books cost? (12 × 24 = 288)

2. Recipe Scaling

Adjust recipes for different numbers of servings. If a recipe for 4 people needs 2 cups of flour, how much flour would you need for 16 people? (2 × 4 = 8 cups)

3. Area Calculations

Calculate the area of rooms, gardens, or other rectangular spaces. If a room is 14 feet by 12 feet, what is its area? (14 × 12 = 168 square feet)

4. Planning Events

Calculate quantities needed for events. If each guest needs 3 napkins and you're expecting 45 guests, how many napkins should you buy? (3 × 45 = 135 napkins)

When Your Child Struggles

1. Break It Down

If your child struggles with the standard algorithm, try breaking the problem into smaller, more manageable parts using expanded form or partial products.

For example, instead of 34 × 7, think of it as:

• 30 × 7 = 210
• 4 × 7 = 28
• 210 + 28 = 238

2. Use Visual Models

If your child is having trouble understanding the concept, use area models or arrays to provide a visual representation of the multiplication.

3. Check Place Value Understanding

Make sure your child understands place value. When multiplying 34 × 7, they need to understand that they're multiplying 7 by 4 ones and 7 by 3 tens.

4. Practice Basic Facts

Multi-digit multiplication relies on knowing basic multiplication facts. If your child struggles with these, practice basic facts regularly.

5-Minute Activities

Activity 1: Multiplication War

Use playing cards to create multi-digit multiplication problems. Each player draws cards to create numbers to multiply. The player with the larger product wins the round.

Activity 2: Estimate First

Before solving a multiplication problem, have your child estimate the answer by rounding the numbers. This helps them check if their final answer is reasonable.

For example, 34 × 56 is about 30 × 60 = 1,800, so the answer should be close to that.

Activity 3: Real-World Problems

Create quick word problems based on everyday situations:

• "If one package of pencils has 12 pencils, how many pencils are in 24 packages?"
• "If a movie theater has 28 rows with 16 seats in each row, how many seats are there in total?"

Mid-Year Expectations

By the middle of the school year, your child should be able to:

• Multiply a two-digit number by a one-digit number using the standard algorithm
• Use area models to represent and solve simple multiplication problems
• Explain the steps in the multiplication process
• Check the reasonableness of answers using estimation

End-of-Year Expectations

By the end of the school year, your child should be able to:

• Multiply a four-digit number by a one-digit number using the standard algorithm
• Multiply two two-digit numbers using various strategies
• Use area models to represent and solve more complex multiplication problems
• Apply multiplication skills to solve real-world problems
• Explain their reasoning and the strategies they used

Signs of Mastery

Your child has mastered this standard when they can:

• Consistently and accurately multiply multi-digit numbers
• Choose appropriate strategies for different types of multiplication problems
• Use multiple representations (standard algorithm, area models, arrays) to solve problems
• Explain the connection between different multiplication methods
• Apply multiplication skills to solve complex real-world problems
• Check the reasonableness of their answers

Questions to Check Understanding:

• "How would you solve 24 × 6? Can you show me using an area model?"
• "What's another way you could solve 24 × 6?"
• "How would you solve 34 × 27? What steps would you take?"
• "How can you check if your answer to 34 × 27 is reasonable?"

Below Grade Level

For students who need additional support with basic multiplication concepts and simpler multi-digit multiplication.

📥 Download Practice Worksheet

At Grade Level

For students who need practice with grade-level multi-digit multiplication problems.

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging multiplication problems and applications.

📥 Download Challenge Worksheet