4.NBT.6: Multi-Digit Division

Visual Models for Multi-Digit Division

1. Area Models

Area models help visualize division as finding the width of a rectangle when you know its area and length.

For example, to solve 728 ÷ 8:

• Draw a rectangle with area 728
• Make one side 8 units long
• The other side will be 91 units (the quotient)
• You can break this down into parts: 8 × 90 = 720 and 8 × 1 = 8, so 720 + 8 = 728

2. Arrays

Arrays show division as organizing objects into equal rows or columns. For example, 728 ÷ 8 can be visualized as arranging 728 objects into 8 equal rows, with 91 objects in each row.

3. Partial Quotients

This method breaks down division into more manageable parts:

For 728 ÷ 8:

• 8 × 80 = 640 (subtract from 728: 728 - 640 = 88)
• 8 × 10 = 80 (subtract from 88: 88 - 80 = 8)
• 8 × 1 = 8 (subtract from 8: 8 - 8 = 0)
• Add the partial quotients: 80 + 10 + 1 = 91

Everyday Applications

1. Fair Sharing

Practice division through fair sharing scenarios:

• If you have 156 stickers to share equally among 6 friends, how many stickers does each friend get?
• If 248 students need to be divided into 8 equal teams, how many students will be on each team?

2. Cost Per Item

Calculate the cost per item in various scenarios:

• If 4 notebooks cost $12, how much does each notebook cost?
• If a package of 8 granola bars costs $3.92, how much does each granola bar cost?

3. Time and Distance Problems

Solve problems involving time and distance:

• If a car travels 392 miles in 7 hours, how many miles does it travel per hour?
• If it takes 9 hours to read a 324-page book, how many pages are read per hour?

When Your Child Struggles

1. Use Multiplication to Check

Remind your child that division and multiplication are inverse operations. They can check their division answer by multiplying the quotient by the divisor to see if they get the dividend.

For example, if 728 ÷ 8 = 91, then 91 × 8 should equal 728.

2. Break It Down

If your child struggles with the standard algorithm, try using partial quotients to break the problem into smaller, more manageable parts.

3. Use Estimation

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

For example, 728 ÷ 8 is about 720 ÷ 8 = 90, so the answer should be close to 90.

4. Review Basic Facts

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

5-Minute Activities

Activity 1: Division Scavenger Hunt

Create division problems based on objects around your home. For example, "We have 24 books on this shelf. If we wanted to arrange them equally on 6 shelves, how many books would go on each shelf?"

Activity 2: Division War

Use playing cards to create division problems. Each player draws cards to create a dividend and a divisor. The player with the larger quotient wins the round.

Activity 3: Missing Factor

Practice thinking of division as finding a missing factor in multiplication. Give your child problems like "8 × ? = 72" and have them find the missing number (9).

Mid-Year Expectations

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

• Divide a two-digit number by a one-digit number using the standard algorithm
• Use area models to represent and solve simple division problems
• Explain the relationship between multiplication and division
• Check division answers using multiplication

End-of-Year Expectations

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

• Divide a four-digit number by a one-digit number using the standard algorithm
• Use various strategies (standard algorithm, area models, partial quotients) to solve division problems
• Interpret remainders in division problems based on the context
• Apply division 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 divide multi-digit numbers by one-digit numbers
• Choose appropriate strategies for different types of division problems
• Use multiple representations (standard algorithm, area models, arrays) to solve problems
• Explain the connection between different division methods
• Apply division skills to solve complex real-world problems
• Check the reasonableness of their answers using estimation and multiplication
• Interpret remainders appropriately based on the context of the problem

Questions to Check Understanding:

• "How would you solve 728 ÷ 8? Can you show me using an area model?"
• "What's another way you could solve 728 ÷ 8?"
• "How can you check if your answer to 728 ÷ 8 is correct?"
• "If 728 ÷ 8 = 91, what does that tell us about the relationship between 728, 8, and 91?"

Below Grade Level

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

📥 Download Practice Worksheet

At Grade Level

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

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging division problems and applications.

📥 Download Challenge Worksheet