5.NBT.6: Division with Two-Digit Divisors

Visual Models for Division with Two-Digit Divisors

1. Area Model for Division

Draw a rectangle with the dividend as the area. The width represents the divisor, and the length represents the quotient. For 1,456 ÷ 28, create a rectangle with area 1,456 and width 28. The length (52) is the quotient.

2. Partial Quotients

Break the division into manageable chunks. For 1,456 ÷ 28: First divide 1,400 ÷ 28 = 50, then 56 ÷ 28 = 2. Add the quotients: 50 + 2 = 52.

3. Number Line Model

Use a number line to show repeated subtraction of the divisor from the dividend. For 1,456 ÷ 28, repeatedly subtract 28 from 1,456 and count how many times you can do this.

4. Base-Ten Blocks

Use base-ten blocks to represent the dividend, then divide them into equal groups based on the divisor. This helps visualize the regrouping process.

Everyday Activities

1. Recipe Scaling

When cooking, have your child help scale a recipe down. "This recipe serves 24 people, but we only need to serve 6. How much of each ingredient do we need?" This requires dividing each measurement by 4.

2. Budget Planning

Give your child a budget scenario: "You have $1,248 to spend on party supplies for 32 guests. How much can you spend per person?" This practical application helps them see the value of division skills.

3. Distance and Rate Problems

Use maps to create distance problems: "If we drive 468 miles at an average speed of 52 miles per hour, how many hours will it take?" This connects division to real-world travel scenarios.

4. Division Card Game

Use playing cards to create division problems. Draw cards to create a 3 or 4-digit dividend and a 2-digit divisor, then solve the division problem. This makes practice more engaging and game-like.

Strategies When Your Child Struggles

1. Estimation Strategy

Teach your child to round the divisor to the nearest ten to make estimation easier. For example, when dividing by 28, think "about 30" to estimate. This helps them get a reasonable first digit in their quotient.

2. Division Steps Checklist

Create a checklist of the division steps: Divide, Multiply, Subtract, Bring down. Have your child check off each step as they complete it. This structured approach helps prevent skipping steps.

3. Multiplication Table Review

Review multiplication facts for the divisor's first digit. For divisor 28, practice multiplying 2 by different numbers to help with estimation. Strong multiplication skills support division success.

4. Start Smaller

If your child is overwhelmed by large numbers, start with smaller problems (2-digit ÷ 2-digit) and gradually increase the size of the dividend. This builds confidence and skills progressively.

5. Check Work with Multiplication

Teach your child to check their answer by multiplying the quotient by the divisor and adding any remainder. The result should equal the dividend. This verification step helps catch errors.

5-Minute Activities

Activity 1: Estimation Challenge

Give your child a division problem and ask them to estimate the quotient by rounding. Then have them solve it exactly and compare. This builds number sense and estimation skills.

Activity 2: Error Hunt

Show your child a multi-digit division problem with an intentional error. Ask them to find and fix the mistake. This develops critical thinking and reinforces proper procedure.

Activity 3: Division Fact Families

Practice related multiplication and division facts. For example, if 28 × 52 = 1,456, then 1,456 ÷ 28 = 52 and 1,456 ÷ 52 = 28. This reinforces the relationship between multiplication and division.

Activity 4: Real-World Problems

Create quick word problems using multi-digit division: "If 1,456 stickers are packaged in boxes of 28, how many full boxes can be made?" This connects the skill to practical applications.

Mid-Year Expectations

By the middle of 5th grade, your child should be able to:

• Divide a 3-digit number by a 2-digit number (e.g., 368 ÷ 16)
• Use the standard algorithm with proper place value alignment
• Make reasonable estimates before dividing
• Check their work using multiplication

End-of-Year Expectations

By the end of 5th grade, your child should be able to:

• Divide a 4-digit number by a 2-digit number (e.g., 1,456 ÷ 28)
• Explain each step of the division process
• Interpret remainders appropriately in word problems
• Solve multi-step word problems involving division

Mastery Signs

Your child has mastered this standard when they can:

• Divide multi-digit numbers fluently (quickly and accurately)
• Apply the standard algorithm consistently without errors
• Explain why the standard algorithm works using place value concepts
• Use division to solve real-world problems
• Verify the reasonableness of their answers through estimation

Questions to Ask:

Ask your child to solve these problems and explain their process:

• 1,456 ÷ 28 = ?
• 3,672 ÷ 36 = ?
• 2,184 ÷ 24 = ?

Ask them to explain how they know their answer is correct.

Below Grade Level

For students who need additional support with basic division concepts and algorithms.

📥 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 multi-digit division problems and applications.

📥 Download Challenge Worksheet