5.NBT.5: Multi-Digit Multiplication

Visual Models for Multi-Digit Multiplication

1. Area Model

Draw a rectangle divided into sections based on place value. For 34 × 25, create a 2×2 grid with dimensions (30+4) by (20+5). Calculate each section: 30×20=600, 30×5=150, 4×20=80, 4×5=20. Add all parts: 600+150+80+20=850.

2. Expanded Form

Break numbers into expanded form: 34 × 25 = (30 + 4) × (20 + 5). Use the distributive property to multiply each part: 30×20 + 30×5 + 4×20 + 4×5 = 600 + 150 + 80 + 20 = 850.

3. Partial Products

Show each step of multiplication separately. For 34 × 25: First multiply 34×5=170, then 34×20=680. Add the partial products: 170+680=850.

4. Grid Paper

Use grid paper to organize the standard algorithm, keeping digits aligned by place value to avoid errors.

Everyday Activities

1. Shopping Math

When shopping, ask your child to calculate the total cost if you buy multiple quantities of an item. "If one shirt costs $12, how much would 5 shirts cost?" Extend to more complex problems: "If one package of 24 pencils costs $3, how much would 12 packages cost?"

2. Recipe Scaling

When cooking, have your child help scale a recipe up. "This recipe serves 4 people, but we need to serve 12. How much of each ingredient do we need?" This requires multiplying each measurement by 3.

3. Area Calculations

Measure rooms in your home and have your child calculate the area by multiplying length by width. Extend to calculating flooring costs if each square foot costs a certain amount. "If our room is 12 feet by 15 feet, and carpet costs $2.50 per square foot, how much would it cost to carpet the room?"

4. Multiplication War

Play with a deck of cards. Each player draws two cards to create a two-digit number. Multiply your numbers, and the highest product wins the round. This helps build fluency with the standard algorithm.

Strategies When Your Child Struggles

1. Place Value Check

If your child is making errors, have them use graph paper with one digit per square to keep columns aligned properly. This visual organization helps prevent place value errors.

2. Multiplication Table Review

Review basic multiplication facts (0-9) if your child is struggling with single-digit multiplication within the algorithm. Fluency with these facts is essential for multi-digit multiplication.

3. Highlight Placeholder Zeros

Use a colored pencil to highlight the placeholder zeros when multiplying by tens, hundreds, etc. This helps your child understand why we "shift over" when multiplying by larger place values.

4. Break It Down

For large numbers, break the problem into smaller steps. Multiply by one digit at a time and add the partial products. This approach makes the process less overwhelming.

5. Estimation First

Before calculating, estimate the answer by rounding to check if the final answer is reasonable. For example, 34 × 25 is about 30 × 30 = 900, so the answer should be close to that.

5-Minute Activities

Activity 1: Multiplication Sprint

Create 5-10 multi-digit multiplication problems. Time your child for 5 minutes as they solve as many as possible. Track improvement over time to build speed and accuracy.

Activity 2: Error Hunt

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

Activity 3: Real-World Problems

Create quick word problems using multi-digit multiplication: "If one package contains 24 cookies and we buy 15 packages, how many cookies do we have?" This connects the skill to practical applications.

Activity 4: Estimation Challenge

Give your child a multiplication problem and ask them to estimate the answer by rounding. Then have them solve it exactly and compare. This builds number sense and helps catch calculation errors.

Mid-Year Expectations

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

• Multiply a 2-digit number by a 2-digit number correctly (e.g., 34 × 25)
• Use the standard algorithm with proper place value alignment
• Remember to use placeholder zeros when multiplying by tens
• Check if their answer is reasonable by estimating

End-of-Year Expectations

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

• Multiply a 3-digit number by a 2-digit number (e.g., 123 × 45)
• Multiply a 4-digit number by a 2-digit number (e.g., 2,384 × 56)
• Solve multi-step word problems involving multiplication
• Explain the steps of the standard algorithm and why they work

Mastery Signs

Your child has mastered this standard when they can:

• Multiply 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 multiplication 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:

• 42 × 36 = ?
• 215 × 24 = ?
• 1,358 × 47 = ?

Ask them to explain why we put a zero in the second row when multiplying by the tens digit.

Below Grade Level

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

📥 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 multi-digit multiplication problems and applications.

📥 Download Challenge Worksheet