Introduction

Multi-Digit Multiplication is an important Grade 4 math skill because students are moving from simple answers toward explaining how the math works.

In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with multi-digit multiplication.

What Is Multi-Digit Multiplication?

Multi-Digit Multiplication means choosing a model, naming what each number means, and explaining the strategy.

The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.

Understanding Multi-Digit Multiplication

Before solving, students should slow down and decide what each number, shape, unit, or label represents.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.

Visual Models

Visual Model 1

Question: Which area model shows \(23\times 14\)?

Visual Model 1

Visual Model 1

Visual Model 1

Visual Model 1

Why it works: An area model splits both factors: \(23 = 20 + 3\) (across) and \(14 = 10 + 4\) (down). Choice A shows these parts correctly.

Answer: A shows \(20 + 3\) across the top and \(10 + 4\) down the side

Visual Model 2

Question: Which area model correctly shows \(31\times 17\)?

Visual Model 2

Visual Model 2

Visual Model 2

Visual Model 2

Why it works: An area model splits \(31 = 30 + 1\) and \(17 = 10 + 7\). Choice A shows these decompositions correctly.

Answer: A correctly shows \(30+1\) across and \(10+7\) down

Worked Examples

Example 1

Question: Which shows the four correct partial products for \(24\times 19\)?

Example 1

Example 1

Example 1

Example 1

  1. Split both: \(24 = 20 + 4\) and \(19 = 10 + 9\).
  2. This creates four areas: \(20 \times 10 = 200\), \(4 \times 10 = 40\), \(20 \times 9 = 180\), \(4 \times 9 = 36\).
  3. Choice A is correct.

Answer: \(200+40+180+36=456\)

Example 2

Question: Which shows the completed standard algorithm, including the final product, for \(37\times 26\)?

Example 2

  1. The standard algorithm: multiply by ones (\(37 \times 6 = 222\)), then by tens (\(37 \times 20 = 740\)), then add (\(222 + 740 = \mathbf{962}\)).
  2. Choice D shows all three numbers.

Answer: Standard algorithm shows \(37\times 6=222\), \(37\times 20=740\), sum \(=962\)

Example 3

Question: What is \(24\times36\)?

  • A. \(84\)
  • B. \(144\)
  • C. \(864\)
  • D. \(924\)
  1. Break \(24 \times 36\) into parts: \(24 \times (30 + 6) = 24 \times 30 + 24 \times 6 = 720 + 144 = \mathbf{864}\).

Answer: \(864\)

Real-World Word Problems

Problem 1

Question: Ava buys \(12\) packs of stickers. Each pack has \(15\) stickers. How many stickers does Ava have in total?

  • A. \(27\)
  • B. \(120\)
  • C. \(240\)
  • D. \(180\)

Why it works: Split \(12 \times 15\) using the distributive property: \(12 \times (10 + 5) = 120 + 60 = \mathbf{180}\) stickers.

Answer: \(180\) stickers

Problem 2

Question: Sam arranges chairs in a rectangle. He makes \(3\) rows with \(24\) chairs in each row. How many chairs are there?

  • A. \(27\)
  • B. \(81\)
  • C. \(54\)
  • D. \(72\)

Why it works: Think: \(3 \times 24 = 3 \times (20 + 4) = 60 + 12 = \mathbf{72}\) chairs.

Answer: \(72\) chairs

Common Mistakes

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.

Strategy Tips

  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.

Practice Questions

Question 1

Which multiplication problem has the product \(156\)?

  • A. \(12\times 12\)
  • B. \(13\times 13\)
  • C. \(14\times 12\)
  • D. \(13\times 12\)

Question 2

What is \(31\times 21\)?

  • A. \(651\)
  • B. \(341\)
  • C. \(551\)
  • D. \(52\)

Question 3

Ming has \(4\) boxes of crayons. Each box has \(18\) crayons. How many crayons does Ming have?

  • A. \(44\)
  • B. \(82\)
  • C. \(64\)
  • D. \(72\)

Question 4

Diego reads \(16\) pages of a book each day. If he reads for \(5\) days, how many pages does he read?

  • A. \(21\)
  • B. \(110\)
  • C. \(70\)
  • D. \(80\)

Question 5

What is \(42\times 13\)?

  • A. \(546\)
  • B. \(526\)
  • C. \(486\)
  • D. \(626\)

Question 6

Mia plants flowers in \(7\) rows with \(25\) flowers in each row. How many flowers does she plant?

  • A. \(140\)
  • B. \(210\)
  • C. \(175\)
  • D. \(245\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(156\)

Break apart \(13 = 10 + 3\) and multiply: \((10 \times 12) + (3 \times 12) = 120 + 36 = \mathbf{156}\).

Question 2

Answer: \(651\)

Use the distributive property: \(31 \times 21 = 31 \times (20 + 1) = 620 + 31 = \mathbf{651}\).

Question 3

Answer: \(72\) crayons

Break \(18\) into tens and ones: \(4 \times (10 + 8) = 40 + 32 = \mathbf{72}\) crayons.

Question 4

Answer: \(80\) pages

Split \(16\): \(5 \times (10 + 6) = 50 + 30 = \mathbf{80}\) pages.

Question 5

Answer: \(546\)

Split the multiplier: \(42 \times (10 + 3) = 420 + 126 = \mathbf{546}\).

Question 6

Answer: \(175\) flowers

Use place value: \(7 \times (20 + 5) = 140 + 35 = \mathbf{175}\) flowers.

Timed practice quizzes

Related Quizzes

After studying Multi-Digit Multiplication, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 4 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.

Summary

Multi-Digit Multiplication becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.