Introduction

Multiplicative Comparison 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 multiplicative comparison.

What Is Multiplicative Comparison?

Multiplicative Comparison 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 Multiplicative Comparison

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: Look at the bar model below. Which equation matches? Noah has \(4\) cards. Ava has \(4\) times as many cards as Noah. Which equation shows the number of cards Ava has?

Visual Model 1

  • A. \(\text{Ava} = 4 + 4\)
  • B. \(\text{Ava} = 4 \div 4\)
  • C. \(\text{Ava} = 4 - 4\)
  • D. \(\text{Ava} = 4 \times 4\)

Why it works: Look at the picture: Ava's bar is split into \(4\) equal pieces, each the same length as Noah's bar. That's exactly what "\(4\) times as many" means---so we multiply: Ava \(= 4 \times 4 = 16\) cards.

Answer: Ava \(= 4 \times 4 = 16\)

Visual Model 2

Question: Look at the groups below. Group 2 has how many times as many counters as Group 1?

Visual Model 2

  • A. \(3\)
  • B. \(9\)
  • C. \(6\)
  • D. \(4\)

Why it works: To find "how many times as many," divide the bigger amount by the smaller. Group 2 has \(12\), Group 1 has \(3\), and \(12 \div 3 = 4\). So Group 2 has \(\mathbf{4}\) times as many counters.

Answer: \(4\) times as many

Worked Examples

Example 1

Question: Which bar model shows "\(15\) is \(3\) times as many as \(5\)"?

Example 1

  • A. Neither model works
  • B. Model B
  • C. Both are the same
  • D. Model A
  1. "\(3\) times as many" means we need exactly \(3\) equal groups.
  2. Model A shows \(3\) groups---so it matches the comparison.
  3. Model B shows only \(2\) groups, so it would represent "\(2\) times as many," not \(3\).

Answer: Model A

Example 2

Question: Look at the bar model. What is the larger amount? The smaller bar is \(3\). The larger bar is \(6\) times as many. What is the larger amount?

Example 2

  • A. \(3\)
  • B. \(9\)
  • C. \(6\)
  • D. \(18\)
  1. The larger bar is \(6\) times the smaller bar, so we multiply: \(3 \times 6 = 18\).
  2. The larger amount is \(\mathbf{18}\).

Answer: \(18\)

Example 3

Question: How many times as many counters are in Group B as in Group A?

Example 3

  • A. \(2\) times as many
  • B. \(8\) times as many
  • C. \(6\) times as many
  • D. \(4\) times as many
  1. To find "how many times," divide the larger group by the smaller: \(8 \div 2 = 4\).
  2. So Group B has \(\mathbf{4}\) times as many counters as Group A.

Answer: \(4\) times as many

Real-World Word Problems

Problem 1

Question: There are \(5\) green marbles. There are \(3\) times as many red marbles as green marbles. Which equation shows how many red marbles there are?

  • A. \(5 + 3 = 8\)
  • B. \(5 - 3 = 2\)
  • C. \(5 \times 3 = 15\)
  • D. \(5 \div 3\)

Why it works: "\(3\) times as many" is a multiplication clue. Make \(3\) groups of the \(5\) green marbles: \(5 \times 3 = 15\) red marbles. Choice C is the equation that shows this.

Answer: \(5 \times 3 = 15\)

Problem 2

Question: Leo reads \(2\) books. His sister reads \(5\) times as many books as Leo. How many books does his sister read?

  • A. \(3\)
  • B. \(7\)
  • C. \(5\)
  • D. \(10\)

Why it works: "\(5\) times as many" means we multiply. Leo's sister reads \(5\) groups of \(2\) books, so \(5 \times 2 = 10\) books.

Answer: \(10\) books

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 equation shows that \(24\) is \(6\) times as many as \(4\)?

  • A. \(24+4=28\)
  • B. \(24-4=20\)
  • C. \(24=6\times4\)
  • D. \(24\div4=9\)

Question 2

Maria has \(3\) stickers. Sam has \(2\) times as many stickers as Maria. How many stickers does Sam have?

  • A. \(3\)
  • B. \(5\)
  • C. \(4\)
  • D. \(6\)

Question 3

Which statement matches the equation \(12 = 3 \times 4\)?

  • A. \(12\) is \(4\) more than \(3\)
  • B. \(12\) is \(3\) less than \(4\)
  • C. \(12\) plus \(3\) equals \(4\)
  • D. \(12\) is \(3\) times as many as \(4\)

Question 4

Diego has \(6\) toy cars. Chen has \(4\) times as many toy cars as Diego. How many more cars does Chen have than Diego?

  • A. \(10\)
  • B. \(4\)
  • C. \(24\)
  • D. \(18\)

Question 5

Mia bakes \(8\) cookies. Max bakes \(2\) times as many cookies as Mia. How many cookies does Max bake?

  • A. \(6\)
  • B. \(8\)
  • C. \(10\)
  • D. \(16\)

Question 6

Which equation does NOT show a multiplicative comparison?

  • A. \(18 = 3 \times 6\)
  • B. \(18 = 12 + 6\)
  • C. \(20 = 4 \times 5\)
  • D. \(35 = 5 \times 7\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(24=6\times4\)

When you see "times as many," think multiplication! "\(6\) times as many as \(4\)" becomes \(6 \times 4\), which equals \(24\). So choice C, \(24 = 6 \times 4\), is the equation that captures that idea.

Question 2

Answer: \(6\) stickers

"\(2\) times as many" is your signal to multiply. Sam has \(2\) groups of Maria's \(3\) stickers: \(2 \times 3 = 6\). So Sam has \(\mathbf{6}\) stickers.

Question 3

Answer: \(12\) is \(3\) times as many as \(4\)

Read \(12 = 3 \times 4\) in words: "\(12\) equals \(3\) groups of \(4\)." That's the same as saying "\(12\) is \(3\) times as many as \(4\)." The other choices use more, plus, or less---those describe adding or subtracting, not multiplying.

Question 4

Answer: \(18\) more cars

This is a two-step problem. Step 1: find Chen's cars: \(4 \times 6 = 24\). Step 2: "how many more" is a subtraction question, so \(24 - 6 = 18\). Chen has \(\mathbf{18}\) more cars than Diego.

Question 5

Answer: \(16\) cookies

"\(2\) times as many" is a multiplication signal. Max bakes \(2\) groups of Mia's \(8\) cookies: \(8 \times 2 = 16\) cookies.

Question 6

Answer: \(18 = 12 + 6\)

Multiplicative comparisons use the symbol \(\times\) (or words like "times as many"). Choices A, C, and D all use \(\times\). Choice B uses \(+\), which is an additive comparison---not multiplicative.

Timed practice quizzes

Related Quizzes

After studying Multiplicative Comparison, 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

Multiplicative Comparison 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.