4.OA.2: Multiplication and Division Word Problems

Visual Models for Multiplicative Comparison Problems

1. Tape Diagrams

Draw rectangles to represent quantities, with the larger rectangle being a multiple of the smaller one.

Example: "Alex has 3 times as many books as Maya. Maya has 5 books."

Draw a small rectangle labeled "Maya: 5 books" and a larger rectangle (3 times as long) labeled "Alex: 15 books"

2. Bar Models

Similar to tape diagrams but with vertical bars instead of horizontal rectangles. These are especially helpful for comparing quantities visually.

3. Number Lines

Show jumps on a number line to represent multiplicative relationships. For example, if one quantity is 4 times another, show 4 equal jumps.

Real-World Comparison Activities

1. Real-World Comparisons

Look for multiplicative comparisons in everyday life:

• "This bottle holds 3 times as much water as that cup."
• "The adult elephant weighs 8 times as much as the baby elephant."
• "The chapter book has 4 times as many pages as the picture book."

2. Comparison Cards

Create cards with different multiplicative comparison statements and have your child match them with the correct equations.

3. Measurement Comparisons

Measure various items around your home and create comparison problems:

• Compare heights of family members
• Compare weights of different objects
• Compare capacities of different containers

When Your Child Struggles

When to Multiply vs. Divide

Use Multiplication When: The larger quantity is unknown.

Example: "Tim has 4 times as many baseball cards as Jake. Jake has 7 cards. How many cards does Tim have?"

Solution: 4 × 7 = 28 cards

Use Division When: The smaller quantity or the comparison factor is unknown.

Example 1: "Tim has 28 baseball cards, which is 4 times as many as Jake. How many cards does Jake have?"

Solution: 28 ÷ 4 = 7 cards

Example 2: "Tim has 28 baseball cards. Jake has 7 cards. Tim has how many times as many cards as Jake?"

Solution: 28 ÷ 7 = 4 times as many

Drawing the Problem

Encourage your child to draw a simple diagram before solving. This helps them visualize the relationship between quantities and decide whether to multiply or divide.

5-Minute Activities

Key Words and Phrases

Practice identifying these phrases in word problems:

• "times as many as"
• "times as much as"
• "times as long as"
• "times as heavy as"
• "times as old as"

Activity: Create Your Own Problems

Take turns creating multiplicative comparison word problems for each other to solve. This helps your child understand the structure of these problems from both sides.

Activity: Drawing Comparisons

Draw pictures to represent multiplicative relationships and write the corresponding equations. This reinforces the visual understanding of multiplication and division.

Mid-Year Expectations

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

• Identify when to multiply in simple comparison word problems
• Solve basic multiplicative comparison problems where the larger quantity is unknown
• Draw simple visual models to represent multiplicative relationships
• Recognize key phrases that indicate multiplicative comparison

End-of-Year Expectations

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

• Identify when to multiply and when to divide in comparison word problems
• Solve multiplicative comparison problems where any quantity is unknown
• Draw detailed visual models to represent and solve comparison problems
• Explain their reasoning when solving problems

Signs of Mastery

Your child has mastered this standard when they can:

• Consistently determine whether to multiply or divide in any comparison situation
• Solve complex word problems involving multiplicative comparisons
• Create their own multiplicative comparison word problems
• Use appropriate visual models to represent and solve problems
• Apply multiplicative comparison understanding to real-world situations

Questions to Check Understanding:

• If Ben has 5 times as many toy cars as Mia, and Mia has 6 cars, how many cars does Ben have?
• Emma has 24 stickers, which is 3 times as many as Liam. How many stickers does Liam have?
• A giraffe is 15 feet tall. This is 5 times as tall as a zebra. How tall is the zebra?
• A blue whale weighs 300,000 pounds. An elephant weighs 15,000 pounds. How many times heavier is the blue whale than the elephant?

Below Grade Level

For students who need additional support with basic multiplication and division concepts in word problems.

📥 Download Practice Worksheet

At Grade Level

For students who need practice with grade-level multiplicative comparison word problems.

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging multiplicative comparison word problems and applications.

📥 Download Challenge Worksheet