4.OA.1: Multiplicative Comparisons

Visual Models for Multiplicative Comparisons

These visual models help your child understand what "times as many" means:

1. Arrays

Draw rows and columns of dots or squares. For example, to show 3 × 4 = 12, draw 3 rows with 4 dots in each row, then explain that 12 is 3 times as many as 4.

2. Number Lines

Use number lines to show jumps of equal size. For example, to show 5 × 3 = 15, draw a number line and make 5 jumps of size 3.

3. Tape Diagrams

Draw rectangles to show one quantity is a multiple of another. For example, to show 4 × 6 = 24, draw a small rectangle labeled "6" and a larger rectangle 4 times as long labeled "24".

Everyday Comparison Activities

1. Comparison Scavenger Hunt

Look for multiplicative comparisons around your home: "This bookshelf has 3 times as many books as that one." "Dad's shoes are 2 times as long as yours."

2. Grocery Store Comparisons

At the store, find examples of multiplicative comparisons: "This package has 4 times as many apples as that one." "This bottle is 2 times as tall as this one."

3. Drawing Comparisons

Draw pictures showing multiplication comparisons. For example, draw a tall tree that is 5 times as tall as a small tree.

When Your Child Struggles

1. Use Concrete Objects

Use small objects like buttons or counters to physically show the comparison. For example, "This pile has 4 times as many buttons as that pile."

2. Practice Verbal Descriptions

Have your child practice saying multiplication equations as comparisons: "6 × 3 = 18 means 18 is 6 times as many as 3."

3. Highlight the Difference

Clearly explain the difference between "times as many" (multiplication) and "times more than" (multiplication plus the original amount).

5-Minute Activities

Activity 1: Equation to Story

Give your child a multiplication equation (like 3 × 4 = 12) and have them create a comparison story: "The blue ribbon is 3 times as long as the red ribbon. The red ribbon is 4 inches long, so the blue ribbon is 12 inches long."

Activity 2: Story to Equation

Tell your child a comparison story and have them write the corresponding equation: "A whale weighs 8 times as much as an elephant. If an elephant weighs 5 tons, how much does the whale weigh?" (8 × 5 = 40)

Activity 3: Both Ways Practice

For any multiplication fact, practice saying it both ways: "4 × 6 = 24 means 24 is 4 times as many as 6, and 24 is also 6 times as many as 4."

Mid-Year Expectations

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

• Explain that 4 × 7 = 28 means 28 is 4 times as many as 7
• Translate simple comparison statements into multiplication equations
• Draw basic visual models to represent multiplicative comparisons

End-of-Year Expectations

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

• Explain that 4 × 7 = 28 means both "28 is 4 times as many as 7" and "28 is 7 times as many as 4"
• Create a multiplication equation from any comparison statement
• Create a comparison statement from any multiplication equation
• Draw detailed visual models to represent multiplicative comparisons

Signs of Mastery

Your child has mastered this standard when they can:

• Consistently translate between verbal multiplicative comparisons and multiplication equations
• Distinguish between "times as many" and "times more than" in word problems
• Create their own multiplicative comparison problems
• Apply multiplicative comparison understanding to solve complex problems
• Explain their reasoning using precise mathematical language

Questions to Ask:

• "If 5 × 9 = 45, what does that tell us about the relationship between 5, 9, and 45?"
• "How would you write an equation for 'The elephant weighs 20 times as much as the dog'?"
• "Can you draw a picture to show that 24 is 6 times as many as 4?"

Below Grade Level

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

📥 Download Practice Worksheet

At Grade Level

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

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging multiplication comparison problems and applications.

📥 Download Challenge Worksheet