4th Grade Multiplicative Comparison Lesson: Notes and Examples (Free PDF)

4th grade multiplicative comparison lesson – Maths PDF

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This 4th grade multiplicative comparison lesson covers multiplicative comparison (Common Core 4.OA.A.1, 4.OA.A.2), with a free PDF to print.

Key takeaway: This lesson helps fourth grade students understand and solve multiplicative comparison problems, where one amount is a number of times as many as another.

Topic: Multiplicative Comparison (4th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 4.OA.A.1, 4.OA.A.2
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

A multiplicative comparison tells how many times as many or times as much one amount is than another. It uses multiplication, such as 28 = 4 × 7, which means 28 is 4 times as many as 7. An additive comparison tells how many more or fewer. Draw a bar model, then multiply or divide.

This lesson helps fourth grade students understand and solve multiplicative comparison problems, where one amount is a number of times as many as another. It separates these from additive comparisons like 3 more than, so students learn when to multiply and when to add.

Students learn to read a statement such as 35 is 5 times as many as 7 as the equation 35 equals 5 times 7. Also, they draw bar models, use a letter for the unknown, and solve for the bigger amount, the smaller amount, or the number of times. Then, plan about 20 minutes. Also, draw a bar model for each example before writing the equation.

Grade 4 · Common Core State Standards: 4.OA.A.1, 4.OA.A.2

Key facts in this 4th grade multiplicative comparison lesson

Key facts

“A is n times as many as B” means A = n × B.
“More than” and “fewer than” are additive comparisons; “times as many” is multiplicative.
To find the bigger amount, multiply. To find the smaller amount or the number of times, divide.
Next, use a letter for the unknown, such as 28 = 4 × b.
A bar model with equal units shows the comparison clearly.

What is a multiplicative comparison?

A comparison can tell how many more or how many times as many. When you say “3 times as many,” you are using multiplication.

Multiplicative comparison

A multiplicative comparison says one amount is a number of times as many (or times as much) as another amount. The equation looks like $a = n \times b$.

Ben has 4 stickers. Ana has 3 times as many: three groups of 4 make 12.

Ben has 4 stickers. Ana has 3 times as many, so Ana has $3 \times 4$ = 12 stickers.

How is it different from an additive comparison?

An additive comparison tells how many more or fewer. A multiplicative comparison tells how many times as many. Look at the key words.

Set A: Ana has 4 more than Ben (add). Set B: Ana has 4 times as many as Ben (multiply).

Sentence	Type	Equation
Ana has 4 more than Ben (6)	additive	$6 + 4 = 10$
Ana has 4 times as many as Ben (6)	multiplicative	$4 \times 6 = 24$

How do you write an equation for a comparison?

Turn a comparison sentence into an equation in three steps.

The amount being compared to is the unit. The number of times tells how many units to take. Use a letter, like a, for the unknown.

How do you find the unknown?

There are three cases. Each one uses the equation $big = n \times small$.

Unknown big amount: multiply. $big = 4 \times 7 = 28$.
Unknown small amount: divide. If $28 = 4 \times b$, then $b = 28 \div 4 = 7$.
Unknown number of times: divide. If $28 = n \times 7$, then $n = 28 \div 7 = 4$.

The tree is 28 feet tall. It is 4 times as tall as the bush, so 4 equal bars make 28 feet.

Example: A tree is 28 feet tall. It is 4 times as tall as a bush. Write $28 = 4 \times b$. Then $b = 28 \div 4 = 7$. The bush is 7 feet tall.

4th grade multiplicative comparison lesson: questions and answers

What does “times as many” mean?

It means you take the smaller amount that number of times. If Maya has 3 times as many stickers as Jamal, who has 5, then Maya has 3 × 5 = 15 stickers.

How can I tell an additive comparison from a multiplicative one?

Look for the key words. “More than” and “fewer than” tell you to add or subtract. “Times as many” or “times as much” tells you to multiply or divide.

How do I find how many times as many one number is than another?

Divide the bigger number by the smaller number. A $72 bike costs how many times as much as a $9 helmet? Since 72 ÷ 9 = 8, it costs 8 times as much.

Why use a letter for the unknown?

A letter holds the place of the number you want to find. In 28 = 4 × b, the letter b stands for the unknown amount, and you solve it with division.

Is 24 = 8 × 3 only one comparison?

No. It says 24 is 8 times as many as 3 and also that 24 is 3 times as many as 8. The two factors can swap roles because multiplication can be done in either order.

Common mistakes with this 4th grade multiplicative comparison lesson

Students add when they see the word more. In a times as many problem, the bigger amount is found by multiplying, so 4 times as many as 5 is 20, not 9.
Students multiply to find the smaller amount. Also, when the bigger amount and the number of times are known, divide the bigger amount by the number of times.
Students write the numbers in the wrong order in a sentence. Instead, in 24 equals 6 times 4, the 24 is the bigger amount, and 6 and 4 are the factors.

How to study this chapter

Draw a bar for the small amount and a bar that is a certain number of times as long. Finally, the picture shows whether to multiply or divide.
Underline the phrase times as many or times as much. Also, it is the signal that the problem is multiplicative.
Parents can ask the child to compare two stacks of coins or two ribbons, once with more than and once with times as many.

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