Write Multiplication Equations from Comparison Statements

Students translate verbal multiplicative comparison statements (e.g., 'Ana has 4 times as many books as Ben, who has 6 books') into multiplication equations. They identify the unknown, the multiplier, and the reference quantity and represent the relationship symbolically.

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Grade 4 · Multiplicative Comparisons · question 1 of 3

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20 rungs. A star at the top.

Rosa wrote 5 postcards. Tom wrote 4 times as many. Write an equation that shows how many postcards Tom wrote.

How it is taught

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Times as many means multiplication, not addition.

The equation multiplies the smaller amount to make the larger.

Read it: Times as many is equal boxes

What is 5 times as many as 6? Draw 6 as one box, then 5 boxes of 6 in a row: 5 × 6 = 30.

Draw the smaller amount as one box.
Draw the larger amount as that many boxes, each the same size.
Multiply to find the larger amount, or divide to find a box or the number of boxes.

Times as many compares by multiplying: every box is the same size as the smaller amount.

The equation says the same thing: 30 = 5 × 6 means 30 is 5 times as many as 6.

Knowing the larger amount and the boxes, divide: 30 ÷ 5 = 6.

k times as many as a number is k boxes of that number: multiply.

Adding: 5 times as many as 6 is not 6 + 5 = 11.

Times as many means 5 boxes of 6, not 5 more. 5 × 6 = 30.

32 = ___ × 8 — 4. 32 is 4 times as many as 8, because 4 × 8 = 32.

Ana has 4 times as many books as Ben (Ben has 6)

Ana has four times as many books as Ben. Ben has six books. Let's figure out how many Ana has — and write a multiplication equation for it.

First, here's Ben. He has six books — that's our starting amount.

Ana has four times as many. So Ana's stack is four copies of Ben's stack.

Each group is six books, and there are four equal groups.

We can write this as a multiplication equation: Ana equals something times something.

The first number is four — that's how many times bigger Ana's stack is.

And we multiply by six — Ben's amount, the number in each group.

Four times six is twenty-four.

Ana has twenty-four books! Whenever you hear 'n times as many,' you can write a multiplication equation just like this one.

Grade 4 · Turning 'times as many' into a multiplication equation

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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