Find the Unknown in a Division Equation

Students determine the missing whole number in division equations where the unknown may be the dividend, divisor, or quotient (e.g., 56 ÷ ? = 7 or ? ÷ 8 = 7). They use the relationship between multiplication and division to rewrite the equation and solve.

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Grade 3 · Finding Unknowns in Multiplication and Division · question 1 of 3

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12 rungs. A star at the top.

4 ÷ 2 =

How it is taught

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A missing number in a division can be a factor.

Ask what times 9 equals 36.

Read it: Find the missing number

___ × 3 = 12. Make groups of 3 from 12 apples and count them: 4 groups, so the missing number is 4.

Read it: ___ × 3 = 12 asks how many groups of 3 make 12.
Make groups of 3 from the 12 and count the groups.
Check it: 4 × 3 = 12, so 12 ÷ 3 = 4.

A multiplication and a division can be the same fact.

The missing factor tells how many equal groups there are in all.

So 4 × 3 = 12 and 12 ÷ 3 = 4 are one fact, written two ways.

To find a missing factor, count the equal groups that make the total.

Writing 3, the number in each group, as the answer.

3 is how many are in each group. Count the groups instead: 4.

81 ÷ ___ = 9 — 9. 9 groups of 9 make 81, so 81 ÷ 9 = 9.

56 ÷ ? = 7

Today we'll find a missing number in a division. Imagine fifty-six cookies, and each friend gets seven. How many friends can we share with?

We can write this as fifty-six divided by something equals seven. The question mark is what we need to find.

The unknown is the divisor — the number we're dividing by.

Division and multiplication are related. We can rewrite this as: something times seven equals fifty-six.

Now ask yourself — what number times seven equals fifty-six?

Grade 3 · Use multiplication to find a missing divisor

Eight! Eight times seven equals fifty-six.

So the unknown is eight. We can put eight back into the division.

Let's check — fifty-six cookies shared with eight friends gives each friend seven cookies. It works!

The unknown is eight. Multiplication helps us solve division. Great job!

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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