Find the Unknown in a Multiplication Equation

Students determine the missing whole number in multiplication equations where the unknown can be in any position (e.g., ? x 6 = 42, 7 x ? = 42, or 7 x 6 = ?). They use known facts, arrays, and the relationship between multiplication and division to find the unknown.

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Real questions from this skill, graded here. No account, and nothing is saved.

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

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12 rungs. A star at the top.

Jada plants 8 tulips in the park. She makes 4 equal rows, and every row gets the same number of tulips. What is that number?

How it is taught

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A missing factor is found by dividing the product.

4 times what number equals 12?

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.

___ × 7 = 63 — 9. 9 groups of 7 make 63, so 9 × 7 = 63 and 63 ÷ 7 = 9.

? × 5 = 35

Thirty-five cookies are arranged in equal rows of five. How many rows are there?

We can write this puzzle as: question mark, times five, equals thirty-five.

The question mark is what we need to find — the missing factor.

Multiplication and division are connected, so we can flip this into a division.

Thirty-five divided by five will give us our missing factor.

Now we ask ourselves: what number times five equals thirty-five?

We know our fives — seven times five is thirty-five!

So the missing factor is seven.

Let's check: seven times five really is thirty-five. It works!

Grade 3 · Use a known fact to find the missing factor

There are seven rows of cookies. Great multiplication thinking!

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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Standard

CCSS.3.OA.A.4

Determine the unknown whole number in a multiplication or division equation relating three whole numbers

Grade 3

Quoted from the Common Core State Standards.

Where this sits

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What a star here means

A star here is the top of a twelve-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 3

This is one rung of 104 in Grade 3 mathematics, in the order they build on each other.

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