Finding the missing number, like 7 x ? = 56
In 3rd grade, children learn to find the missing number in equations like 7 x ? = 56 or ? ÷ 3 = 6, using how multiplication and division fit together.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 3rd grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
What is the missing number? ? × 2 = 18
- 16
- 9
- 36
Why this matters
Solving 7 x ? = 56 is your child's first real taste of algebra. It teaches that the equal sign means the same amount as, which matters every time an equation looks unfamiliar. In later grades the question mark becomes a letter, as in 7 x n = 56, and children who are comfortable working backward from an answer find that change much less strange.
Where kids can get stuck
- Multiplying the two numbers showing, so 7 x ? = 56 gets the answer 392, because the blank is usually the answer.
- Getting stuck on an equation written backward, like 40 = ? x 5, and thinking it must be wrong.
- Dividing when the unknown comes first in a division problem, so ? ÷ 3 = 6 gets 2 instead of 18.
How you can help
- Play a guess-my-number game in the car: say "I multiplied my number by 4 and got 28. What was it?" and let your child explain how they found 7.
- Hide some buttons under a cup after telling your child you split them into 3 equal piles of 5, and ask how many were under the cup to begin with.
- Pack snack bags together and ask how many bags you need if there are 24 pretzels and each bag holds 6, then write it as ? x 6 = 24.
If it’s helpful, you can sign up for free, adaptive practice in Bobby's Math Club.
Questions parents ask
Why is my child learning to find missing numbers in different places?
Putting the blank in different places checks whether your child truly understands what an equation says. A child who sees 7 x ? = 56 as "7 groups of how many make 56" is reasoning, not following a pattern. This flexible thinking is the start of algebra, and it makes later work with unknown numbers far less intimidating.
My child says 40 = 8 x 5 is written wrong. How should I explain it?
Tell your child that the equal sign means both sides are worth the same amount, like a balanced scale. 40 and 8 x 5 are the same amount, so it does not matter which side comes first. Showing a few true sentences written both ways, such as 12 = 3 x 4 and 3 x 4 = 12, usually helps this idea settle.
Is this the same as algebra?
It is an early form of it. Your child is finding an unknown number in an equation, which is what algebra does. In 3rd grade the unknown is shown as a box or question mark and the numbers stay within 100. Later this year children start using a letter for the unknown in word problems, and that grows into formal algebra in middle school.
Make learning math fun
Bobby's Math Club turns 3rd grade math practice into something fun to do together.
- Unlimited practice, completely free
- A few minutes a day, at just the right level
- You see their progress and what to work on next
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 3.OA.A.4: “Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ?.” Learn how Bobby's Math Club can help your students grow. (Common Core 3.OA.4)