Skill by skill
Missing Number Problems: How to Help Your Child Solve □ + 3 = 7
Help your child solve missing number problems like □ + 3 = 7: the equals sign as “the same as”, balance thinking, bar models, games and quick fixes.
Quick answer
A missing number problem asks which number makes both sides equal, as in □ + 3 = 7. Teach your child to read = as “is the same as”, then think in parts and a whole: 7 is the whole and 3 is one part, so the missing part is 7 − 3 = 4. Balances, bar drawings and real objects help, and putting the answer back in (4 + 3 = 7) checks it.
Key takeaways
- The equals sign means “is the same as”, not “the answer comes next”. In one US study, how well 2nd graders understood it strongly predicted their algebra skills in 4th grade.
- Every addition or subtraction links two parts and a whole. Whole missing? Add. Part missing? Subtract, however the problem is written.
- Draw it: a part–whole diagram or a bar model shows which number is missing.
- Mix up the format: write 7 = 3 + 4 and 4 + 3 = 2 + 5, not only 3 + 4 = □.
- Always check by putting the number back in the box.
What are missing number problems?
A missing number problem is a number sentence with a gap, usually a box or a question mark, such as □ + 3 = 7: your child finds the number that makes it true. Teachers also call these missing addend problems or unknowns. They are early algebra, because the box is the x of middle school.
They appear in every early curriculum. Common Core asks 1st graders to find the unknown in sentences like 8 + ? = 11 and 5 = □ − 3, and 3rd graders to do the same with multiplication and division, like 8 × ? = 48. England's Year 1 curriculum names them directly: “missing number problems such as 7 = ? − 9”.
- □ + 3 = 7 → □ = 4, because 4 + 3 = 7
- 9 − □ = 5 → □ = 4, because 9 − 4 = 5
- □ × 4 = 20 → □ = 5, because 5 × 4 = 20
- 12 ÷ □ = 3 → □ = 4, because 12 ÷ 4 = 3
- 7 = □ − 9 → □ = 16, because 16 − 9 = 7
Tip Start with “make 10” (2 minutes)
Even kindergartners solve missing number problems: Common Core asks them to find the number that makes 10 with any number from 1 to 9. Hold up 7 fingers and ask, “How many more to make 10?” That's 7 + □ = 10, and the answer is 3.
When do children learn missing number problems?
| Age | US (Common Core) | England (national curriculum) |
|---|---|---|
| 5–6 | Kindergarten: find the number that makes 10, such as 7 + □ = 10 | Year 1: missing number problems such as 7 = □ − 9 |
| 6–7 | 1st grade: decide if equations are true or false; find unknowns such as 8 + □ = 11 | Year 2: use the link between addition and subtraction to solve them |
| 7–8 | 2nd grade: word problems within 100 with the unknown in any position | Year 3: missing number problems with multiplication and division |
| 8–9 | 3rd grade: unknowns in multiplication and division, such as 8 × □ = 48 | Year 4: all tables up to 12 × 12, so □ × 7 = 56 becomes a known fact |
Missing numbers grow with your child: from “how many more to make 10?” at 5 to two-step problems with a letter for the unknown by 3rd and 4th grade. For the bigger picture, see math skills by age.
Why does the equals sign confuse so many children?
Most sums children see look like 3 + 4 = □, with the answer on the right, so many conclude that = means “put the answer here”. England's official maths guidance warns against exactly this: children should not think of the equals sign as meaning “and the answer is”, but understand that both sides have the same value.
Researchers test this with one simple question: 8 + 4 = □ + 5. Most elementary school children answer 12 or 17 instead of 7, and in a classic 1999 study all 145 sixth graders gave one of those two answers. It matters later, too: in a US study that followed children from 2nd to 4th grade, equals-sign knowledge in 2nd grade was a powerful predictor of 4th-grade algebra skills, even after accounting for other differences.
- Left side: 8 + 4 = 12
- The right side must also make 12: □ + 5 = 12
- So □ = 7
- Common wrong answers: 12 (the answer to 8 + 4) and 17 (8 + 4 + 5)
What helps is simple. Read = aloud as “is the same as”, and write sums both ways: 7 = 3 + 4 as well as 3 + 4 = 7. In a randomized study, 7- and 8-year-olds who practiced addition written answer-first (17 = 9 + 8) understood equivalence better than children who practiced the usual 9 + 8 = 17.
Tip True or false? (2 minutes at dinner)
Say a sentence and let your child judge it: “6 + 1 is the same as 7. True or false?” Then “7 is the same as 3 + 4?” and “5 + 2 is the same as 4 + 4?” (false: 7 is not 8).
What is balance thinking?
An equation works like a seesaw or an old-fashioned balance scale: both sides must weigh the same. If one side is heavier, you add to the other side until it balances. This picture makes 8 + 4 = □ + 5 feel natural, because the question becomes “what balances 12?”
The 2021 What Works Clearinghouse practice guide shows a teacher building this idea with counters: a row of 7 and a row of 9. “How many must we add to the 7 to make it the same as the 9?” (2). Then she adds 2 to the row of 9 instead, writes 7 + □ = 9 + 2, and the children find that the 7 now needs 4.
Human Balance
- Your child stands with arms stretched out like a balance scale.
- Put 3 blocks in one hand and 5 in the other. Which hand has more? Lean that way, like a scale.
- Ask: “How many blocks does the lighter hand need to balance?” (2)
- Say it as a sentence: 3 + 2 is the same as 5. Then swap roles and let your child set you a puzzle.
Part–whole and bar models: how does drawing help?
Every addition or subtraction links three numbers: two parts and a whole. In 3 + 4 = 7, the parts are 3 and 4 and the whole is 7. A part–whole model writes the whole in one circle joined to two circles for the parts. A bar model draws a long bar for the whole, split into the parts.
Once your child knows which number is missing, the method follows. England's maths guidance puts it simply: addition finds an unknown whole and subtraction finds an unknown part, however the problem is written. So 25 + □ = 40 looks like addition, but a part is missing, so you subtract.
- 25 + □ = 40 → a part is missing → 40 − 25 = 15
- □ − 6 = 9 → the whole is missing → 9 + 6 = 15
- 14 − □ = 8 → a part is missing → 14 − 8 = 6
- □ × 4 = 20 → a bar of 20 cut into 4 equal parts → 20 ÷ 4 = 5
One bar model gives a whole family of facts. With parts 3 and 4 and whole 7, your child can write 8 true sentences: 3 + 4 = 7, 4 + 3 = 7, 7 − 3 = 4, 7 − 4 = 3, 7 = 3 + 4, 7 = 4 + 3, 4 = 7 − 3 and 3 = 7 − 4.
Tip Draw it on a napkin
Next time homework has a missing number, draw a long rectangle, write the whole above it and split it into two parts. Fill in what you know; the empty part is the box. Our subtraction guide explains subtraction as undoing addition.
Step by step: how to solve a missing number problem
- Read it with “is the same as”: “Something plus 3 is the same as 7.”
- Build or draw it: lay out 3 blocks and add blocks until there are 7, or sketch a bar.
- Ask: part or whole? Here 7 is the whole, and a part is missing.
- Choose the operation: missing whole, add the parts; missing part, subtract the part you know from the whole, or count on from it (3… 4, 5, 6, 7 is 4 more).
- Check: put the number in the box and read it again: “4 + 3 is the same as 7. True!”
- Maya had some stickers. She got 5 more. Now she has 12.
- □ + 5 = 12
- 12 is the whole and 5 is a part: 12 − 5 = 7
- Check: 7 + 5 = 12, so Maya started with 7 stickers
Stories with an unknown start, like Maya's, are missing number problems in disguise. The number bonds in our addition guide make them quick.
Screen-free missing number games
Hide the Bears
- Count 7 toys together.
- While your child closes their eyes, hide some under the cup.
- Show the rest, for example 3: “How many are hiding?”
- Lift the cup to check, then say it: 3 and 4 make 7, so 3 + □ = 7 means □ = 4.
I'm Thinking of a Number
- Say: “I'm thinking of a number. If I add 5, I get 12. What's my number?” (7)
- Take turns making up mystery numbers.
- Harder: “I doubled my number and got 18” (9), or “I took away 4 and got 10” (14).
- Ask how they worked it out; the explanation matters more than speed.
Fill the Box
- Lay the pencil down as the equals sign.
- Put two cards to its left, for example 6 and 3, and one card to its right, for example 4.
- Read it as 6 + 3 = 4 + □. The first player to say the missing number (5) wins the cards.
- If the single card is bigger than the total of the pair, deal a new single card.
More ideas are in our math games for home.
Common mistakes (and quick fixes)
- Adding the numbers you see. 5 + □ = 8 answered as 13. Fix: read it as “5 plus what is the same as 8?” and build it with objects.
- Adding everything. 8 + 4 = □ + 5 answered as 17. Fix: work out the complete side first (12), then make the other side match.
- Subtracting when the whole is missing. □ − 6 = 9 answered as 3. Fix: draw the bar. The whole is missing, so add: 9 + 6 = 15.
- Rejecting sentences that start with =. “7 = 3 + 4 is backwards!” Fix: play true or false with sentences written both ways.
- Not checking. Fix: make “put it back in the box” a habit.
When to talk to the teacher
If your 8-year-old still writes the total in every box, or refuses any sentence that doesn't end with the answer, tell the teacher and ask which pictures the class uses, such as bar models or number lines. The symbols < and > follow the same both-sides logic; see comparing numbers.
Frequently asked questions
What is a missing number problem?
It is a number sentence with a blank or a box, like □ + 3 = 7, where your child finds the number that makes it true. It is an early form of algebra, and children meet it from kindergarten onward.
How do you explain a missing addend to a child?
Use parts and a whole. In □ + 3 = 7, 7 is the whole and 3 is one part, so the missing part is 7 − 3 = 4. Building it with objects or drawing a bar makes this easy to see.
Why does my child write 12 in 8 + 4 = □ + 5?
Many children read the equals sign as “the answer goes here”. Teach it as “is the same as”: 8 + 4 is 12, so □ + 5 must also be 12, which makes the missing number 7.
What grade are missing number problems taught in?
In the US, kindergartners find the number that makes 10, 1st graders solve problems like 8 + ? = 11 and 3rd graders solve ones like 8 × ? = 48. In England, missing number problems are named in the Year 1 curriculum.
What is a bar model in math?
A bar model is a drawing of a long bar for the whole, split into parts. It shows at a glance whether the missing number is a part, which you find by subtracting, or the whole, which you find by adding.
Is □ + 3 = 7 really algebra?
Yes, in an early form. The box stands for an unknown number, just like x later on, and research suggests that children who understand the equals sign well in 2nd grade do better in algebra by 4th grade.
Sources
Written by the Matobur team at Edict Digital and checked against these sources:
- Kindergarten: Operations & Algebraic Thinking (K.OA) (opens in a new tab)Common Core State Standards Initiative
- Grade 1: Operations & Algebraic Thinking (1.OA) (opens in a new tab)Common Core State Standards Initiative
- Grade 2: Operations & Algebraic Thinking (2.OA) (opens in a new tab)Common Core State Standards Initiative
- Grade 3: Operations & Algebraic Thinking (3.OA) (opens in a new tab)Common Core State Standards Initiative
- National curriculum in England: mathematics programmes of study (opens in a new tab)UK Department for Education
- Mathematics guidance: key stages 1 and 2 (Teaching mathematics in primary schools) (opens in a new tab)UK Department for Education
- Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (practice guide, 2021) (opens in a new tab)Institute of Education Sciences, What Works Clearinghouse (US Department of Education)
- Matthews, P. G., & Fuchs, L. S. (2020). Keys to the Gate? Equal Sign Knowledge at Second Grade Predicts Fourth-Grade Algebra Competence. Child Development, 91(1) (opens in a new tab)Child Development (Society for Research in Child Development), via PubMed Central
- McNeil, N. M., et al. (2011). Benefits of Practicing 4 = 2 + 2: Nontraditional Problem Formats Facilitate Children's Understanding of Mathematical Equivalence. Child Development, 82(5), 1620–1633 (opens in a new tab)ERIC, Institute of Education Sciences (US Department of Education)