Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-010
Find Unknowns in Multiplication and Division Equations
Represent find unknowns in multiplication and division equations with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent find unknowns in multiplication and division equations with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving find unknowns in multiplication and division equations accurately and explain why the method works.
- Check results for reasonableness using a second representation, inverse relationship, benchmark, or property when appropriate.
Prerequisite check
Make sure the foundation is ready.
Checks conceptual readiness before new Grade 3 reasoning.
Checks whether prior skills are available for use, not only recalled by name.
Learn
Build the idea from meaning, not memorization.
Meaning of Find Unknowns in Multiplication and Division Equations
An unknown can appear in any position of a multiplication or division equation.
A reliable reasoning strategy
Use the relationship among factors, product, dividend, divisor, and quotient to choose the inverse operation.
Representations that should agree
A fact family keeps the equation balanced while revealing the missing value. A correct model, equation, verbal explanation, or diagram should preserve the same quantities and relationships.
How to check the result
Check whether the answer fits the quantities, units, and structure of the problem. Use a second representation or inverse relationship when available, and explain what would make an answer unreasonable.
Interactive math lab
Change it. See what stays true.
Equation Balance
Adjust both sides. Equality means both expressions have the same value.
Balanced: both sides have equal value.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
15 ÷ ? = 5. Find the unknown divisor.
3 × 5 = 15Use the related multiplication fact.
32 ÷ 4 = ?.
32 ÷ 4 = 8The quotient is the missing factor in the related multiplication fact.
? × 3 = 15. Find the unknown.
15 ÷ 3 = 5Divide the product by the known factor.
36 ÷ ? = 6. Find the unknown divisor.
6 × 6 = 36Use the related multiplication fact.
63 ÷ 7 = ?.
63 ÷ 7 = 9The quotient is the missing factor in the related multiplication fact.
? × 4 = 32. Find the unknown.
32 ÷ 4 = 8Divide the product by the known factor.
63 ÷ ? = 7. Find the unknown divisor.
9 × 7 = 63Use the related multiplication fact.
4 ÷ 2 = ?.
4 ÷ 2 = 2The quotient is the missing factor in the related multiplication fact.
? × 5 = 15. Find the unknown.
15 ÷ 5 = 3Divide the product by the known factor.
32 ÷ ? = 8. Find the unknown divisor.
4 × 8 = 32Use the related multiplication fact.
15 ÷ 5 = ?.
15 ÷ 5 = 3The quotient is the missing factor in the related multiplication fact.
? × 6 = 36. Find the unknown.
36 ÷ 6 = 6Divide the product by the known factor.
63 ÷ ? = 9. Find the unknown divisor.
7 × 9 = 63Use the related multiplication fact.
32 ÷ 8 = ?.
32 ÷ 8 = 4The quotient is the missing factor in the related multiplication fact.
? × 7 = 63. Find the unknown.
63 ÷ 7 = 9Divide the product by the known factor.
4 ÷ ? = 2. Find the unknown divisor.
2 × 2 = 4Use the related multiplication fact.
15 ÷ 3 = ?.
15 ÷ 3 = 5The quotient is the missing factor in the related multiplication fact.
? × 8 = 32. Find the unknown.
32 ÷ 8 = 4Divide the product by the known factor.
15 ÷ ? = 3. Find the unknown divisor.
5 × 3 = 15Use the related multiplication fact.
36 ÷ 6 = ?.
36 ÷ 6 = 6The quotient is the missing factor in the related multiplication fact.
Practice
Guided practice with hints
0163 ÷ ? = 7. Find the unknown divisor.
Hint: Use the relationship among factors, product, dividend, divisor, and quotient to choose the inverse operation.
Answer: 9
024 ÷ 2 = ?.
Hint: Use the relationship among factors, product, dividend, divisor, and quotient to choose the inverse operation.
Answer: 2
03? × 5 = 15. Find the unknown.
Hint: Use the relationship among factors, product, dividend, divisor, and quotient to choose the inverse operation.
Answer: 3
0432 ÷ ? = 8. Find the unknown divisor.
Hint: Use the relationship among factors, product, dividend, divisor, and quotient to choose the inverse operation.
Answer: 4
0515 ÷ 5 = ?.
Hint: Use the relationship among factors, product, dividend, divisor, and quotient to choose the inverse operation.
Answer: 3
06? × 6 = 36. Find the unknown.
Hint: Use the relationship among factors, product, dividend, divisor, and quotient to choose the inverse operation.
Answer: 6
Practice
Independent practice
01? × 3 = 15. Find the unknown.
Answer: 5
0236 ÷ ? = 6. Find the unknown divisor.
Answer: 6
0363 ÷ 7 = ?.
Answer: 9
04? × 4 = 32. Find the unknown.
Answer: 8
0563 ÷ ? = 7. Find the unknown divisor.
Answer: 9
064 ÷ 2 = ?.
Answer: 2
07? × 5 = 15. Find the unknown.
Answer: 3
0832 ÷ ? = 8. Find the unknown divisor.
Answer: 4
Common mistakes
Learn to catch the error, not just the answer.
Read the whole equation and identify what role the missing number plays.
Reconnect the answer to find unknowns in multiplication and division equations and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Find missing quantities in equal-group and sharing situations.
- Use find unknowns in multiplication and division equations to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
63 ÷ 9 = ?.
7
? × 2 = 4. Find the unknown.
2
15 ÷ ? = 5. Find the unknown divisor.
3
32 ÷ 4 = ?.
8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Find Unknowns in Multiplication and Division Equations Challenge
Solve and explain Grade 3 problems involving find unknowns in multiplication and division equations without relying on answer guessing.
Practice
Mastery check
0115 ÷ ? = 3. Find the unknown divisor.
Answer: 5
0236 ÷ 6 = ?.
Answer: 6
03? × 9 = 63. Find the unknown.
Answer: 7
0432 ÷ ? = 4. Find the unknown divisor.
Answer: 8
0563 ÷ 9 = ?.
Answer: 7
06? × 2 = 4. Find the unknown.
Answer: 2
0715 ÷ ? = 5. Find the unknown divisor.
Answer: 3
0832 ÷ 4 = ?.
Answer: 8
Terminology
Words to know
- unknown
- A value that must be determined.
- equation
- A statement that two expressions have equal value.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.OA.4
Primary standards alignment for Find Unknowns in Multiplication and Division Equations.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.