Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-005
Relate Multiplication and Division
Represent relate multiplication and division with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent relate multiplication and division with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving relate multiplication and division 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 Relate Multiplication and Division
Multiplication and division describe the same equal-group relationship from different directions.
A reliable reasoning strategy
Use one multiplication fact to write the two related division facts and the commuted multiplication fact.
Representations that should agree
Fact families reduce memorization because known products unlock related quotients. 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.
Use 3 × 4 = 12. What is 12 ÷ 4?
3The same factors and product form related multiplication and division facts.
Write the commuted multiplication fact for 4 × 6 = 24.
6 × 4 = 24The same factors and product form related multiplication and division facts.
Which three numbers form the fact family containing 5 × 8 = 40?
5, 8, 40The same factors and product form related multiplication and division facts.
Use 6 × 3 = 18. What is 18 ÷ 6?
3The same factors and product form related multiplication and division facts.
Use 7 × 5 = 35. What is 35 ÷ 5?
7The same factors and product form related multiplication and division facts.
Write the commuted multiplication fact for 8 × 7 = 56.
7 × 8 = 56The same factors and product form related multiplication and division facts.
Which three numbers form the fact family containing 2 × 2 = 4?
2, 2, 4The same factors and product form related multiplication and division facts.
Use 3 × 4 = 12. What is 12 ÷ 3?
4The same factors and product form related multiplication and division facts.
Use 4 × 6 = 24. What is 24 ÷ 6?
4The same factors and product form related multiplication and division facts.
Write the commuted multiplication fact for 5 × 8 = 40.
8 × 5 = 40The same factors and product form related multiplication and division facts.
Which three numbers form the fact family containing 6 × 3 = 18?
6, 3, 18The same factors and product form related multiplication and division facts.
Use 7 × 5 = 35. What is 35 ÷ 7?
5The same factors and product form related multiplication and division facts.
Use 8 × 7 = 56. What is 56 ÷ 7?
8The same factors and product form related multiplication and division facts.
Write the commuted multiplication fact for 2 × 2 = 4.
2 × 2 = 4The same factors and product form related multiplication and division facts.
Which three numbers form the fact family containing 3 × 4 = 12?
3, 4, 12The same factors and product form related multiplication and division facts.
Use 4 × 6 = 24. What is 24 ÷ 4?
6The same factors and product form related multiplication and division facts.
Use 5 × 8 = 40. What is 40 ÷ 8?
5The same factors and product form related multiplication and division facts.
Write the commuted multiplication fact for 6 × 3 = 18.
3 × 6 = 18The same factors and product form related multiplication and division facts.
Which three numbers form the fact family containing 7 × 5 = 35?
7, 5, 35The same factors and product form related multiplication and division facts.
Use 8 × 7 = 56. What is 56 ÷ 8?
7The same factors and product form related multiplication and division facts.
Practice
Guided practice with hints
01Which three numbers form the fact family containing 5 × 8 = 40?
Hint: Use one multiplication fact to write the two related division facts and the commuted multiplication fact.
Answer: 5, 8, 40
02Use 6 × 3 = 18. What is 18 ÷ 6?
Hint: Use one multiplication fact to write the two related division facts and the commuted multiplication fact.
Answer: 3
03Use 7 × 5 = 35. What is 35 ÷ 5?
Hint: Use one multiplication fact to write the two related division facts and the commuted multiplication fact.
Answer: 7
04Write the commuted multiplication fact for 8 × 7 = 56.
Hint: Use one multiplication fact to write the two related division facts and the commuted multiplication fact.
Answer: 7 × 8 = 56
05Which three numbers form the fact family containing 2 × 2 = 4?
Hint: Use one multiplication fact to write the two related division facts and the commuted multiplication fact.
Answer: 2, 2, 4
06Use 3 × 4 = 12. What is 12 ÷ 3?
Hint: Use one multiplication fact to write the two related division facts and the commuted multiplication fact.
Answer: 4
Practice
Independent practice
01Which three numbers form the fact family containing 4 × 6 = 24?
Answer: 4, 6, 24
02Use 5 × 8 = 40. What is 40 ÷ 5?
Answer: 8
03Use 6 × 3 = 18. What is 18 ÷ 3?
Answer: 6
04Write the commuted multiplication fact for 7 × 5 = 35.
Answer: 5 × 7 = 35
05Which three numbers form the fact family containing 8 × 7 = 56?
Answer: 8, 7, 56
06Use 2 × 2 = 4. What is 4 ÷ 2?
Answer: 2
07Use 3 × 4 = 12. What is 12 ÷ 4?
Answer: 3
08Write the commuted multiplication fact for 4 × 6 = 24.
Answer: 6 × 4 = 24
Common mistakes
Learn to catch the error, not just the answer.
Keep the same three numbers and change only the operation or factor order.
Reconnect the answer to relate multiplication and division and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Check division answers by multiplying the quotient and divisor.
- Use relate multiplication and division to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Which three numbers form the fact family containing 3 × 4 = 12?
3, 4, 12
Use 4 × 6 = 24. What is 24 ÷ 4?
6
Use 5 × 8 = 40. What is 40 ÷ 8?
5
Write the commuted multiplication fact for 6 × 3 = 18.
3 × 6 = 18
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Relate Multiplication and Division Challenge
Solve and explain Grade 3 problems involving relate multiplication and division without relying on answer guessing.
Practice
Mastery check
01Which three numbers form the fact family containing 2 × 2 = 4?
Answer: 2, 2, 4
02Use 3 × 4 = 12. What is 12 ÷ 3?
Answer: 4
03Use 4 × 6 = 24. What is 24 ÷ 6?
Answer: 4
04Write the commuted multiplication fact for 5 × 8 = 40.
Answer: 8 × 5 = 40
05Which three numbers form the fact family containing 6 × 3 = 18?
Answer: 6, 3, 18
06Use 7 × 5 = 35. What is 35 ÷ 7?
Answer: 5
07Use 8 × 7 = 56. What is 56 ÷ 7?
Answer: 8
08Write the commuted multiplication fact for 2 × 2 = 4.
Answer: 2 × 2 = 4
Terminology
Words to know
- fact family
- Related multiplication and division equations using the same numbers.
- inverse operations
- Operations that undo one another.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.OA.6
Primary standards alignment for Relate Multiplication and Division.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.