Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-006
Use Multiplication Properties
Represent use multiplication properties with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent use multiplication properties with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving use multiplication properties 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 Use Multiplication Properties
The commutative, associative, and distributive properties let multiplication be rearranged or decomposed without changing value.
A reliable reasoning strategy
Choose a property that turns a difficult product into easier known facts, then recombine the parts.
Representations that should agree
Properties explain why array rotations, regrouped factors, and split rectangles preserve total quantity. 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.
Array Builder
Build equal rows and columns, then connect the grid to repeated addition.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
Split 3 × 8 using 5+3.
3 × 8 = 24; 3 × 5 = 15; 3 × 3 = 9; 15 + 9 = 24The distributive property splits one factor while preserving the total.
Regroup 4 × 7 × 4 without changing factor order.
4 × 7 = 28; 28 × 4 = 112; 7 × 4 = 28; 4 × 28 = 112The associative property changes grouping, not factor order.
Use commutativity to rewrite 5 × 3.
5 × 3 = 15; 3 × 5 = 15Changing factor order does not change the product.
Split 6 × 8 using 5+3.
6 × 8 = 48; 6 × 5 = 30; 6 × 3 = 18; 30 + 18 = 48The distributive property splits one factor while preserving the total.
Regroup 2 × 7 × 4 without changing factor order.
2 × 7 = 14; 14 × 4 = 56; 7 × 4 = 28; 2 × 28 = 56The associative property changes grouping, not factor order.
Use commutativity to rewrite 3 × 3.
3 × 3 = 9; 3 × 3 = 9Changing factor order does not change the product.
Split 4 × 8 using 5+3.
4 × 8 = 32; 4 × 5 = 20; 4 × 3 = 12; 20 + 12 = 32The distributive property splits one factor while preserving the total.
Regroup 5 × 7 × 4 without changing factor order.
5 × 7 = 35; 35 × 4 = 140; 7 × 4 = 28; 5 × 28 = 140The associative property changes grouping, not factor order.
Use commutativity to rewrite 6 × 3.
6 × 3 = 18; 3 × 6 = 18Changing factor order does not change the product.
Split 2 × 8 using 5+3.
2 × 8 = 16; 2 × 5 = 10; 2 × 3 = 6; 10 + 6 = 16The distributive property splits one factor while preserving the total.
Regroup 3 × 7 × 4 without changing factor order.
3 × 7 = 21; 21 × 4 = 84; 7 × 4 = 28; 3 × 28 = 84The associative property changes grouping, not factor order.
Use commutativity to rewrite 4 × 3.
4 × 3 = 12; 3 × 4 = 12Changing factor order does not change the product.
Split 5 × 8 using 5+3.
5 × 8 = 40; 5 × 5 = 25; 5 × 3 = 15; 25 + 15 = 40The distributive property splits one factor while preserving the total.
Regroup 6 × 7 × 4 without changing factor order.
6 × 7 = 42; 42 × 4 = 168; 7 × 4 = 28; 6 × 28 = 168The associative property changes grouping, not factor order.
Use commutativity to rewrite 2 × 3.
2 × 3 = 6; 3 × 2 = 6Changing factor order does not change the product.
Split 3 × 8 using 5+3.
3 × 8 = 24; 3 × 5 = 15; 3 × 3 = 9; 15 + 9 = 24The distributive property splits one factor while preserving the total.
Regroup 4 × 7 × 4 without changing factor order.
4 × 7 = 28; 28 × 4 = 112; 7 × 4 = 28; 4 × 28 = 112The associative property changes grouping, not factor order.
Use commutativity to rewrite 5 × 3.
5 × 3 = 15; 3 × 5 = 15Changing factor order does not change the product.
Split 6 × 8 using 5+3.
6 × 8 = 48; 6 × 5 = 30; 6 × 3 = 18; 30 + 18 = 48The distributive property splits one factor while preserving the total.
Regroup 2 × 7 × 4 without changing factor order.
2 × 7 = 14; 14 × 4 = 56; 7 × 4 = 28; 2 × 28 = 56The associative property changes grouping, not factor order.
Practice
Guided practice with hints
01Split 3 × 8 using 5+3.
Hint: Choose a property that turns a difficult product into easier known facts, then recombine the parts.
Answer: 3 × 5 + 3 × 3
02Regroup 4 × 7 × 4 without changing factor order.
Hint: Choose a property that turns a difficult product into easier known facts, then recombine the parts.
Answer: 4 × (7 × 4)
03Use commutativity to rewrite 5 × 3.
Hint: Choose a property that turns a difficult product into easier known facts, then recombine the parts.
Answer: 3 × 5
04Split 6 × 8 using 5+3.
Hint: Choose a property that turns a difficult product into easier known facts, then recombine the parts.
Answer: 6 × 5 + 6 × 3
05Regroup 2 × 7 × 4 without changing factor order.
Hint: Choose a property that turns a difficult product into easier known facts, then recombine the parts.
Answer: 2 × (7 × 4)
06Use commutativity to rewrite 3 × 3.
Hint: Choose a property that turns a difficult product into easier known facts, then recombine the parts.
Answer: 3 × 3
Practice
Independent practice
01Use commutativity to rewrite 3 × 3.
Answer: 3 × 3
02Split 4 × 8 using 5+3.
Answer: 4 × 5 + 4 × 3
03Regroup 5 × 7 × 4 without changing factor order.
Answer: 5 × (7 × 4)
04Use commutativity to rewrite 6 × 3.
Answer: 3 × 6
05Split 2 × 8 using 5+3.
Answer: 2 × 5 + 2 × 3
06Regroup 3 × 7 × 4 without changing factor order.
Answer: 3 × (7 × 4)
07Use commutativity to rewrite 4 × 3.
Answer: 3 × 4
08Split 5 × 8 using 5+3.
Answer: 5 × 5 + 5 × 3
Common mistakes
Learn to catch the error, not just the answer.
Track exactly which quantities are reordered, regrouped, or decomposed.
Reconnect the answer to use multiplication properties and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Break harder products into friendly facts during mental math.
- Use use multiplication properties to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Regroup 3 × 7 × 4 without changing factor order.
3 × (7 × 4)
Use commutativity to rewrite 4 × 3.
3 × 4
Split 5 × 8 using 5+3.
5 × 5 + 5 × 3
Regroup 6 × 7 × 4 without changing factor order.
6 × (7 × 4)
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Use Multiplication Properties Challenge
Solve and explain Grade 3 problems involving use multiplication properties without relying on answer guessing.
Practice
Mastery check
01Split 3 × 8 using 5+3.
Answer: 3 × 5 + 3 × 3
02Regroup 4 × 7 × 4 without changing factor order.
Answer: 4 × (7 × 4)
03Use commutativity to rewrite 5 × 3.
Answer: 3 × 5
04Split 6 × 8 using 5+3.
Answer: 6 × 5 + 6 × 3
05Regroup 2 × 7 × 4 without changing factor order.
Answer: 2 × (7 × 4)
06Use commutativity to rewrite 3 × 3.
Answer: 3 × 3
07Split 4 × 8 using 5+3.
Answer: 4 × 5 + 4 × 3
08Regroup 5 × 7 × 4 without changing factor order.
Answer: 5 × (7 × 4)
Terminology
Words to know
- commutative property
- Changing factor order without changing the product.
- distributive property
- Breaking a factor into parts and adding partial products.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.OA.5
Primary standards alignment for Use Multiplication Properties.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.