Unit Plan 5 (Grade 3 Math): Properties of Operations—Strategy Builders
Build multiplication fact power by using commutative, associative, and distributive properties to turn hard facts into easier ones; model with arrays and area/tape diagrams to justify efficient strategies and solve real-world problems.
Focus: Apply commutative, associative, and distributive properties to build efficient fact strategies from known facts and patterns.
Grade Level: 3
Subject Area: Mathematics (Operations & Algebraic Thinking)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students use structure to make multiplication facts within 100 more accessible. They discover how turnarounds (commutative), regrouping factors (associative), and breaking apart (distributive) transform hard facts into easy ones. Word problems provide purpose for choosing a property-based strategy.
Essential Questions
- How can properties of operations turn a hard fact into an easier one?
- When is the distributive property (break apart) more helpful than a commutative turnaround?
- How does noticing regularity (MP.8) help me predict and check results?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Explain and use the commutative, associative, and distributive properties to generate and justify multiplication strategies within 100.
- Represent property-based reasoning with arrays, area models, tape (bar) diagrams, and equations with an unknown.
- Solve word problems by selecting a property that simplifies computation and communicate why it works.
- Look for and express regularity in repeated reasoning (MP.8) to extend from known to unknown facts.
- Check strategies for reasonableness and relate to known facts and patterns.
Standards Alignment — CCSS Grade 3
- 3.OA.5: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide.
- 3.OA.3: Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities (drawings/equations with a symbol for the unknown).
- 3.OA.7 (fluency build): Fluently multiply and divide within 100 using strategies such as properties and the relationship between multiplication and division.
- Mathematical Practices: MP.8 (regularity in repeated reasoning).
Success Criteria — Student Language
- I can name the property I used (commutative, associative, or distributive) and explain why it helps.
- I can show my strategy with an array/area model/tape diagram and an equation.
- I can solve a word problem by choosing a property that makes the numbers easier and justify my choice.