Unit Plan 23 (Grade 6 Math): GCF, LCM, and the Distributive Property
6th graders find the greatest common factor (GCF) and least common multiple (LCM) using prime factorization and apply the distributive property to factor sums. Students connect these skills to real-world grouping, scheduling, and mental math problems for deeper number sense.
Focus: Find GCF/LCM; use the distributive property to factor sums and support mental computation.
Grade Level: 6
Subject Area: Mathematics (Number System — Factors/Multiples; Expressions — Distributive Property)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students build fluency with factors and multiples through hands-on strategies: factor lists, prime factorization (trees/ladders), and Venn diagrams of prime factors. They apply these to compute GCF (greatest common factor) and LCM (least common multiple) and then use the distributive property to factor sums (for example, 36 + 24 = 12*(3 + 2)) to simplify calculations and reason about grouping and repeated events.
Essential Questions
- When should I use GCF vs LCM in a real situation?
- How does prime factorization help me find GCF/LCM reliably?
- How does the distributive property let me factor a sum and compute more easily?
- How can I explain my choice of method and units so others can follow my reasoning?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Distinguish factors and multiples; identify prime vs composite numbers up to 100.
- Use prime factorization (trees or ladders) to find GCF and LCM of two whole numbers ≤ 100.
- Choose GCF to solve partitioning/tiling problems (greatest equal groups, largest equal tiles).
- Choose LCM to solve scheduling/repeat problems (when cycles align, smallest common batch size).
- Use the distributive property to factor sums with a common factor (for example, 48 + 72 = 24*(2 + 3)) and explain how factoring supports mental computation and modeling.
Standards Alignment — CCSS Grade 6
- 6.NS.4: Find GCF and LCM of two whole numbers ≤ 100; use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers (for example, 36 + 8 = 4*(9 + 2)); apply GCF/LCM to real-world and mathematical problems.
- Mathematical Practices emphasized: MP.1 (make sense), MP.2 (reason quantitatively), MP.3 (justify), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can tell whether a problem needs GCF (share/partition) or LCM (line up/repeat).
- I can make a prime factorization and use it to find GCF/LCM correctly.
- I can factor a sum using the distributive property and explain why the factoring works.
- I can write a clear unit sentence that interprets my answer in the situation.
- I can check my result by expanding or by listing factors/multiples to verify.