Unit Plan 12 (Grade 3 Math): Multiplication & Division Facts—7s, 8s, 9s

Focus: Apply the distributive property (break apart factors) and leverage patterns to master higher facts (7s, 8s, 9s) and their related division facts.

Grade Level: 3

Subject Area: Mathematics (Operations & Algebraic Thinking)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

Students extend fact fluency to the “harder” sets by using structure and patterns instead of memorizing blindly. They decompose factors to make friendly facts (e.g., 9×n = (10×n) − n, 7×n = (5×n) + (2×n), 8×n = (4×n) + (4×n)), represent ideas with arrays/equal groups, and connect multiplication to division with fact families. Attention to regularity (3.OA.9) helps students predict and check results efficiently.

Essential Questions

• How can I break apart factors to make 7s, 8s, and 9s easier?
• What patterns do I notice in the 9s facts (and others), and how can I use them to check?
• How do fact families help me move between × and ÷ confidently?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Use the distributive property to derive 7s, 8s, 9s facts (e.g., 7×n = 5×n + 2×n, 8×n = 4×n + 4×n, 9×n = 10×n − n).
2. Model strategies with arrays, equal groups, and number lines; explain why they work.
3. Build and use fact families to connect multiplication and division for the same three numbers.
4. Identify and explain arithmetic patterns (especially in 9s) and use them to verify results (digit sums, stair-step increases).
5. Improve accuracy and efficiency on targeted higher facts with clear justifications.

Standards Alignment — CCSS Grade 3

• 3.OA.7: Fluently multiply and divide within 100 using strategies and the relationship between multiplication and division.
• 3.OA.5: Apply properties of operations (e.g., distributive, associative, commutative) as strategies to multiply and divide.
• 3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.
• Mathematical Practices: MP.7 (look for and make use of structure) and MP.8 (express regularity in repeated reasoning).

Success Criteria — Student Language

• I can break apart a factor to solve (e.g., 9×7 = 10×7 − 7).
• I can show my thinking with an array or equal groups and explain the distributive property.
• I can write the fact family and use it to solve a division problem quickly.
• I can describe a pattern (like 9s digits summing to 9) and use it to check my answer.