Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-009
Build Facts with 6s, 7s, 8s, and 9s
Represent build facts with 6s, 7s, 8s, and 9s with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent build facts with 6s, 7s, 8s, and 9s with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving build facts with 6s, 7s, 8s, and 9s 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 Build Facts with 6s, 7s, 8s, and 9s
Larger multiplication facts can be derived from easier facts using near-10, double, and distributive strategies.
A reliable reasoning strategy
Choose a nearby fact you know, then add or subtract one group or split a factor into friendly parts.
Representations that should agree
Strategic derivation strengthens both fluency and understanding of properties. 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.
Find 7 × 2.
7 × 2 = 14Use a known 7s pattern or derive the product from a nearby fact.
Find 8 × 3.
8 × 3 = 24Use a known 8s pattern or derive the product from a nearby fact.
Find 9 × 4.
9 × 4 = 36Use a known 9s pattern or derive the product from a nearby fact.
Find 6 × 5.
6 × 5 = 30Use a known 6s pattern or derive the product from a nearby fact.
Find 7 × 6.
7 × 6 = 42Use a known 7s pattern or derive the product from a nearby fact.
Find 8 × 7.
8 × 7 = 56Use a known 8s pattern or derive the product from a nearby fact.
Find 9 × 8.
9 × 8 = 72Use a known 9s pattern or derive the product from a nearby fact.
Find 6 × 9.
6 × 9 = 54Use a known 6s pattern or derive the product from a nearby fact.
Find 7 × 10.
7 × 10 = 70Use a known 7s pattern or derive the product from a nearby fact.
Find 8 × 1.
8 × 1 = 8Use a known 8s pattern or derive the product from a nearby fact.
Find 9 × 2.
9 × 2 = 18Use a known 9s pattern or derive the product from a nearby fact.
Find 6 × 3.
6 × 3 = 18Use a known 6s pattern or derive the product from a nearby fact.
Find 7 × 4.
7 × 4 = 28Use a known 7s pattern or derive the product from a nearby fact.
Find 8 × 5.
8 × 5 = 40Use a known 8s pattern or derive the product from a nearby fact.
Find 9 × 6.
9 × 6 = 54Use a known 9s pattern or derive the product from a nearby fact.
Find 6 × 7.
6 × 7 = 42Use a known 6s pattern or derive the product from a nearby fact.
Find 7 × 8.
7 × 8 = 56Use a known 7s pattern or derive the product from a nearby fact.
Find 8 × 9.
8 × 9 = 72Use a known 8s pattern or derive the product from a nearby fact.
Find 9 × 10.
9 × 10 = 90Use a known 9s pattern or derive the product from a nearby fact.
Find 6 × 1.
6 × 1 = 6Use a known 6s pattern or derive the product from a nearby fact.
Practice
Guided practice with hints
01Find 9 × 2.
Hint: Choose a nearby fact you know, then add or subtract one group or split a factor into friendly parts.
Answer: 18
02Find 6 × 3.
Hint: Choose a nearby fact you know, then add or subtract one group or split a factor into friendly parts.
Answer: 18
03Find 7 × 4.
Hint: Choose a nearby fact you know, then add or subtract one group or split a factor into friendly parts.
Answer: 28
04Find 8 × 5.
Hint: Choose a nearby fact you know, then add or subtract one group or split a factor into friendly parts.
Answer: 40
05Find 9 × 6.
Hint: Choose a nearby fact you know, then add or subtract one group or split a factor into friendly parts.
Answer: 54
06Find 6 × 7.
Hint: Choose a nearby fact you know, then add or subtract one group or split a factor into friendly parts.
Answer: 42
Practice
Independent practice
01Find 9 × 2.
Answer: 18
02Find 6 × 3.
Answer: 18
03Find 7 × 4.
Answer: 28
04Find 8 × 5.
Answer: 40
05Find 9 × 6.
Answer: 54
06Find 6 × 7.
Answer: 42
07Find 7 × 8.
Answer: 56
08Find 8 × 9.
Answer: 72
Common mistakes
Learn to catch the error, not just the answer.
Rebuild uncertain facts from a known anchor and verify with an array or related division fact.
Reconnect the answer to build facts with 6s, 7s, 8s, and 9s and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Calculate equal bundles, rows, and repeated quantities efficiently.
- Use build facts with 6s, 7s, 8s, and 9s to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Find 9 × 2.
18
Find 6 × 3.
18
Find 7 × 4.
28
Find 8 × 5.
40
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Build Facts with 6s, 7s, 8s, and 9s Challenge
Solve and explain Grade 3 problems involving build facts with 6s, 7s, 8s, and 9s without relying on answer guessing.
Practice
Mastery check
01Find 9 × 2.
Answer: 18
02Find 6 × 3.
Answer: 18
03Find 7 × 4.
Answer: 28
04Find 8 × 5.
Answer: 40
05Find 9 × 6.
Answer: 54
06Find 6 × 7.
Answer: 42
07Find 7 × 8.
Answer: 56
08Find 8 × 9.
Answer: 72
Terminology
Words to know
- derived fact
- A fact found from another known fact.
- near-ten strategy
- Use ten groups, then adjust by one or more groups.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.OA.7
Primary standards alignment for Build Facts with 6s, 7s, 8s, and 9s.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.