Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-007
Build Facts with 2s, 5s, and 10s
Represent build facts with 2s, 5s, and 10s with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent build facts with 2s, 5s, and 10s with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving build facts with 2s, 5s, and 10s 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 2s, 5s, and 10s
Facts with 2, 5, and 10 follow strong patterns that anchor multiplication fluency.
A reliable reasoning strategy
Use doubles for 2s, clock/skip-count patterns for 5s, and place-value patterns for 10s.
Representations that should agree
These facts become building blocks for harder products through the distributive property. 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 5 × 2.
5 × 2 = 10Use a known 5s pattern or derive the product from a nearby fact.
Find 10 × 3.
10 × 3 = 30Use a known 10s pattern or derive the product from a nearby fact.
Find 2 × 4.
2 × 4 = 8Use a known 2s pattern or derive the product from a nearby fact.
Find 5 × 5.
5 × 5 = 25Use a known 5s pattern or derive the product from a nearby fact.
Find 10 × 6.
10 × 6 = 60Use a known 10s pattern or derive the product from a nearby fact.
Find 2 × 7.
2 × 7 = 14Use a known 2s pattern or derive the product from a nearby fact.
Find 5 × 8.
5 × 8 = 40Use a known 5s pattern or derive the product from a nearby fact.
Find 10 × 9.
10 × 9 = 90Use a known 10s pattern or derive the product from a nearby fact.
Find 2 × 10.
2 × 10 = 20Use a known 2s pattern or derive the product from a nearby fact.
Find 5 × 1.
5 × 1 = 5Use a known 5s pattern or derive the product from a nearby fact.
Find 10 × 2.
10 × 2 = 20Use a known 10s pattern or derive the product from a nearby fact.
Find 2 × 3.
2 × 3 = 6Use a known 2s pattern or derive the product from a nearby fact.
Find 5 × 4.
5 × 4 = 20Use a known 5s pattern or derive the product from a nearby fact.
Find 10 × 5.
10 × 5 = 50Use a known 10s pattern or derive the product from a nearby fact.
Find 2 × 6.
2 × 6 = 12Use a known 2s pattern or derive the product from a nearby fact.
Find 5 × 7.
5 × 7 = 35Use a known 5s pattern or derive the product from a nearby fact.
Find 10 × 8.
10 × 8 = 80Use a known 10s pattern or derive the product from a nearby fact.
Find 2 × 9.
2 × 9 = 18Use a known 2s pattern or derive the product from a nearby fact.
Find 5 × 10.
5 × 10 = 50Use a known 5s pattern or derive the product from a nearby fact.
Find 10 × 1.
10 × 1 = 10Use a known 10s pattern or derive the product from a nearby fact.
Practice
Guided practice with hints
01Find 5 × 2.
Hint: Use doubles for 2s, clock/skip-count patterns for 5s, and place-value patterns for 10s.
Answer: 10
02Find 10 × 3.
Hint: Use doubles for 2s, clock/skip-count patterns for 5s, and place-value patterns for 10s.
Answer: 30
03Find 2 × 4.
Hint: Use doubles for 2s, clock/skip-count patterns for 5s, and place-value patterns for 10s.
Answer: 8
04Find 5 × 5.
Hint: Use doubles for 2s, clock/skip-count patterns for 5s, and place-value patterns for 10s.
Answer: 25
05Find 10 × 6.
Hint: Use doubles for 2s, clock/skip-count patterns for 5s, and place-value patterns for 10s.
Answer: 60
06Find 2 × 7.
Hint: Use doubles for 2s, clock/skip-count patterns for 5s, and place-value patterns for 10s.
Answer: 14
Practice
Independent practice
01Find 2 × 2.
Answer: 4
02Find 5 × 3.
Answer: 15
03Find 10 × 4.
Answer: 40
04Find 2 × 5.
Answer: 10
05Find 5 × 6.
Answer: 30
06Find 10 × 7.
Answer: 70
07Find 2 × 8.
Answer: 16
08Find 5 × 9.
Answer: 45
Common mistakes
Learn to catch the error, not just the answer.
Pair each fact with an array, equal-groups model, or known property.
Reconnect the answer to build facts with 2s, 5s, and 10s and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Count pairs, nickels, and groups of ten quickly.
- Use build facts with 2s, 5s, and 10s to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Find 10 × 2.
20
Find 2 × 3.
6
Find 5 × 4.
20
Find 10 × 5.
50
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Build Facts with 2s, 5s, and 10s Challenge
Solve and explain Grade 3 problems involving build facts with 2s, 5s, and 10s without relying on answer guessing.
Practice
Mastery check
01Find 5 × 2.
Answer: 10
02Find 10 × 3.
Answer: 30
03Find 2 × 4.
Answer: 8
04Find 5 × 5.
Answer: 25
05Find 10 × 6.
Answer: 60
06Find 2 × 7.
Answer: 14
07Find 5 × 8.
Answer: 40
08Find 10 × 9.
Answer: 90
Terminology
Words to know
- multiple
- A product formed by multiplying a number by a whole number.
- fluency
- Accurate, efficient recall supported by understanding.
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 2s, 5s, and 10s.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.