Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-008
Build Facts with 3s and 4s
Represent build facts with 3s and 4s with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent build facts with 3s and 4s with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving build facts with 3s and 4s 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 3s and 4s
Facts with 3 and 4 can be built from known doubles and smaller facts instead of memorized in isolation.
A reliable reasoning strategy
For 4s, double twice; for 3s, combine a double with one more group.
Representations that should agree
Decomposition turns each fact into a transparent chain of known products. 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.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
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 3 × 1.
3 × 1 = 3Count 1 groups of 3, or use the 3s pattern to reach 3.
Find 3 × 2.
3 × 2 = 6Count 2 groups of 3, or use the 3s pattern to reach 6.
Find 3 × 3.
3 × 3 = 9Count 3 groups of 3, or use the 3s pattern to reach 9.
Find 3 × 4.
3 × 4 = 12Count 4 groups of 3, or use the 3s pattern to reach 12.
Find 3 × 5.
3 × 5 = 15Count 5 groups of 3, or use the 3s pattern to reach 15.
Find 3 × 6.
3 × 6 = 18Count 6 groups of 3, or use the 3s pattern to reach 18.
Find 3 × 7.
3 × 7 = 21Count 7 groups of 3, or use the 3s pattern to reach 21.
Find 3 × 8.
3 × 8 = 24Count 8 groups of 3, or use the 3s pattern to reach 24.
Find 3 × 9.
3 × 9 = 27Count 9 groups of 3, or use the 3s pattern to reach 27.
Find 3 × 10.
3 × 10 = 30Count 10 groups of 3, or use the 3s pattern to reach 30.
Find 4 × 1.
4 × 1 = 4Count 1 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 2.
4 × 2 = 8Count 2 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 3.
4 × 3 = 12Count 3 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 4.
4 × 4 = 16Count 4 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 5.
4 × 5 = 20Count 5 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 6.
4 × 6 = 24Count 6 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 7.
4 × 7 = 28Count 7 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 8.
4 × 8 = 32Count 8 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 9.
4 × 9 = 36Count 9 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Find 4 × 10.
4 × 10 = 40Count 10 groups of 4, double a doubles fact, or use a nearby known 4s fact.
Practice
Guided practice with hints
01Find 4 × 2.
Hint: For 4s, double twice; for 3s, combine a double with one more group.
Answer: 8
02Find 3 × 3.
Hint: For 4s, double twice; for 3s, combine a double with one more group.
Answer: 9
03Find 4 × 4.
Hint: For 4s, double twice; for 3s, combine a double with one more group.
Answer: 16
04Find 3 × 5.
Hint: For 4s, double twice; for 3s, combine a double with one more group.
Answer: 15
05Find 4 × 6.
Hint: For 4s, double twice; for 3s, combine a double with one more group.
Answer: 24
06Find 3 × 7.
Hint: For 4s, double twice; for 3s, combine a double with one more group.
Answer: 21
Practice
Independent practice
01Find 4 × 2.
Answer: 8
02Find 3 × 3.
Answer: 9
03Find 4 × 4.
Answer: 16
04Find 3 × 5.
Answer: 15
05Find 4 × 6.
Answer: 24
06Find 3 × 7.
Answer: 21
07Find 4 × 8.
Answer: 32
08Find 3 × 9.
Answer: 27
Common mistakes
Learn to catch the error, not just the answer.
Use a reasoning strategy while learning, then aim for efficient recall.
Reconnect the answer to build facts with 3s and 4s and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Count legs on groups of animals or sets of three items.
- Use build facts with 3s and 4s to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Find 4 × 2.
8
Find 3 × 3.
9
Find 4 × 4.
16
Find 3 × 5.
15
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Build Facts with 3s and 4s Challenge
Solve and explain Grade 3 problems involving build facts with 3s and 4s without relying on answer guessing.
Practice
Mastery check
01Find 4 × 2.
Answer: 8
02Find 3 × 3.
Answer: 9
03Find 4 × 4.
Answer: 16
04Find 3 × 5.
Answer: 15
05Find 4 × 6.
Answer: 24
06Find 3 × 7.
Answer: 21
07Find 4 × 8.
Answer: 32
08Find 3 × 9.
Answer: 27
Terminology
Words to know
- double
- Twice a quantity.
- decompose
- Break a quantity into useful parts.
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 3s and 4s.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.