Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-013
Identify Arithmetic Patterns
Represent identify arithmetic patterns with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent identify arithmetic patterns with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving identify arithmetic patterns 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 Identify Arithmetic Patterns
Arithmetic patterns reveal predictable changes in sums, products, parity, and place value.
A reliable reasoning strategy
List several cases, describe what changes, and explain why the pattern must continue.
Representations that should agree
Patterns can be justified with properties rather than accepted from a few examples alone. 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.
Number Line Explorer
Move along the number line.
4 is one less. 5 and 6 is one more.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
Pattern: 3, 6, 9, 12, __. What comes next and why?
Add 3 each time, so the next value is 15.The constant difference identifies the arithmetic pattern.
Pattern: 8, 12, 16, 20, __. What comes next and why?
Add 4 each time, so the next value is 24.The constant difference identifies the arithmetic pattern.
Pattern: 15, 20, 25, 30, __. What comes next and why?
Add 5 each time, so the next value is 35.The constant difference identifies the arithmetic pattern.
Pattern: 0, 10, 20, 30, __. What comes next and why?
Add 10 each time, so the next value is 40.The constant difference identifies the arithmetic pattern.
Pattern: 2, 4, 6, 8, __. What comes next and why?
Add 2 each time, so the next value is 10.The constant difference identifies the arithmetic pattern.
Pattern: 6, 9, 12, 15, __. What comes next and why?
Add 3 each time, so the next value is 18.The constant difference identifies the arithmetic pattern.
Pattern: 12, 16, 20, 24, __. What comes next and why?
Add 4 each time, so the next value is 28.The constant difference identifies the arithmetic pattern.
Pattern: 0, 5, 10, 15, __. What comes next and why?
Add 5 each time, so the next value is 20.The constant difference identifies the arithmetic pattern.
Pattern: 10, 20, 30, 40, __. What comes next and why?
Add 10 each time, so the next value is 50.The constant difference identifies the arithmetic pattern.
Pattern: 4, 6, 8, 10, __. What comes next and why?
Add 2 each time, so the next value is 12.The constant difference identifies the arithmetic pattern.
Pattern: 9, 12, 15, 18, __. What comes next and why?
Add 3 each time, so the next value is 21.The constant difference identifies the arithmetic pattern.
Pattern: 0, 4, 8, 12, __. What comes next and why?
Add 4 each time, so the next value is 16.The constant difference identifies the arithmetic pattern.
Pattern: 5, 10, 15, 20, __. What comes next and why?
Add 5 each time, so the next value is 25.The constant difference identifies the arithmetic pattern.
Pattern: 20, 30, 40, 50, __. What comes next and why?
Add 10 each time, so the next value is 60.The constant difference identifies the arithmetic pattern.
Pattern: 6, 8, 10, 12, __. What comes next and why?
Add 2 each time, so the next value is 14.The constant difference identifies the arithmetic pattern.
Pattern: 0, 3, 6, 9, __. What comes next and why?
Add 3 each time, so the next value is 12.The constant difference identifies the arithmetic pattern.
Pattern: 4, 8, 12, 16, __. What comes next and why?
Add 4 each time, so the next value is 20.The constant difference identifies the arithmetic pattern.
Pattern: 10, 15, 20, 25, __. What comes next and why?
Add 5 each time, so the next value is 30.The constant difference identifies the arithmetic pattern.
Pattern: 30, 40, 50, 60, __. What comes next and why?
Add 10 each time, so the next value is 70.The constant difference identifies the arithmetic pattern.
Pattern: 0, 2, 4, 6, __. What comes next and why?
Add 2 each time, so the next value is 8.The constant difference identifies the arithmetic pattern.
Practice
Guided practice with hints
01Pattern: 9, 12, 15, 18, __. What comes next and why?
Hint: List several cases, describe what changes, and explain why the pattern must continue.
Answer: 21
02Pattern: 0, 4, 8, 12, __. What comes next and why?
Hint: List several cases, describe what changes, and explain why the pattern must continue.
Answer: 16
03Pattern: 5, 10, 15, 20, __. What comes next and why?
Hint: List several cases, describe what changes, and explain why the pattern must continue.
Answer: 25
04Pattern: 20, 30, 40, 50, __. What comes next and why?
Hint: List several cases, describe what changes, and explain why the pattern must continue.
Answer: 60
05Pattern: 6, 8, 10, 12, __. What comes next and why?
Hint: List several cases, describe what changes, and explain why the pattern must continue.
Answer: 14
06Pattern: 0, 3, 6, 9, __. What comes next and why?
Hint: List several cases, describe what changes, and explain why the pattern must continue.
Answer: 12
Practice
Independent practice
01Pattern: 9, 12, 15, 18, __. What comes next and why?
Answer: 21
02Pattern: 0, 4, 8, 12, __. What comes next and why?
Answer: 16
03Pattern: 5, 10, 15, 20, __. What comes next and why?
Answer: 25
04Pattern: 20, 30, 40, 50, __. What comes next and why?
Answer: 60
05Pattern: 6, 8, 10, 12, __. What comes next and why?
Answer: 14
06Pattern: 0, 3, 6, 9, __. What comes next and why?
Answer: 12
07Pattern: 4, 8, 12, 16, __. What comes next and why?
Answer: 20
08Pattern: 10, 15, 20, 25, __. What comes next and why?
Answer: 30
Common mistakes
Learn to catch the error, not just the answer.
Test multiple cases and connect the pattern to a mathematical property or structure.
Reconnect the answer to identify arithmetic patterns and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Predict products, skip-count sequences, and place-value changes.
- Use identify arithmetic patterns to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Pattern: 9, 12, 15, 18, __. What comes next and why?
21
Pattern: 0, 4, 8, 12, __. What comes next and why?
16
Pattern: 5, 10, 15, 20, __. What comes next and why?
25
Pattern: 20, 30, 40, 50, __. What comes next and why?
60
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Identify Arithmetic Patterns Challenge
Solve and explain Grade 3 problems involving identify arithmetic patterns without relying on answer guessing.
Practice
Mastery check
01Pattern: 9, 12, 15, 18, __. What comes next and why?
Answer: 21
02Pattern: 0, 4, 8, 12, __. What comes next and why?
Answer: 16
03Pattern: 5, 10, 15, 20, __. What comes next and why?
Answer: 25
04Pattern: 20, 30, 40, 50, __. What comes next and why?
Answer: 60
05Pattern: 6, 8, 10, 12, __. What comes next and why?
Answer: 14
06Pattern: 0, 3, 6, 9, __. What comes next and why?
Answer: 12
07Pattern: 4, 8, 12, 16, __. What comes next and why?
Answer: 20
08Pattern: 10, 15, 20, 25, __. What comes next and why?
Answer: 30
Terminology
Words to know
- pattern
- A regular mathematical relationship or sequence.
- even number
- A whole number divisible into pairs with no remainder.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.OA.9
Primary standards alignment for Identify Arithmetic Patterns.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.