Grade 4 · Operations & Algebraic Thinking · MAT-04-OA-007
Classify Prime and Composite Numbers
Represent and solve classify prime and composite numbers problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve classify prime and composite numbers problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for classify prime and composite numbers works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Classify Prime and Composite Numbers describes multiplicative structure inside whole numbers. Factor relationships explain exact products and divisibility, while multiples extend repeated equal groups.
Represent the idea
The Math Box uses multiplication grid as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
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 one example of classify prime and composite numbers in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
Classify 2 as prime or composite.
2 is prime.2 has exactly two positive factors: 1 and 2.
Classify 6 as prime or composite.
6 is composite.6 has a factor other than 1 and itself, so it is composite.
Classify 5 as prime or composite.
5 is prime.5 has exactly two positive factors: 1 and 5.
Classify 9 as prime or composite.
9 is composite.9 has a factor other than 1 and itself, so it is composite.
Classify 11 as prime or composite.
11 is prime.11 has exactly two positive factors: 1 and 11.
Classify 12 as prime or composite.
12 is composite.12 has a factor other than 1 and itself, so it is composite.
Classify 17 as prime or composite.
17 is prime.17 has exactly two positive factors: 1 and 17.
Classify 15 as prime or composite.
15 is composite.15 has a factor other than 1 and itself, so it is composite.
Classify 23 as prime or composite.
23 is prime.23 has exactly two positive factors: 1 and 23.
Classify 18 as prime or composite.
18 is composite.18 has a factor other than 1 and itself, so it is composite.
Classify 31 as prime or composite.
31 is prime.31 has exactly two positive factors: 1 and 31.
Classify 21 as prime or composite.
21 is composite.21 has a factor other than 1 and itself, so it is composite.
Classify 41 as prime or composite.
41 is prime.41 has exactly two positive factors: 1 and 41.
Classify 24 as prime or composite.
24 is composite.24 has a factor other than 1 and itself, so it is composite.
Classify 47 as prime or composite.
47 is prime.47 has exactly two positive factors: 1 and 47.
Classify 4 as prime or composite.
4 is composite.4 has a factor other than 1 and itself, so it is composite.
Classify 3 as prime or composite.
3 is prime.3 has exactly two positive factors: 1 and 3.
Classify 8 as prime or composite.
8 is composite.8 has a factor other than 1 and itself, so it is composite.
Classify 7 as prime or composite.
7 is prime.7 has exactly two positive factors: 1 and 7.
Classify 10 as prime or composite.
10 is composite.10 has a factor other than 1 and itself, so it is composite.
Practice
Guided practice with hints
01Classify 13 as prime or composite.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 13 is prime.
02Classify 14 as prime or composite.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 14 is composite.
03Classify 19 as prime or composite.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 19 is prime.
04Classify 16 as prime or composite.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 16 is composite.
05Classify 29 as prime or composite.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 29 is prime.
06Classify 20 as prime or composite.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 20 is composite.
Practice
Independent practice
01Classify 37 as prime or composite.
Answer: 37 is prime.
02Classify 22 as prime or composite.
Answer: 22 is composite.
03Classify 43 as prime or composite.
Answer: 43 is prime.
04Classify 25 as prime or composite.
Answer: 25 is composite.
05Classify 2 as prime or composite.
Answer: 2 is prime.
06Classify 6 as prime or composite.
Answer: 6 is composite.
07Classify 5 as prime or composite.
Answer: 5 is prime.
08Classify 9 as prime or composite.
Answer: 9 is composite.
Common mistakes
Learn to catch the error, not just the answer.
Identify what each number represents and how the quantities are related before selecting an operation.
Estimate, use an inverse operation, or compare with a second representation.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Use classify prime and composite numbers when solving multi-step problems in measurement, data, money, design, or everyday quantitative decisions.
- Explain the result with units and a second check so another person can audit the reasoning.
Challenge problems
Classify 11 as prime or composite.
11 is prime.
Classify 12 as prime or composite.
12 is composite.
Classify 17 as prime or composite.
17 is prime.
Classify 15 as prime or composite.
15 is composite.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain classify prime and composite numbers problems accurately, then check each result with a second method.
Practice
Mastery check
01Classify 23 as prime or composite.
Answer: 23 is prime.
02Classify 18 as prime or composite.
Answer: 18 is composite.
03Classify 31 as prime or composite.
Answer: 31 is prime.
04Classify 21 as prime or composite.
Answer: 21 is composite.
05Classify 41 as prime or composite.
Answer: 41 is prime.
06Classify 24 as prime or composite.
Answer: 24 is composite.
07Classify 47 as prime or composite.
Answer: 47 is prime.
08Classify 4 as prime or composite.
Answer: 4 is composite.
Terminology
Words to know
- factor
- A whole number that divides another whole number without a remainder.
- multiple
- A product of a number and a whole number.
- prime
- A whole number greater than 1 with exactly two positive factors.
- composite
- A whole number greater than 1 with more than two positive factors.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.