Prime Composite Sort

Overview

This lesson is the fourth in a unit called “Mastering Multiplication Concepts.” Today students use multiplication and factor thinking to define prime and composite numbers and then classify numbers correctly.

Learning intentions

Students will be able to:

• define prime numbers as numbers with exactly two factors (1 and itself)
• define composite numbers as numbers with more than two factors
• identify factors using multiplication relationships and divisibility by 2, 3, 5, and 10
• classify given numbers as prime or composite and justify their classification using factor reasoning

Success criteria

Students can correctly categorize at least 10 numbers in a class activity as prime or composite, with most justifications referencing factor counts or a clear multiplication/divisibility check.

Curriculum links

• Number and Operations in Base Ten: apply place value reasoning that supports understanding of divisibility patterns used to find factors and classify numbers
• Number and Operations in Base Ten: explain patterns related to multiplication by powers of 10 to support systematic factor checks (e.g., understanding how zeros affect divisibility by 10)
• Add, subtract, multiply, and divide decimals to hundredths: use known place-value strategies and reasoning to support accurate work when converting factor checks into written explanations
• Fractions and multiplication interpretation: use “a parts of q” thinking as a model for factor reasoning (factors represent equal parts/amounts in a multiplicative relationship)

Lesson structure (30 minutes)

1. 0–5 min · Bell work + factor warm-up. Teacher displays 6 small prompts on the board: “Which numbers have 1 and themselves as factors only?” Teacher says, “Use any factor check you know.” Students work silently for 2 minutes, then volunteer 1 example each.

Teacher prompts (quick):

• Is 7 prime or composite? Why?
• Is 9 prime or composite? Why?

2. 5–12 min · Mini-lesson: definitions with examples. Teacher writes: “Prime = 2 factors” and “Composite = more than 2 factors,” then demonstrates with factor pairs using a quick table for 2, 3, 4, 6, and 9. Students record the definitions and complete a 2-column organizer: “Prime examples” and “Composite examples.”

3. 12–20 min · Guided practice: factor testing strategy. Teacher teaches a simple, age-appropriate method for factor checking up to half of a number and uses divisibility shortcuts:

• If a number is even, it has factors 2 and itself
• If it ends in 0, it has factor 10
• If it’s divisible by 3, it has factor 3 Teacher models classifying 12 and 13 aloud, focusing on counting factors (not guessing). Students work in pairs on 6 numbers from a provided set (e.g., 11, 12, 14, 15, 16, 19), marking factor pairs.

4. 20–26 min · Independent check: “Prime/Composite Sort.” Teacher distributes a “Sort & Justify” sheet with 20 numbers. Students cut (or circle) numbers into two categories and must write a one-sentence justification for 3 of them: either “It has exactly two factors” or “It has more than two factors,” plus one factor example.

5. 26–30 min · Share-out + exit check. Teacher selects 2 student examples and asks, “What factors did you find?” Students complete a 1-question exit ticket: classify 21 or 23 (teacher chooses one) and write the key factor reason.

Resources

• Prime/Composite Definitions and Factor Pairs handout (teacher-made)
• “Sort & Justify” printable sheet (20 numbers)
• Partner set cards or number strips for guided practice
• Whiteboard or chart paper with a factor-pair table
• Small counters or index cards (optional: “factor pair” cards to build factor sets)
• Timer for segmenting the lesson
• Exit ticket slip for each student

Assessment

• Formative: teacher listens during guided practice for correct factor thinking (especially avoiding “even/odd only” misconceptions)
• Formative: quick pair-share at minute 12–20—students must name at least one factor pair
• Summative-for-today: collect the Sort & Justify sheet to verify at least 10 correct classifications; review justifications on 3 chosen numbers
• Exit ticket: prime/composite classification with a short factor reason

Differentiation

• Support: provide a partially completed factor-pair chart for numbers 4–20 and sentence starters: “I know it is composite because…” “I know it is prime because…”
• Support: allow students to use divisibility checks (2, 3, 5, 10) before listing all factor pairs
• Extension: challenge students to explain why 1 is neither prime nor composite and include it as a “special case” note on the sort sheet
• EAL/SEN: offer an optional word bank (“factor,” “divisible by,” “two factors,” “more than two factors”) and allow oral justification with a partner before writing