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Grade 4 Math Units

Unit Plan 6 (Grade 4 Math): Factors, Multiples, Prime/Composite

Find factor pairs and multiples for numbers 1–100, and determine whether each is prime or composite using arrays, factor rainbows, and divisibility reasoning.

Dr. Michael Kester-Haynes

• 6 min read
Unit Plan 6 (Grade 4 Math): Factors, Multiples, Prime/Composite

Focus: Find factor pairs, identify multiples, and classify numbers (1–100) as prime or composite.

Grade Level: 4

Subject Area: Mathematics (Operations & Algebraic Thinking • Number Theory)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

This week builds number sense through factors and multiples. Students use arrays and rectangle models to generate factor pairs, apply divisibility reasoning, and decide whether numbers from 1–100 are prime or composite. The emphasis is on clear models, complete lists, and convincing explanations.

Essential Questions

  • How do factors and multiples relate to one another?
  • What makes a number prime or composite, and how can I prove it?
  • Which representations (arrays, factor rainbows, divisibility tests) best justify my classification?

II. Objectives and Standards

Learning Objectives — Students will be able to:

  1. Generate factor pairs for whole numbers (1–100) using arrays/rectangle models and factor rainbows.
  2. List and describe multiples of a whole number; connect skip-counting to multiplication.
  3. Use divisibility reasoning (e.g., by 2, 3, 5, 10) to test factor relationships efficiently.
  4. Classify numbers as prime or composite and justify the decision with evidence.
  5. Communicate with precision: show complete factor sets, label units, and check for reasonableness.

Standards Alignment — CCSS Grade 4 (spiral across the unit)

  • 4.OA.4: Find all factor pairs for a whole number in the range 1–100; recognize a number as a multiple of each of its factors; determine whether a given whole number in the range 1–100 is prime or composite.
  • Mathematical Practices (MP.1–MP.8) threaded throughout.

Success Criteria — Student Language

  • I can list all factor pairs for a number and show how I know the list is complete.
  • I can explain that if a × b = n, then n is a multiple of a and b, and a and b are factors of n.
  • I can prove a number is prime or composite using arrays, factor rainbows, or divisibility checks.