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Factors & Primes: The Building Blocks of Numbers

Students find the factor pairs of numbers and discover that some numbers can only be built one way — those special numbers are called primes.

Grade 4Factors & Primes45 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Find all the factor pairs of a number.
  • ✓Tell prime from composite numbers.
  • ✓Explain that a prime has exactly two factors.
  • ✓List multiples of a number.
Essential Question

Some numbers split into lots of equal groups; some can only split into 1 and themselves. What makes a number “prime”?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Factor Finder

Project this and change the number. Watch its factor pairs appear, and see whether it turns out prime or composite.

🔍 Change the number — find its factorsTry it
12
Number: 12

The Lesson · Gradual Release (I Do · We Do · You Do)

45 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Build 12

5 min

How many ways can you make an array of 12?

👩‍🏫 Teacher Moves

  • Ask students to build arrays of 12.
  • List the factor pairs (1×12, 2×6, 3×4).
  • Set the goal: factors and primes.

🎒 Student Actions

  • Build arrays of 12.
  • Find factor pairs.
  • Predict what “prime” means.
2

I Do — Factors & Primes

10 min

Teacher models finding factors.

👩‍🏫 Teacher Moves

  • Find all factors of a number.
  • Show prime = exactly 2 factors.
  • Show composite = more than 2.

🎒 Student Actions

  • Find all factors.
  • Count them.
  • Sort prime vs. composite.
3

We Do — Find Together

12 min

Class drives the Factor Finder.

👩‍🏫 Teacher Moves

  • Use the Finder for several numbers.
  • Predict prime or composite first.
  • Notice patterns (evens are composite).

🎒 Student Actions

  • Predict prime/composite.
  • Read the factor pairs.
  • Spot a pattern.
4

You Do — On Your Own

13 min

Students find factors + primes.

👩‍🏫 Teacher Moves

  • Assign numbers to factor.
  • Identify primes up to 20.
  • List multiples of a number.

🎒 Student Actions

  • List factor pairs.
  • Circle the primes.
  • List some multiples.
5

Close — Close

5 min

Prime or composite?

👩‍🏫 Teacher Moves

  • Show a number; students decide.
  • Justify with factors.
  • Hand out the exit ticket.

🎒 Student Actions

  • Decide prime/composite.
  • Give the factors.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
4.OA.4

Find all factor pairs for a whole number 1–100; recognize a number as prime or composite.

CCSS
4.OA.5

Generate a number pattern that follows a given rule.

CCSS
3.OA.B.5

Apply properties of operations as strategies to multiply.

SMP
MP.7

Look for and make use of structure in the factors of numbers.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Build arrays with tiles to see factors.
  • Sentence frame: “The factors of ___ are ___.”
  • Sort number cards into prime/composite.

Support & Access

IEP / 504
  • Start with numbers under 20.
  • Provide arrays already drawn.
  • Focus on prime = only 1 and itself.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Find primes up to 50 (a sieve).
  • Find the greatest common factor of two numbers.
  • Explain why 1 is neither prime nor composite.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Factor Finder
  • 🟦Square tiles
  • 📊A hundreds chart
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

factora number that divides evenly into anotherfactor pairtwo factors that multiply to a numbermultiplethe product of a number and a whole numberprimea number with exactly two factorscompositea number with more than two factorsproductthe answer to a multiplicationdivisiblecan be divided with no remainderarrayequal rows and columns
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
List all the factor pairs of 18.
1×18, 2×9, 3×6.
QUESTION 2
Is 7 prime or composite? How do you know?
Prime — its only factors are 1 and 7 (exactly two factors).
QUESTION 3
List the first four multiples of 5.
5, 10, 15, 20.

Going deeper? Build a prime sieve.

Have students cross out multiples on a hundreds chart to reveal all the prime numbers up to 100 (the Sieve of Eratosthenes). A printable hundreds chart is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Factors, Multiples & PrimesFlip
Card 1
Term
Tap to flip →
Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Factors, Multiples & PrimesQuiz
Score: 0
1 / 6
Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Factors, Multiples & PrimesPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: array, composite, divisible, factor, factor pair, multiple, prime, product
  1. two factors that multiply to a number
  2. a number that divides evenly into another
  3. a number with exactly two factors
  4. a number with more than two factors
  5. can be divided with no remainder
  6. the product of a number and a whole number
  7. equal rows and columns
  8. the answer to a multiplication

Part B · Show what you learned

  1. List all the factor pairs of 18.
  2. Is 7 prime or composite? How do you know?
  3. List the first four multiples of 5.
Answer key — Part A: 1) factor pair · 2) factor · 3) prime · 4) composite · 5) divisible · 6) multiple · 7) array · 8) product
Part B: 1) 1×18, 2×9, 3×6. 2) Prime — its only factors are 1 and 7 (exactly two factors). 3) 5, 10, 15, 20.