Home›Lesson Plans›Mathematics›Operations & Algebraic Thinking · Grade 5

Divisibility Rules

Fifth graders learn shortcuts that reveal whether a number can be split evenly by 2, 3, 5, 9, or 10, just by looking at its digits, then check what they know.

Grade 5Divisibility Rules50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Assign or share this lesson

Copy link works with Canvas, Schoology, Moodle and any other LMS — paste it in as a resource or assignment.

Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Use rules for 2, 5, and 10.
  • ✓Add digits for 3 and 9.
  • ✓Test a number fast.
  • ✓Check what you know.
Essential Question

Is 1,230 divisible by 5? You could do the long division, or just glance at the last digit. How do divisibility rules let you tell at a glance?

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Model · Interactive Tool

Divisibility Check

Project this and answer each question about the divisibility rules for 2, 3, 5, 9, and 10 — read the explanation after each one.

➗ Check what you know about divisibility rulesTry it
Answer each question about the divisibility rules for 2, 3, 5, 9, and 10.
The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

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

1

Hook — A Shortcut to Dividing

5 min

Is 1,230 divisible by 5? You could divide it out, or you could just glance at the last digit. Divisibility rules let you tell at a glance. How do they work?

👩‍🏫 Teacher Moves

  • Show 1,230.
  • Ask if it splits by 5.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Divisibility Check

12 min

Students answer questions about divisibility rules.

👩‍🏫 Teacher Moves

  • Send students to the Divisibility Check.
  • Answer each question.
  • Read the why.

🎒 Student Actions

  • Answer.
  • Check.
  • Read it.
3

Modify — Test a Number

13 min

Students test numbers against the rules.

👩‍🏫 Teacher Moves

  • Pick a three-digit number.
  • Check it against each rule.
  • List what divides it.

🎒 Student Actions

  • Pick.
  • Check.
  • List.
4

Create — My Rule Chart

15 min

Students make a divisibility reference.

👩‍🏫 Teacher Moves

  • List the rules for 2, 3, 5, 9, 10.
  • Give an example for each.
  • Add one number that passes all of them.

🎒 Student Actions

  • List.
  • Show.
  • Add.
5

Reflect — Tell at a Glance

5 min

Students reflect on the rules.

👩‍🏫 Teacher Moves

  • How can you tell a number is divisible by 5?
  • What is the rule for divisibility by 3?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
4.OA.B.4

Find factor pairs and multiples, and tell whether a number is prime or composite.

CCSS
5.NBT.B.6

Find whole-number quotients using place value and the properties of operations.

CCSS
MP.7

Look for and make use of structure.

CCSS
MP.8

Look for and express regularity in repeated reasoning.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Rule reference cards.
  • Sentence frame: “___ is divisible by ___ because ___ .”
  • Answer one question at a time.

Support & Access

IEP / 504
  • Start with the rules for 2, 5, and 10.
  • Test small numbers first.
  • Review one question at a time.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Add the rules for 4, 6, and 8.
  • Use digit sums on four-digit numbers.
  • Explain why the rule for 3 and 9 works with digit sums.
Materials

What to gather

  • 📽️Projector / board
  • 🧮Number cards
  • 💻Divisibility Check
  • 🃏Rule reference cards
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

divisibleable to be divided evenly, with no remainderdivisibility rulea shortcut that tells whether one number divides anotherfactora number that divides another evenlymultiplethe product of a number and a whole numberremainderwhat is left over when a number does not divide evenlydigit sumthe total you get by adding all the digits of a numberevena number whose ones digit is 0, 2, 4, 6, or 8quotientthe result of dividing one number by another
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
How can you tell a number is divisible by 5?
Its last digit is 0 or 5, such as 60 or 85.
QUESTION 2
What is the rule for divisibility by 3?
Add the digits; if the sum is divisible by 3, so is the number. For 213, 2 + 1 + 3 = 6, which divides by 3.
QUESTION 3
Is 724 divisible by 2? How do you know?
Yes, because its last digit, 4, is even.

Create: my rule chart.

Have students list the rules for 2, 3, 5, 9, and 10 with an example each, then find one number that passes all of them, so the shortcuts stick. A printable divisibility-rules worksheet is in the Mathematics 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.

🃏 Divisibility RulesFlip
Card 1
Term
Tap to flip →
Meaning
0

Nice work!

Practice · Quiz

Check your understanding

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

📝 Divisibility RulesQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

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.

🖨️ Divisibility RulesPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: digit sum, divisibility rule, divisible, even, factor, multiple, quotient, remainder
  1. the product of a number and a whole number
  2. what is left over when a number does not divide evenly
  3. a number whose ones digit is 0, 2, 4, 6, or 8
  4. the result of dividing one number by another
  5. a number that divides another evenly
  6. the total you get by adding all the digits of a number
  7. able to be divided evenly, with no remainder
  8. a shortcut that tells whether one number divides another

Part B · Show what you learned

  1. How can you tell a number is divisible by 5?
  2. What is the rule for divisibility by 3?
  3. Is 724 divisible by 2? How do you know?
Answer key — Part A: 1) multiple · 2) remainder · 3) even · 4) quotient · 5) factor · 6) digit sum · 7) divisible · 8) divisibility rule
Part B: 1) Its last digit is 0 or 5, such as 60 or 85. 2) Add the digits; if the sum is divisible by 3, so is the number. For 213, 2 + 1 + 3 = 6, which divides by 3. 3) Yes, because its last digit, 4, is even.