Mathematics · Class 6 · The World of Numbers · Term 1

Divisibility Rules for 2, 3, 5, 10

Discovering and applying divisibility rules for 2, 3, 5, and 10 to quickly check for factors.

• CBSE Learning Outcomes
• NCERT: Playing with Numbers - Divisibility Rules - Class 6

About This Topic

Divisibility rules for 2, 3, 5, and 10 offer quick methods to check factors without performing division each time. A number is divisible by 2 if its ones digit is even (0, 2, 4, 6, or 8); by 5 if it ends with 0 or 5; by 10 if it ends with 0; and by 3 if the sum of its digits is divisible by 3. These rules connect to place value: for example, multiples of 10 in higher places are already divisible by 2, 5, and 10, while the base-10 system explains the digit sum for 3.

In the CBSE Class 6 unit on Playing with Numbers, students discover these rules, justify them using place value, and predict numbers meeting multiple criteria. This builds number sense, logical reasoning, and skills for factors and multiples, aligning with NCERT standards. Teachers can link it to real-life applications like checking dates or prices for divisibility.

Active learning benefits this topic greatly because rules are pattern-based and verifiable through exploration. When students sort numbers, play matching games, or test predictions in groups, they uncover rules themselves, leading to deeper understanding and retention compared to rote memorisation.

Key Questions

1. How do divisibility rules simplify the process of finding factors?
2. Justify why certain divisibility rules work based on place value.
3. Predict which numbers will be divisible by multiple rules simultaneously.

Learning Objectives

• Identify the ones digit or sum of digits that determines divisibility by 2, 3, 5, and 10.
• Explain the place value reasoning behind the divisibility rules for 2, 3, 5, and 10.
• Calculate whether a given number is divisible by 2, 3, 5, and 10 without performing long division.
• Predict which numbers will satisfy divisibility by multiple rules (e.g., by both 2 and 5) and justify the prediction.
• Classify numbers based on their divisibility by 2, 3, 5, and 10.

Before You Start

Understanding Place Value

Why: Students need a firm grasp of place value to understand why the ones digit or sum of digits is important for divisibility.

Basic Operations: Addition and Division

Why: Students must be able to add digits to find their sum and understand the concept of division and remainders.

Identifying Even and Odd Numbers

Why: The divisibility rule for 2 is directly related to whether a number is even or odd.

Key Vocabulary

Divisibility Rule	A shortcut method to determine if a number can be divided by another number without leaving a remainder.
Factor	A number that divides another number exactly, without leaving any remainder.
Ones Digit	The rightmost digit in a number, representing the value of units.
Sum of Digits	The result obtained by adding all the individual digits of a number together.
Place Value	The value of a digit based on its position within a number (e.g., ones, tens, hundreds).

Watch Out for These Misconceptions

Common Misconception

A number is divisible by 3 only if its last digit is 3, 6, or 9.

What to Teach Instead

The correct rule uses the sum of all digits. Sorting activities help students test various numbers, revealing the pattern across positions and correcting the focus on last digit alone through peer comparison.

Common Misconception

Numbers ending in 5 are divisible by 10.

What to Teach Instead

Divisibility by 10 requires ending in 0. Hands-on card matching games allow students to group numbers by endings, observe differences, and build criteria collaboratively.

Common Misconception

All even numbers end in 0.

What to Teach Instead

Even ones digits include 0,2,4,6,8. Prediction relays expose this by testing counterexamples, helping students refine definitions via group discussion.

Active Learning Ideas

Card Sort: Divisibility Hunt

Prepare cards with 20-30 two-digit numbers. Students work in small groups to sort cards into four piles for each rule (divisible or not). Groups then share one pattern they notice and test it on new numbers.

30 min·Small Groups

Bingo Game: Rule Masters

Create bingo cards with numbers; call out rules randomly. Students mark numbers on their card divisible by the called rule and justify with a partner before claiming bingo. Review justifications as a class.

40 min·Whole Class

Place Value Chain: Digit Sum Relay

In pairs, students add digits of a number; if sum >9, repeat until single digit, checking divisibility by 3. Pairs race to classify 10 numbers and explain why the process works.

25 min·Pairs

Prediction Challenge: Multi-Rule Grid

Provide a 5x5 grid of numbers. Individually predict and colour cells divisible by 2,3,5,or 10. Share grids in small groups to verify and discuss overlaps.

35 min·Small Groups

Real-World Connections

• Cashiers use divisibility rules to quickly count out change. For instance, if a customer pays with a ₹100 note for an item costing ₹20, the cashier can mentally check if the change (₹80) is easily divisible by common coin denominations like ₹2, ₹5, or ₹10.
• Event planners might use divisibility rules when arranging seating. If they need to divide 120 guests into equal groups, they can quickly see it's divisible by 2, 3, 5, and 10, allowing for various table arrangements like rows of 10 or groups of 5.

Assessment Ideas

Quick Check

Present a list of numbers (e.g., 150, 234, 555, 780, 999). Ask students to write beside each number which of the rules (2, 3, 5, 10) it satisfies. For example, '150: 2, 3, 5, 10'.

Discussion Prompt

Pose the question: 'If a number is divisible by both 2 and 5, what must be true about its ones digit? Explain your reasoning using place value.' Facilitate a class discussion where students share their answers and justifications.

Exit Ticket

Give each student a card with a number (e.g., 360). Ask them to write down: 1. Is this number divisible by 3? (Yes/No) 2. Show the sum of its digits. 3. Is this number divisible by 2, 5, or 10? (List all that apply).

Frequently Asked Questions

How do divisibility rules for 2, 3, 5, 10 work in Class 6 maths?

These rules simplify factor checks: even ones digit for 2; ends in 0 or 5 for 5; ends in 0 for 10; digit sum divisible by 3 for 3. They rely on place value, like tens being multiples of 10. Practice with mixed numbers builds speed and accuracy for NCERT problems on factors.

Why do divisibility rules relate to place value?

Place value explains the rules: higher places are multiples of 10 (divisible by 2,5,10), so only ones digit matters for those. For 3, since 10 ≡ 1 mod 3, digit sum equals the number mod 3. Exploring with expanded forms helps students justify this logically.

How can active learning help teach divisibility rules?

Active methods like card sorts, bingo, and relays engage students in discovering patterns firsthand. Grouping encourages justification and error correction through discussion, making rules memorable. This approach shifts from rote learning to conceptual grasp, improving application in factor-finding tasks.

What are common errors with divisibility by 3 rule?

Students often check only the last digit or reduce sum incorrectly. Group testing activities reveal these gaps, as peers challenge assumptions. Structured reflections post-activity solidify the full-digit-sum process, reducing errors in multi-digit numbers.