Class VIII: Number Play

CLASS VIII • NUMBER SENSETopic: Patterns & Divisibility

Investigate divisibility, products of consecutive integers, pattern rules, remainders, and mathematical reasoning.

Fact Sheet: Patterns and Divisibility

Number play is not just about calculating. It is about investigating patterns, making claims, testing examples, and explaining why something always works.

Key Claim: The product of three consecutive integers is always divisible by 6.

nn+1n+2multiple of 6

Why? In any three consecutive integers, one number is even and one number is divisible by 3. Together, they provide factors 2 and 3, so the product is divisible by 6.

Good mathematical explanation uses both examples and a general reason.

Investigation Hub

Consecutive Integers

Numbers one after another.

Example: 7, 8, 9.

Multiple of 2

Every second integer is even.

So any 2 consecutive numbers contain one multiple of 2.

Multiple of 3

Every third integer is a multiple of 3.

So any 3 consecutive numbers contain one multiple of 3.

Why Multiple of 6?

6 = 2 × 3.

If a product has factors 2 and 3, it is divisible by 6.

Testing a Claim

Try examples first, then give a general argument.

Counterexample

One example that fails is enough to disprove an “always” claim.

Online Lab: Divisibility Detective

Score: 0Current Streak: 🔥 0Badge: Pattern Starter

Activity Zone

🔢 Consecutive Product Tester

Start integer How many consecutive numbers?

🧮 Divisibility Highlighter

Highlight multiples of 2, 3, or 6 from 1 to 60.

✅ Always, Sometimes, Never?

🔍 Counterexample Finder

Test whether a claim works for numbers you choose.

Number n

📋 Pattern Table Generator

Worksheet Generator

Generate practice on consecutive integers, divisibility by 2, 3, 6, claims, examples, and counterexamples.

Number of problems:

Real-World Use

Grouping: Divisibility helps decide whether objects can be equally grouped.

Scheduling: Multiples help identify repeated patterns and common times.

Proof Thinking: Testing claims and finding counterexamples builds mathematical reasoning.

🌍 Real-Life Case Generator

Teacher Tools

Learning Outcomes

Test divisibility claims using examples.
Explain why the product of three consecutive integers is divisible by 6.
Identify multiples of 2, 3, and 6.
Distinguish between always, sometimes, and never statements.
Use counterexamples to disprove false claims.

Exit Ticket Prompts

Why must one of three consecutive integers be divisible by 3?
Give an example of three consecutive integers and show the product is divisible by 6.
Find a counterexample for a false “always” statement.