Teacher Guide: Divisibility by 2, 5, and 10
Learn the quick rules to tell if a number is divisible by 2, 5, or 10 just by looking at its last digit.
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10 questions on Divisibility. Students join with a name, you see everyone's score.
For Teachers
- State the divisibility rules for 2, 5, and 10
- Apply divisibility rules to determine if a number is divisible by 2, 5, or 10
- Explain why the last digit determines divisibility by 2, 5, and 10
- Solve real-world problems using divisibility rules
- • Understanding of division as equal sharing
- • Recognizing even and odd numbers
- • Identifying place values (ones, tens, hundreds)
- 1. Why do you think the last digit is so important for these rules?
- 2. Can a number be divisible by 5 but not by 10? Give an example.
- 3. If you know a number is divisible by 10, what else do you know about it?
- 4. How could divisibility rules help you at a store or when sharing snacks?
All numbers ending in 5 are divisible by 10
Large numbers need special rules
For Struggling Students:
- • Use physical manipulatives to show equal grouping
- • Focus on two-digit numbers first
- • Create a reference chart with the three rules
For On-Level Students:
- • Apply rules to three and four-digit numbers
- • Solve word problems involving divisibility
- • Explore why these rules work mathematically
For Advanced Students:
- • Investigate combined divisibility (e.g., divisible by both 2 and 5)
- • Discover rules for 4 and 25 (related to these rules)
- • Create their own divisibility problems
- 4.OA.B.4 (CCSS.MATH.CONTENT.4.OA.B.4)
Find all factor pairs for a whole number. Recognize that a whole number is a multiple of each of its factors.
- 4.NBT.B.6 (CCSS.MATH.CONTENT.4.NBT.B.6)
Find whole-number quotients and remainders using strategies based on place value.
- visualLast Digit Detector
Highlight the last digit and apply divisibility rules
- activitySort the Numbers
Categorize numbers by divisibility by 2, 5, and 10
- worksheetDivisibility Practice
Apply rules to lists of numbers
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
Divisibility by 2
Divisibility by 5
Divisibility by 10
Worked Examples
Is 1,458 divisible by 2?
Look at the last digit
The last digit of is → Last digit:
Check if it's even
Is in the set ? → Yes, is even
Apply the rule
Since the last digit is even, is divisible by →
Answer: Yes, 1,458 is divisible by 2 because its last digit (8) is even.
Common Mistakes
Looking at the first digit instead of the last digit
Why it's wrong: For divisibility by 2, 5, and 10, only the last digit matters. The first digit tells us the size of the number, not its divisibility.
Correct: Always look at the rightmost (last) digit: in 847, check 7, not 8.
Thinking a number ending in 5 is divisible by 10
Why it's wrong: Divisibility by 10 is stricter than by 5. A number must end in 0 (not just 0 or 5) to be divisible by 10.
Correct: 75 is divisible by 5 but NOT by 10. Only 70, 80, 90... are divisible by 10.
Confusing 'even' with 'divisible by 10'
Why it's wrong: All numbers divisible by 10 are even, but not all even numbers are divisible by 10.
Correct: 24 is even (divisible by 2) but not divisible by 10. 20 is both even AND divisible by 10.
Why It Matters
- Mental math: Quickly check if you can split things evenly without a calculator
- Simplifying fractions: Know instantly if you can divide both numerator and denominator by 2, 5, or 10
- Real-world sharing: Can 24 cookies be shared equally between 2 friends? Can 35 students form groups of 5?
- Building blocks: These simple rules prepare you for more complex divisibility tests (3, 4, 6, 9)
Real World Applications
Sharing Equally
When splitting items between people, divisibility rules help you know instantly if it works.
Example:
Can 36 candies be shared equally between 2 children? Yes! ends in (even), so each.
You have 125 stickers to put in packs of 5.
Can you make packs with no stickers left over?
Step 1: Write the mathematical expression
Check the last digit of 125:
Counting Money
Money often uses denominations of 10, making divisibility by 10 very practical.
Example:
If you have 240 cents, can you exchange them for dimes (10 cents)? Yes! ends in , so dimes.
A piggy bank has 375 cents.
Can these be exchanged for an exact number of dimes?
Step 1: Write the mathematical expression
Check if 375 is divisible by 10:
Key Takeaways
- 1A number is divisible by 2 if its last digit is even ()
- 2A number is divisible by 5 if its last digit is or
- 3A number is divisible by 10 if its last digit is
- 4Every number divisible by 10 is also divisible by both 2 and 5
- 5Only the last digit matters for these three rules
Frequently Asked Questions
Why does the last digit rule work?
If a number is divisible by 10, is it always divisible by 2 and 5?
What about large numbers like 1,000,000?
Glossary
- Divisible
- A number is divisible by another if dividing them gives a whole number with no remainder
- Even number
- A number divisible by 2, ending in 0, 2, 4, 6, or 8
- Odd number
- A number not divisible by 2, ending in 1, 3, 5, 7, or 9
- Last digit
- The digit in the ones place (rightmost position)
- Remainder
- The amount left over after division