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Teacher Guide: Even and Odd Numbers

Learn to identify even and odd numbers and discover the patterns they create.

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Printable worksheet

All practice problems on paper, with a separate answer key.

Worksheet Answer key

Class quiz

10 questions on Number Properties. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Identify even and odd numbers by examining the last digit
  • Explain why a number is even or odd using division by 2
  • Predict whether sums of even and odd numbers will be even or odd
  • Apply even and odd concepts to real-world situations
Prerequisites
  • • Counting numbers from 0 to 100
  • • Basic division concepts
  • • Understanding of remainders
Discussion Starters
  • 1. Why do you think we call them 'even' numbers? What makes them 'even'?
  • 2. Can you think of situations where knowing if a number is even or odd would be helpful?
  • 3. If you add two odd numbers, will the result be even or odd? Why?
  • 4. Is there a largest even number? A largest odd number?
Common Misconceptions

Zero is not even because it's nothing

Remediation: Show that 0÷2=00 \div 2 = 0 with no remainder. Use the number line to show 0 fits the even pattern.

Looking at the first digit to determine even/odd

Remediation: Practice with numbers like 52 and 25 or 34 and 43 to emphasize last digit matters.

Differentiation Ideas

For Struggling Students:

  • • Use physical counters to pair objects
  • • Focus on single-digit numbers first
  • • Create an even/odd reference card with digits 0-9

For On-Level Students:

  • • Work with two and three-digit numbers
  • • Explore addition patterns (even+odd, odd+odd, etc.)
  • • Solve word problems involving fair sharing

For Advanced Students:

  • • Explore multiplication patterns with even and odd
  • • Investigate even and odd patterns in sequences
  • • Apply to negative integers
Standards Alignment
  • 2.OA.C.3 (CCSS.MATH.CONTENT.2.OA.C.3)

    Determine whether a group of objects (up to 20) has an odd or even number of members

  • 3.OA.D.9 (CCSS.MATH.CONTENT.3.OA.D.9)

    Identify arithmetic patterns and explain them using properties of operations

Lesson Resources
  • visualNumber Line Coloring

    Color even numbers one color and odd numbers another

  • activityPairing Game

    Use physical objects to demonstrate pairing

  • worksheetEven or Odd Sort

    Sort numbers into even and odd categories

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

Even numbers can be divided by 2 with no remainder. They end in 0, 2, 4, 6, or 8.
Odd numbers cannot be divided evenly by 2. They end in 1, 3, 5, 7, or 9.
Even: 0,2,4,6,8,10,12,…\text{Even: } 0, 2, 4, 6, 8, 10, 12, \ldots
Odd: 1,3,5,7,9,11,13,…\text{Odd: } 1, 3, 5, 7, 9, 11, 13, \ldots
Quick test: To check if a number is even or odd, just look at the last digit!

Worked Examples

Is 48 an even or odd number?
1

Look at the last digit

The last digit of 48 is 8 → Last digit: 8
2

Check if it's in the even list

Even digits are 0, 2, 4, 6, 8. Is 8 in this list? → Yes, 8 is even
3

Conclusion

Since 48 ends in 8, it is even → 48 is even

Common Mistakes

Thinking 0 is neither even nor odd

Why it's wrong: Zero can be confusing because it's special in many ways.

Correct: 0 IS even! It divides by 2 with no remainder: 0÷2=00 \div 2 = 0

Looking at the first digit instead of the last

Why it's wrong: It's easy to read left-to-right and check the wrong digit.

Correct: Always check the LAST digit. For 52, check 2 (not 5). For 87, check 7 (not 8).

Thinking bigger numbers must be even

Why it's wrong: Large numbers seem more "complete" but size doesn't matter.

Correct: Any size number can be even or odd. 1,000,001 is odd. 2 is even.

Why It Matters

Even and odd numbers are everywhere:
  • Sharing equally: Can you split 12 cookies between 2 friends? Yes, because 12 is even!
  • Pairing: Socks come in pairs. An even number of socks means no sock is left alone.
  • Sports: Tennis doubles needs 4 players (even). A relay race team has 4 runners (even).
  • House numbers: On many streets, the houses on one side have even numbers and the houses on the other side have odd numbers.
Understanding even and odd helps with division, multiplication patterns, and problem-solving!

Real World Applications

Fair Sharing

When dividing things between 2 people, even numbers split perfectly.

Example:

You have 14 candies to share with your friend. 14÷2=714 \div 2 = 7 each. Fair!

1Try It Yourself

You have 15 stickers to share equally between 2 friends.

Can you share them fairly? If not, how many are left over?

Step 1: Write the mathematical expression

Divide: 15÷215 \div 2

Pairing Objects

Even numbers pair up perfectly. Odd numbers always have one left alone.

Example:

8 socks make 4 complete pairs. 9 socks make 4 pairs with 1 sock left over.

2Try It Yourself

A class has 23 students. The teacher wants them to work in pairs.

How many pairs can be formed? Will anyone work alone?

Step 1: Write the mathematical expression

Calculate pairs: 23÷223 \div 2

Key Takeaways

  • 1Even numbers end in 0, 2, 4, 6, or 8 and divide evenly by 2
  • 2Odd numbers end in 1, 3, 5, 7, or 9 and have a remainder of 1 when divided by 2
  • 3Zero is an even number
  • 4Even + Even = Even, Odd + Odd = Even, Even + Odd = Odd

Frequently Asked Questions

Is zero even or odd?

Zero is EVEN. It divides by 2 with no remainder (0÷2=00 \div 2 = 0), and it fits the pattern: ..., −4-4, −2-2, 0, 2, 4, ...

Are negative numbers even or odd?

Both kinds exist! Negative numbers can be even or odd, just like positive ones. −4-4 is even (ends in 4), and −7-7 is odd (ends in 7).

What happens when you multiply even and odd numbers?

Even ×\times anything = Even. Odd ×\times Odd = Odd. So 3×4=123 \times 4 = 12 (even), 3×5=153 \times 5 = 15 (odd).

Glossary

Even number
A number divisible by 2 with no remainder (ends in 0, 2, 4, 6, or 8)
Odd number
A number that has a remainder of 1 when divided by 2 (ends in 1, 3, 5, 7, or 9)
Divisible
A number is divisible by another if it divides evenly with no remainder
Remainder
The amount left over after division

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