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2nd Grade Math (Common Core) • Operations and Algebraic Thinking

Odd or Even? Pairing and Counting by 2s

Learn to tell if numbers are odd or even by making pairs.

Explore the lesson 7 min read
Friendly shapes with counting blocks and a calculator for elementary math
Inside this lesson 10 sections 5 questions 7 figures

SECTION 1

Where Did Odd and Even Come From?

Long ago, people needed to count things like sheep, apples, and coins. They noticed something special about numbers. Some numbers could be split into two equal groups, and some couldn't! This discovery helped people organize and understand numbers better.

Ancient Times • Counting Begins

People started counting objects and noticed that some numbers could be split evenly into pairs.

Ancient Egypt • Pairing Objects

Egyptians used pairing to organize items like grain and tools into equal groups.

Ancient Greece • Mathematical Names

Greek mathematicians gave these numbers special names: even and odd.

Today • Everyday Use

We use odd and even numbers in games, sports teams, and organizing groups.

The question people asked was simple: Can this number be split into two equal groups? This question led to understanding odd and even numbers.

SECTION 2

What Makes Numbers Odd or Even?

Numbers are like groups of friends. Some groups can make perfect pairs, and some have one friend left over. This helps us understand the difference between even numbers and odd numbers.

1

Even Numbers

Even numbers can be split into two equal groups with no leftover. Examples: 2, 4, 6, 8, 10.
2

Odd Numbers

Odd numbers always have one leftover when you try to make pairs. Examples: 1, 3, 5, 7, 9.
3

Making Pairs

You can test any number by grouping objects into pairs of two.
4

Counting by 2s

When you count by 2s, you land on all the even numbers: 2, 4, 6, 8, 10...
✦

KEY TAKEAWAY

Think of numbers like socks in your drawer. Even numbers are like having matching pairs of socks with none left over. Odd numbers are like having one sock without a match!

SECTION 3

Seeing Odd and Even Numbers

Even Numbers (Make Perfect Pairs)Odd Numbers (One Left Over)Number 4Number 5Number 6Number 7Number 8Number 92 pairs = EVEN2 pairs + 1 = ODD3 pairs = EVEN3 pairs + 1 = ODD4 pairs = EVEN4 pairs + 1 = ODD
The blue circles show even numbers making perfect pairs. The orange circles with one red leftover show odd numbers. Pink lines connect the pairs.

Look at the diagram above! The blue circles show even numbers. Notice how they all make perfect pairs with no circles left over. The orange circles show odd numbers, and they always have one red circle left over that can't make a pair.

SECTION 4

The Math Behind Odd and Even

We can use simple math to understand odd and even numbers. The key is dividing by 2 and seeing if there's a leftover.

EVEN NUMBERS

EvenNumber÷2=WholeNumberEven Number ÷ 2 = Whole Number

When you divide an even number by 2, you get a whole number with no leftover.

ODD NUMBERS

OddNumber÷2=WholeNumber+½Odd Number ÷ 2 = Whole Number + ½

When you divide an odd number by 2, you get a whole number plus a leftover of ½.

COUNTING BY 2S

2,4,6,8,10,12,14,16,18,20...2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

When you count by 2s, you land on all the even numbers. The numbers you skip are odd!

SECTION 5

Number Patterns and Rules

Number Line: Odd and Even Patterns123456789101112Orange = Odd NumbersBlue = Even NumbersCounting by 2s Pattern24681012Keep going: 14, 16, 18, 20...Last Digit RuleEven ends in:0, 2, 4, 6, 8Odd ends in:1, 3, 5, 7, 9
The number line shows how odd and even numbers alternate. Counting by 2s lands on even numbers. You can tell if any number is odd or even by looking at its last digit.

Numbers follow a special pattern! On the number line, odd and even numbers take turns. When you count by 2s, you hop over all the odd numbers and land only on even ones. There's also a quick trick: just look at the last digit of any number to tell if it's odd or even!

SECTION 6

Step-by-Step: Testing Numbers

Let's practice with the number 15. We'll use different methods to figure out if it's odd or even.

Is 15 Odd or Even?

  1. 1

    Step 1 — Look at the Last Digit

    The number 15 ends in 5. We learned that numbers ending in 1, 3, 5, 7, or 9 are odd.
    15 is odd!
  2. 2

    Step 2 — Try Making Pairs

    Let's check by drawing 15 circles and trying to pair them up. We can make 7 pairs of circles, but 1 circle is left over.
    7 pairs + 1 leftover = odd
  3. 3

    Step 3 — Divide by 2

    15 ÷ 2 = 7 with a remainder of 1. When we divide by 2 and get a leftover, the number is odd.
    Remainder means odd
  4. 4

    Step 4 — Check with Counting by 2s

    Count by 2s: 2, 4, 6, 8, 10, 12, 14, 16. We skip over 15, which means it's not an even number.
    15 is skipped = odd

SECTION 7

When Do We Use Odd and Even?

Odd and even numbers help us in many real-life situations. They make organizing and sharing things much easier!

SituationHow Odd and Even HelpExample
Making TeamsEven numbers can split into equal teams12 kids make 2 teams of 6
Sharing ToysEven toys can be shared equally8 crayons = 4 for each friend
GamesSome games need even playersPartners for dance class
OrganizingEven things fit in neat rows10 books = 5 on each shelf
🎯

KEY TAKEAWAY

Think of odd and even like building with blocks. Even numbers build perfect rectangular towers with no blocks sticking out. Odd numbers always have one block that doesn't fit the pattern!

SECTION 8

What Comes Next with Numbers?

Learning odd and even is just the beginning! As you grow, you'll discover more amazing number patterns and rules.

What You Know NowWhat You'll Learn Later
Numbers can be odd or evenNumbers can be prime, composite, or square
Count by 2s to find even numbersCount by other numbers like 3s, 5s, and 10s
Make pairs with objectsUse multiplication and division
Look at the last digitLearn divisibility rules for many numbers

Understanding odd and even numbers gives you a strong foundation for all the math you'll learn in the future. Keep practicing with the numbers around you every day!

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

You have 7 stickers. Can you share them equally between 2 friends so each gets the same amount?
Show answer
No, you cannot share 7 stickers equally between 2 friends. Since 7 is an odd number, when you try to split it into two equal groups, one person would get 4 stickers and the other would get 3 stickers. There would be 1 sticker left over. Odd numbers cannot be split into equal pairs.

Question 2: BASIC CALCULATION

Look at these numbers: 13, 16, 21, 24. Which ones are even and which ones are odd?
Show answer
Looking at the last digit of each number: 13 ends in 3 (odd), 16 ends in 6 (even), 21 ends in 1 (odd), and 24 ends in 4 (even). So 13 and 21 are odd numbers, while 16 and 24 are even numbers. Remember: numbers ending in 1, 3, 5, 7, 9 are odd, and numbers ending in 0, 2, 4, 6, 8 are even.

Question 3: INTERMEDIATE

Maya is counting by 2s starting from 2. She counts: 2, 4, 6, 8, 10, 12, ?, ?. What are the next two numbers? Are they odd or even?
Show answer
The next two numbers are 14 and 16. When you count by 2s starting from an even number, you always land on even numbers. This is because you're adding 2 (an even number) each time, and even + even = even. Both 14 and 16 are even numbers because they end in 4 and 6.

Question 4: APPLIED

There are 18 kids in your class who want to work in pairs for a science project. Will everyone be able to have a partner? Explain how you know.
Show answer
Yes, everyone will be able to have a partner! Since there are 18 kids and 18 is an even number, they can form exactly 9 pairs with no one left out. You can check this by dividing: 18 ÷ 2 = 9. Since 18 ends in 8 (an even digit), it's an even number, which means it can be split perfectly into equal groups of 2.

Question 5: CRITICAL THINKING

If you add two even numbers together, will the result be odd or even? What about adding two odd numbers? Test your ideas with examples.
Show answer
Adding two even numbers always gives an even result. Example: 4 + 6 = 10 (even). Adding two odd numbers also always gives an even result. Example: 3 + 5 = 8 (even). This happens because pairs + pairs = more pairs (even), and a leftover + leftover = one pair (even). However, adding one even and one odd number gives an odd result, like 4 + 3 = 7 (odd).

SUMMARY

Odd and Even Numbers: Key Points

Summary

Even numbers can be split into perfect pairs with no leftovers. They end in 0, 2, 4, 6, or 8. When you count by 2s (2, 4, 6, 8, 10...), you land on all the even numbers. Odd numbers always have one leftover when you try to make pairs. They end in 1, 3, 5, 7, or 9.

You can test any number three ways: look at the last digit (fastest method), divide by 2 to see if there's a remainder, or make pairs with objects. Understanding odd and even helps you share things fairly, make equal teams, and organize groups. These number patterns appear everywhere in math and everyday life!

Varsity Tutors • 2nd Grade Math • Odd or Even? Pairing and Counting by 2s