Solved Exercises on Odd and Even Numbers Introduction in Grade 1

Master basic odd and even numbers: identification, pairing, and simple patterns through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Basic identification of odd and even
Exercise 1
Look at these numbers: 1, 2, 3, 4, 5. Circle the even numbers and put a square around the odd numbers.
Definition:

Even numbers: Numbers that can be shared equally between 2 people (no one left out). Odd numbers: Numbers that cannot be shared equally between 2 people (someone is left out).

Identification method:
  1. Look at each number one by one
  2. Imagine sharing that many objects with a friend
  3. If everyone gets the same amount with nothing left over, it's even
  4. If someone is left out, it's odd
Original List
1, 2, 3, 4, 5
Classification
O, E, O, E, O
Result
2,4 even; 1,3,5 odd
Step 1: Look at number 1

If you have 1 cookie and share with 1 friend, you can't share equally. 1 is odd.

Step 2: Look at number 2

If you have 2 cookies and share with 1 friend, each gets 1 cookie. 2 is even.

Step 3: Continue for remaining numbers

3 cookies: not equal sharing (odd), 4 cookies: equal sharing (even), 5 cookies: not equal sharing (odd)

Even: 2, 4
Odd: 1, 3, 5
Final answer:

Even numbers: 2, 4
Odd numbers: 1, 3, 5

Applied rules:

• Even numbers: Can be divided by 2 with no remainder

• Odd numbers: Cannot be divided by 2 without remainder

• Sharing concept: Even numbers can be shared equally between 2 people

2 Pairing objects to identify odd/even
Exercise 2
Draw 6 stars and circle pairs. Is 6 odd or even? Explain how you know.
Definition:

Pairing method: Drawing objects and grouping them into pairs to determine if a number is odd or even

Number of Stars
6
Pairing Process
6 ÷ 2 = 3 pairs
Result
No stars left over
Step 1: Draw 6 stars

⭐ ⭐ ⭐ ⭐ ⭐ ⭐

Step 2: Circle pairs

(⭐ ⭐) (⭐ ⭐) (⭐ ⭐) - 3 pairs formed

Step 3: Check for leftovers

All 6 stars are in pairs, no star is left alone

6 is even because all stars can be paired
Final answer:

6 is an even number because all 6 stars can be paired into 3 groups of 2 with no stars left over.

Applied rules:

• Even numbers: Can be perfectly divided into pairs (no remainder)

• Odd numbers: Cannot be perfectly divided into pairs (remainder of 1)

• Visual pairing: A helpful method to understand odd/even concept

3 Continuing simple patterns
Exercise 3
Fill in the missing numbers in this pattern: 2, 4, ___, 8, ___, 12
Definition:

Even number pattern: A sequence where each number is 2 more than the previous number

Given Pattern
2, 4, ___, 8, ___, 12
Rule
Add 2
Completed
2, 4, 6, 8, 10, 12
Step 1: Identify the pattern

Looking at 2, 4, 8, 12 - each number increases by 2 from the previous

Step 2: Confirm these are even numbers

All shown numbers (2, 4, 8, 12) are divisible by 2

Step 3: Apply the pattern to find missing numbers

4 + 2 = 6, 8 + 2 = 10

Step 4: Verify the results

6 and 10 are both even numbers (divisible by 2)

2, 4, 6, 8, 10, 12
Final answer:

The missing numbers are 6 and 10. The complete pattern is: 2, 4, 6, 8, 10, 12

Applied rules:

• Pattern recognition: Identify the consistent operation between consecutive numbers

• Even number pattern: Even numbers increase by 2 (2, 4, 6, 8...)

• Consistency: Apply the same operation to find missing values

Visual Infographic: Odd and Even Numbers Introduction

Odd and Even Numbers

Learning to Share Equally

1
2
3
4
5
6
7
8
9
10
→
2
Even
3
Odd
4
Even
5
Odd
Even Numbers
Can be shared equally between 2 people. Examples: 2, 4, 6, 8, 10.
Odd Numbers
Cannot be shared equally between 2 people. Examples: 1, 3, 5, 7, 9.
Sharing Concept
Even = equal sharing, Odd = unequal sharing
Pairing Method
Even = all objects can be paired, Odd = one object left alone
Rules and methods, laws,...
\(n \div 2 = \text{whole number (even)}\)
Even Number Test
Even
\(n \div 2 = \text{no remainder}\)
Can share equally
Odd
\(n \div 2 = \text{remainder 1}\)
Cannot share equally
Pattern
\(2, 4, 6... / 1, 3, 5...\)
Alternating sequence
Even numbers: Can be shared equally between 2 people. Examples: 2, 4, 6, 8, 10.
Odd numbers: Cannot be shared equally between 2 people. Examples: 1, 3, 5, 7, 9.
Key Concepts: Odd and Even Numbers Introduction
\(n \mod 2\)
Remainder Check
Key definitions:

Even number: A number that can be divided by 2 with no remainder, allowing equal sharing

Odd number: A number that cannot be divided by 2 without a remainder, preventing equal sharing

Equal sharing: Distributing objects so each person gets the same amount

Complete methodology:
  1. Identify the number: Look at the number you want to classify
  2. Apply sharing concept: Imagine sharing that many objects equally
  3. Use pairing method: Group objects into pairs to see if any remain
  4. Verify with division: Divide by 2 and check for remainder
Tip 1: Think of sharing cookies with a friend to understand even/odd.
Tip 2: Draw objects and circle pairs to visualize the concept.
Tip 3: Remember: even numbers can be split equally, odd numbers cannot.
Tip 4: Odd and even numbers alternate: even, odd, even, odd...
Common errors: Thinking that odd numbers are "bad" numbers, forgetting the alternating pattern.
Practice tips: Start with small numbers (1-10), then extend to larger numbers.
Key rules to remember:

• Even numbers: Can be divided by 2 with no remainder

• Odd numbers: Cannot be divided by 2 without remainder

• Sharing concept: Even = equal sharing, Odd = unequal sharing

• Alternating pattern: Even and odd numbers alternate in sequence

Questions & Answers

Question: Is zero odd or even? Can you share zero things with a friend?

Answer: Zero is an even number! This might seem strange, but think about it:

If you have zero cookies and share with a friend, you both get zero cookies. That's equal sharing! Zero divided by 2 equals zero with no remainder, so zero fits the definition of an even number.

Zero also follows the pattern rule - it ends in 0, which is one of the even digits (0, 2, 4, 6, 8).

Question: My child understands the concept with small numbers but struggles with larger numbers. How can I help?

Answer: The key insight for larger numbers is that only the last digit matters! Once your child understands the concept with small numbers:

  • Teach them to focus only on the last digit
  • If the last digit is 0, 2, 4, 6, or 8, the whole number is even
  • If the last digit is 1, 3, 5, 7, or 9, the whole number is odd
  • Practice with various numbers like 24, 37, 58, 63

This shortcut makes it easy to identify odd/even for any size number!

Question: Why do we learn about odd and even numbers? When will I use this?

Answer: Learning odd and even numbers is important because it builds your number sense and prepares you for more math! You'll use this knowledge:

  • When learning multiplication and division
  • To understand number patterns and sequences
  • When working with fractions and grouping
  • In daily life: sharing items fairly with friends

It also helps you notice patterns in numbers, which makes math more interesting and easier to understand!

Detailed Summary: Odd and Even Numbers Introduction

Definitions

Even Numbers: Numbers that can be shared equally between 2 people or divided by 2 with no remainder. These numbers allow for fair sharing.

Odd Numbers: Numbers that cannot be shared equally between 2 people or divided by 2 without a remainder. These numbers leave someone out when trying to share fairly.

Equal Sharing: The concept of distributing objects so each person gets exactly the same amount.

Pairing Method: Grouping objects into sets of 2 to determine if a number is odd or even.

Core Rules and Laws
  • Even Rule: n ÷ 2 = whole number (no remainder), where n is even
  • Odd Rule: n ÷ 2 = whole number with remainder 1, where n is odd
  • Sharing Rule: Even numbers allow equal sharing between 2 people; odd numbers don't
  • Alternating Pattern Rule: In counting order, even and odd numbers alternate (even, odd, even, odd...)
Step-by-Step Methods
  1. Identify the Number: Look at the number you want to classify
  2. Apply Sharing Concept: Imagine sharing that many objects equally between 2 people
  3. Use Pairing Method: Group objects into pairs to see if any are left over
  4. Check Division: Divide the number by 2 and check for remainder
  5. Verify Result: Double-check using a different method
Examples (Simple → Advanced)
Simple Example
Number 2: Can share 2 cookies equally (1 each) → Even
Number 3: Cannot share 3 cookies equally (some left over) → Odd
Intermediate Example
Number 12: Ends in 2 (even digit) → Even
Number 13: Ends in 3 (odd digit) → Odd
Advanced Example
Number 124: Ends in 4 (even digit) → Even
Number 357: Ends in 7 (odd digit) → Odd
Tips, Tricks, and Common Pitfalls
  • Tip 1: Use the sharing concept: even = fair sharing, odd = unfair sharing
  • Tip 2: Practice with physical objects like counters or toys to visualize pairing
  • Tip 3: Notice that even and odd numbers alternate in counting order
  • Pitfall 1: Thinking 0 is odd (zero is actually even: 0 ÷ 2 = 0 remainder 0)
  • Pitfall 2: Forgetting that only the last digit matters for larger numbers
  • Pitfall 3: Misunderstanding that odd doesn't mean "strange" - it's just a math term
Key Notes for Memorization
  • Even numbers allow equal sharing between 2 people
  • Odd numbers do not allow equal sharing between 2 people
  • Even numbers: 0, 2, 4, 6, 8 - end in these digits
  • Odd numbers: 1, 3, 5, 7, 9 - end in these digits
  • Remember: 0 is even (not odd) because 0 ÷ 2 = 0 remainder 0
  • For any number, only the last digit determines if it's odd or even