Solved Exercises on Odd and Even Numbers in 1st Grade

Master odd and even numbers: definition, identification, patterns, and properties through these 5 detailed exercises with visual methods.

Solution: Exercises 1 to 3
1 Basic Even Number Recognition
Exercise 1
Which numbers are even? Circle the even numbers from this list: 2, 5, 8, 3, 6, 9, 4, 7, 10
2
5
8
3
6
9
4
7
10
Definition:

Even number: A number that can be divided by 2 without leaving a remainder. It can be grouped into pairs with none left over.

Identification method:
  1. Try to divide the number by 2
  2. If there's no remainder, it's even
  3. Or, try to make pairs of objects
  4. If all objects pair up, the number is even
Number
2
Division
2 ÷ 2 = 1
Remainder
0
Step 1: Examine each number

Take each number in the list: 2, 5, 8, 3, 6, 9, 4, 7, 10

Step 2: Test divisibility by 2

2÷2=1 (remainder 0), 5÷2=2 (remainder 1), 8÷2=4 (remainder 0), etc.

Step 3: Identify even numbers

Numbers with remainder 0 when divided by 2 are even: 2, 4, 6, 8, 10

Even numbers: 2, 4, 6, 8, 10
Final answer:

The even numbers are: 2, 4, 6, 8, 10

Applied rules:

• Divisibility rule: Even numbers divide evenly by 2

• Pairing rule: Even numbers can form complete pairs

• Pattern rule: Even numbers end in 0, 2, 4, 6, or 8

2 Basic Odd Number Recognition
Exercise 2
Which numbers are odd? Circle the odd numbers from this list: 1, 4, 7, 2, 9, 6, 3, 8, 5
1
4
7
2
9
6
3
8
5
Definition:

Odd number: A number that cannot be divided by 2 without leaving a remainder. When grouped into pairs, one object is left over.

Number
5
Division
5 ÷ 2 = 2 R1
Remainder
1
Step 1: Examine each number

Take each number in the list: 1, 4, 7, 2, 9, 6, 3, 8, 5

Step 2: Test divisibility by 2

1÷2=0 (remainder 1), 4÷2=2 (remainder 0), 7÷2=3 (remainder 1), etc.

Step 3: Identify odd numbers

Numbers with remainder 1 when divided by 2 are odd: 1, 3, 5, 7, 9

Odd numbers: 1, 3, 5, 7, 9
Final answer:

The odd numbers are: 1, 3, 5, 7, 9

Applied rules:

• Divisibility rule: Odd numbers leave a remainder of 1 when divided by 2

• Pairing rule: Odd numbers have one object left over when pairing

• Pattern rule: Odd numbers end in 1, 3, 5, 7, or 9

3 Pattern Recognition
Exercise 3
Look at this sequence: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
What pattern do you notice? Are these numbers odd or even?
Even Numbers
2
4
6
Continue Pattern
8
10
12
Definition:

Number pattern: A sequence of numbers that follows a specific rule or relationship.

Sequence
2, 4, 6, 8...
Rule
Add 2
Type
Even
Step 1: Observe the sequence

The numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Step 2: Identify the pattern

Each number increases by 2 (skip counting by 2s)

Step 3: Determine number type

All numbers can be divided by 2 with no remainder, so they are all even

All numbers are even, pattern: add 2 each time
Final answer:

All numbers in the sequence are even. The pattern is counting by 2s.

Applied rules:

• Pattern rule: Counting by 2s gives even numbers

• Even sequence: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

• Odd sequence: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19...

Odd and Even Number Patterns
Even = Divisible by 2
Even Number Rule
Even
÷2 = Whole
No Remainder
Odd
÷2 = Whole R1
Remainder 1
End Digits
Even: 0,2,4,6,8
Odd: 1,3,5,7,9
2
3
4
5
6
7
8
9
10
Even Pairing:
= Complete Pairs
Odd Pairing:
= 1 Left Over
Solution: Exercises 4 to 5
4 Counting Objects
Exercise 4
There are 7 apples. Can you put them in pairs? Is 7 odd or even?
Pairs: (1,2), (3,4), (5,6)
Left: 7
Definition:

Counting objects: Using physical items to demonstrate the concept of pairing for odd/even classification.

Objects
7
Pairs
3
Leftover
1
Step 1: Count total objects

We have 7 apples to work with.

Step 2: Try to make pairs

Apple 1 pairs with Apple 2, Apple 3 pairs with Apple 4, Apple 5 pairs with Apple 6.

Step 3: Check for leftovers

Apple 7 has no partner, so it's left alone.

7 is odd because 1 apple is left over
Final answer:

7 is an odd number because when we try to pair the 7 apples, 1 apple is left over.

Applied rules:

• Pairing test: If objects can't be perfectly paired, the number is odd

• Remainder test: If division by 2 leaves a remainder, the number is odd

• Visual test: Draw objects and see if they form complete pairs

5 Mixed Number Classification
Exercise 5
Sort these numbers into odd and even groups: 11, 14, 17, 20, 23, 26, 29, 32
11
14
17
20
23
26
29
32
Definition:

Mixed classification: Sorting numbers into odd and even categories by examining each number individually.

Mixed
Numbers
Classify
Each
Test
Division
Step 1: Examine each number

Take each number: 11, 14, 17, 20, 23, 26, 29, 32

Step 2: Apply divisibility test

11÷2=5R1 (odd), 14÷2=7 (even), 17÷2=8R1 (odd), etc.

Step 3: Group by type

Even: 14, 20, 26, 32; Odd: 11, 17, 23, 29

Step 4: Verify by last digit

Even numbers end in 0,2,4,6,8; Odd numbers end in 1,3,5,7,9

Even: 14, 20, 26, 32 | Odd: 11, 17, 23, 29
Final answer:

Even numbers: 14, 20, 26, 32 | Odd numbers: 11, 17, 23, 29

Applied rules:

• Systematic approach: Test each number separately

• Alternative method: Check the last digit for quick classification

• Verification: Use both methods to confirm accuracy

Odd and Even Number Properties
n ÷ 2 = Whole Number ↔ Even
Even Number Definition
Key definitions:

Even number: Any integer that can be exactly divided by 2 (remainder 0)

Odd number: Any integer that cannot be exactly divided by 2 (remainder 1)

Divisibility: Whether one number divides another without remainder

Complete identification methods:
  1. Division method: Divide by 2, check remainder
  2. Last digit method: Check if last digit is 0,2,4,6,8 (even) or 1,3,5,7,9 (odd)
  3. Pairing method: Try to group objects into pairs
  4. Number line method: Even numbers appear every other number starting from 0
Tip 1: Remember: "Even" means "level" or "balanced" - all objects pair up perfectly.
Tip 2: Count the last digit: 0,2,4,6,8 = even; 1,3,5,7,9 = odd.
Tip 3: Start counting from 0: 0(even), 1(odd), 2(even), 3(odd), 4(even)...
Tip 4: Zero is even because 0 ÷ 2 = 0 with no remainder.
Common errors: Thinking 0 is odd, forgetting that 2 is the smallest positive even number.
Key insight: Odd and even numbers alternate: even, odd, even, odd...
Important properties:

• Every integer is either odd or even (never both)

• Even numbers: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

• Odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21...

• Adding two even numbers gives even result

• Adding two odd numbers gives even result

• Adding even and odd gives odd result

Number Pattern Visualization
Odd vs Even Distribution
Visual representation of odd and even numbers from 1 to 20:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Observation: Odd and even numbers alternate in a predictable pattern.

  • Pattern: Odd, Even, Odd, Even, Odd, Even...
  • Even numbers end in: 0, 2, 4, 6, 8
  • Odd numbers end in: 1, 3, 5, 7, 9
  • Half the numbers in any range are odd, half are even

Questions & Answers

Question: My child is having trouble understanding why zero is considered an even number. Can you explain this concept?

Answer: This is a common point of confusion! Here's why zero is even:

  • Division test: 0 ÷ 2 = 0 with no remainder, so it fits the definition of even
  • Pattern continuation: In the sequence ..., -2, -1, 0, 1, 2, ..., zero continues the even-odd pattern
  • Pairing concept: If you have zero objects, there are no objects left over when trying to pair them
  • Mathematical consistency: Zero must be even for mathematical operations to work consistently

Think of it this way: if you have zero items, you can make zero pairs with nothing left over, which is the definition of even.

Question: How can I help students who struggle to remember which digits make a number odd or even?

Answer: Here are effective memory strategies for the ending digits:

  • Even digits: "0, 2, 4, 6, 8" - Remember "Zero, Two, Four, Six, Eight - These are Even!"
  • Odd digits: "1, 3, 5, 7, 9" - Remember "One, Three, Five, Seven, Nine - These are Prime and Odd!"
  • Visual grouping: Draw circles around the last digit when identifying numbers
  • Hands-on practice: Use number cards and sort them by last digit

Start with single-digit numbers first, then extend to larger numbers focusing only on the last digit.

Question: Are there any fun activities or games to reinforce odd and even number concepts?

Answer: Absolutely! Here are engaging activities for odd and even numbers:

  • Number hopscotch: Mark squares as odd/even and have kids hop only on even or odd numbers
  • Object sorting: Give kids collections of objects and have them make pairs to determine if the total is odd or even
  • Odd/Even song: Create or use existing songs that emphasize the pattern of odd/even numbers
  • Calculator challenge: Use calculators to divide numbers by 2 and see remainders

Make it physical and interactive - children learn better when they can move and touch while learning!