Complete Worksheet: Finding Multiples of Numbers in Grade 4

Master finding multiples of numbers through comprehensive worksheet with detailed explanations and practice problems.

Complete Summary: Finding Multiples of Numbers
Comprehensive Summary
Key Definitions:

Multiple: A number that results from multiplying a given number by an integer. If a × b = c, then c is a multiple of both a and b.

Base Number: The number for which we are finding multiples (the number we multiply).

Multiplier: The integer we multiply the base number by (1, 2, 3, 4, 5...).

Product: The result of multiplying the base number by the multiplier (the multiple).

Core Rules and Laws:

• Every number is a multiple of itself (n × 1 = n)

• Zero is a multiple of every number (n × 0 = 0)

• Multiples continue infinitely in the positive direction

• The smallest positive multiple of a number is the number itself

• Multiples of a number are evenly spaced by the base number

Step-by-Step Method:
  1. Identify the base number for which you want to find multiples
  2. Multiply the base number by 1, 2, 3, 4, 5, etc.
  3. Record each result as a multiple
  4. Continue until you reach the desired count or range
  5. List multiples in ascending order for clarity
Pattern Recognition: Multiples of a number form an arithmetic sequence with a common difference equal to the base number.
Factor-Multiple Relationship: If a is a factor of b, then b is a multiple of a.
Tip 1: Use skip counting to find multiples (count by the number).
Tip 2: The first multiple of any number is the number itself.
Tip 3: Multiples are evenly spaced by the base number.
Tip 4: Check by dividing: if the division results in a whole number, it's a multiple.
Simple Example: Multiples of 3

• 3 × 1 = 3 → first multiple

• 3 × 2 = 6 → second multiple

• 3 × 3 = 9 → third multiple

• 3 × 4 = 12 → fourth multiple

• 3 × 5 = 15 → fifth multiple

• Multiples of 3: 3, 6, 9, 12, 15, 18, 21...

Intermediate Example: Multiples of 4

• 4 × 1 = 4 → first multiple

• 4 × 2 = 8 → second multiple

• 4 × 3 = 12 → third multiple

• 4 × 4 = 16 → fourth multiple

• 4 × 5 = 20 → fifth multiple

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28...

Advanced Example: Multiples of 7

• 7 × 1 = 7 → first multiple

• 7 × 2 = 14 → second multiple

• 7 × 3 = 21 → third multiple

• 7 × 4 = 28 → fourth multiple

• 7 × 5 = 35 → fifth multiple

• Multiples of 7: 7, 14, 21, 28, 35, 42, 49...

Key Takeaways:

• Multiples are created by multiplying a number by counting numbers

• Multiples continue infinitely

• Multiples of a number are evenly spaced

• Practice skip counting to build fluency with multiples

Worksheet Exercises
a × n = multiple of a
Multiplication Principle
Rule 1
n × 1 = n
n is a multiple of itself
Rule 2
n × 0 = 0
0 is a multiple of n
Rule 3
Arithmetic Sequence
Multiples form an arithmetic sequence
Practice Problems
Problem 1
Find the first 5 multiples of 6.
Problem 2
Find the first 5 multiples of 8.
Problem 3
Find the first 5 multiples of 9.
Problem 4
Find the first 5 multiples of 10.
Problem 5
Find the first 5 multiples of 12.
Problem 6
Find the first 5 multiples of 15.
Problem 7
Find the first 5 multiples of 16.
Problem 8
Find the first 5 multiples of 20.
Problem 9
Find the first 5 multiples of 25.
Problem 10
Find the first 5 multiples of 30.
Problem 11
Find the first 5 multiples of 35.
Problem 12
Find the first 5 multiples of 40.
Worksheet Solutions
Solution 1: Multiples of 6
Step 1: Multiply 6 by 1

6 × 1 = 6

Step 2: Multiply 6 by 2

6 × 2 = 12

Step 3: Multiply 6 by 3

6 × 3 = 18

Step 4: Multiply 6 by 4

6 × 4 = 24

Step 5: Multiply 6 by 5

6 × 5 = 30

First 5 multiples of 6: 6, 12, 18, 24, 30
Solution 2: Multiples of 8
Step 1: Multiply 8 by 1

8 × 1 = 8

Step 2: Multiply 8 by 2

8 × 2 = 16

Step 3: Multiply 8 by 3

8 × 3 = 24

Step 4: Multiply 8 by 4

8 × 4 = 32

Step 5: Multiply 8 by 5

8 × 5 = 40

First 5 multiples of 8: 8, 16, 24, 32, 40
Solution 3: Multiples of 9
Step 1: Multiply 9 by 1

9 × 1 = 9

Step 2: Multiply 9 by 2

9 × 2 = 18

Step 3: Multiply 9 by 3

9 × 3 = 27

Step 4: Multiply 9 by 4

9 × 4 = 36

Step 5: Multiply 9 by 5

9 × 5 = 45

First 5 multiples of 9: 9, 18, 27, 36, 45
Solution 4: Multiples of 10
Step 1: Multiply 10 by 1

10 × 1 = 10

Step 2: Multiply 10 by 2

10 × 2 = 20

Step 3: Multiply 10 by 3

10 × 3 = 30

Step 4: Multiply 10 by 4

10 × 4 = 40

Step 5: Multiply 10 by 5

10 × 5 = 50

First 5 multiples of 10: 10, 20, 30, 40, 50
Solution 5: Multiples of 12
Step 1: Multiply 12 by 1

12 × 1 = 12

Step 2: Multiply 12 by 2

12 × 2 = 24

Step 3: Multiply 12 by 3

12 × 3 = 36

Step 4: Multiply 12 by 4

12 × 4 = 48

Step 5: Multiply 12 by 5

12 × 5 = 60

First 5 multiples of 12: 12, 24, 36, 48, 60
Solution 6: Multiples of 15
Step 1: Multiply 15 by 1

15 × 1 = 15

Step 2: Multiply 15 by 2

15 × 2 = 30

Step 3: Multiply 15 by 3

15 × 3 = 45

Step 4: Multiply 15 by 4

15 × 4 = 60

Step 5: Multiply 15 by 5

15 × 5 = 75

First 5 multiples of 15: 15, 30, 45, 60, 75
Solution 7: Multiples of 16
Step 1: Multiply 16 by 1

16 × 1 = 16

Step 2: Multiply 16 by 2

16 × 2 = 32

Step 3: Multiply 16 by 3

16 × 3 = 48

Step 4: Multiply 16 by 4

16 × 4 = 64

Step 5: Multiply 16 by 5

16 × 5 = 80

First 5 multiples of 16: 16, 32, 48, 64, 80
Solution 8: Multiples of 20
Step 1: Multiply 20 by 1

20 × 1 = 20

Step 2: Multiply 20 by 2

20 × 2 = 40

Step 3: Multiply 20 by 3

20 × 3 = 60

Step 4: Multiply 20 by 4

20 × 4 = 80

Step 5: Multiply 20 by 5

20 × 5 = 100

First 5 multiples of 20: 20, 40, 60, 80, 100
Solution 9: Multiples of 25
Step 1: Multiply 25 by 1

25 × 1 = 25

Step 2: Multiply 25 by 2

25 × 2 = 50

Step 3: Multiply 25 by 3

25 × 3 = 75

Step 4: Multiply 25 by 4

25 × 4 = 100

Step 5: Multiply 25 by 5

25 × 5 = 125

First 5 multiples of 25: 25, 50, 75, 100, 125
Solution 10: Multiples of 30
Step 1: Multiply 30 by 1

30 × 1 = 30

Step 2: Multiply 30 by 2

30 × 2 = 60

Step 3: Multiply 30 by 3

30 × 3 = 90

Step 4: Multiply 30 by 4

30 × 4 = 120

Step 5: Multiply 30 by 5

30 × 5 = 150

First 5 multiples of 30: 30, 60, 90, 120, 150
Solution 11: Multiples of 35
Step 1: Multiply 35 by 1

35 × 1 = 35

Step 2: Multiply 35 by 2

35 × 2 = 70

Step 3: Multiply 35 by 3

35 × 3 = 105

Step 4: Multiply 35 by 4

35 × 4 = 140

Step 5: Multiply 35 by 5

35 × 5 = 175

First 5 multiples of 35: 35, 70, 105, 140, 175
Solution 12: Multiples of 40
Step 1: Multiply 40 by 1

40 × 1 = 40

Step 2: Multiply 40 by 2

40 × 2 = 80

Step 3: Multiply 40 by 3

40 × 3 = 120

Step 4: Multiply 40 by 4

40 × 4 = 160

Step 5: Multiply 40 by 5

40 × 5 = 200

First 5 multiples of 40: 40, 80, 120, 160, 200
Worksheet Practice Tips
Practice Strategies
Effective Learning
Worksheet Components:

Instructions: Clear directions for completing the worksheet

Guided Examples: Step-by-step worked problems

Practice Problems: Exercises for independent work

Answer Key: Solutions for self-checking

Review Questions: Mixed problems for reinforcement

Worksheet Completion Strategy:
  1. Read instructions carefully before starting
  2. Review the guided examples to understand the format
  3. Work systematically through each problem
  4. Check your work using the answer key
  5. Practice regularly to build fluency
Tip 1: Use skip counting to find multiples (count by the number).
Tip 2: Write multiples in ascending order for clarity.
Tip 3: Always verify by dividing: if the division results in a whole number, it's a multiple.
Tip 4: Circle or highlight your final answer for clarity.
Common Mistakes: Forgetting the base number itself as the first multiple, missing multiples due to calculation errors, not listing in ascending order.
Success Strategies: Practice with numbers 1-30, memorize multiplication tables, check your work systematically.
Worksheet Format:

• Title and header information

• Clear problem statements

• Space for working out solutions

• Answer boxes for final responses

• Progress tracking sections

Visualization: Multiples Patterns
Comparing Multiples of Different Numbers
Compare the first 6 multiples for: 3, 4, 5, 6
Visual: 📊 Multiples form distinct patterns

Analysis: The chart shows how multiples of different numbers form distinct linear patterns.

  • Multiples of 3: 3, 6, 9, 12, 15, 18
  • Multiples of 4: 4, 8, 12, 16, 20, 24
  • Multiples of 5: 5, 10, 15, 20, 25, 30
  • Multiples of 6: 6, 12, 18, 24, 30, 36

Questions & Answers

Question: I'm confused about the difference between factors and multiples. They seem very similar to me.

Answer: Great question! Factors and multiples are opposite relationships:

Factors: Numbers that divide INTO another number. For example, the factors of 12 are 1, 2, 3, 4, 6, 12 because these numbers divide evenly into 12.

Multiples: Numbers that result FROM multiplying a number. For example, the multiples of 3 are 3, 6, 9, 12, 15... because these are the results of 3×1, 3×2, 3×3, 3×4, 3×5...

Think of it this way: 3 is a factor of 12, and 12 is a multiple of 3. They work in opposite directions!

Question: How many multiples does a number have? Is there a limit?

Answer: Unlike factors, which are limited in number, multiples go on forever! A number has infinitely many multiples.

For example, the multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50... and this pattern continues forever.

This is because you can keep multiplying by larger and larger numbers: 5×1, 5×2, 5×3, 5×4... up to 5×∞ (infinity).

However, when doing problems, teachers usually ask for the "first few multiples" to make the task manageable.

Question: How can I quickly find multiples of a number? It takes me a long time to multiply.

Answer: Here are some helpful strategies to quickly find multiples:

  • Skip counting: Count by the number (for multiples of 4: 4, 8, 12, 16, 20...)
  • Use known facts: If you know 6×4=24, then 24 is a multiple of both 6 and 4
  • Add the base number: Once you have one multiple, add the base number to get the next (if 15 is a multiple of 5, then 15+5=20 is also a multiple)
  • Look for patterns: Multiples of 10 always end in 0, multiples of 5 end in 0 or 5

With practice, these patterns will become automatic!