Multiplying by 2 pattern: This is the sequence of even numbers, where each number is 2 more than the previous one. It's the same as counting by twos.
- Identify the pattern: each number increases by 2
- Continue the sequence by adding 2 to the last number
- The next numbers are 10, 12, 14
We see that each number is 2 more than the previous one
8 + 2 = 10, then 10 + 2 = 12, then 12 + 2 = 14
2, 4, 6, 8, 10, 12, 14
2, 4, 6, 8, 10, 12, 14
• Pattern rule: Each number increases by the same amount (2)
• Even numbers: All results are even numbers
• Counting by 2s: This is the same as multiplying by 2
Multiplying by 5 pattern: This is the sequence where each number is 5 more than the previous one. All numbers end in 0 or 5.
We see that each number is 5 more than the previous one
20 + 5 = 25, then 25 + 5 = 30, then 30 + 5 = 35
5, 10, 15, 20, 25, 30, 35
5, 10, 15, 20, 25, 30, 35
• Pattern rule: Each number increases by the same amount (5)
• Ending digits: All results end in 0 or 5
• Counting by 5s: This is the same as multiplying by 5
Multiplying by 10 pattern: This is the sequence where each number is 10 more than the previous one. All numbers end in 0.
We see that each number is 10 more than the previous one
40 + 10 = 50, then 50 + 10 = 60, then 60 + 10 = 70
10, 20, 30, 40, 50, 60, 70
10, 20, 30, 40, 50, 60, 70
• Pattern rule: Each number increases by the same amount (10)
• Ending digits: All results end in 0
• Counting by 10s: This is the same as multiplying by 10
Multiplying by 3 pattern: This is the sequence where each number is 3 more than the previous one. These are multiples of 3.
We see that each number is 3 more than the previous one
12 + 3 = 15, then 15 + 3 = 18, then 18 + 3 = 21
3, 6, 9, 12, 15, 18, 21
3, 6, 9, 12, 15, 18, 21
• Pattern rule: Each number increases by the same amount (3)
• Digit sum property: Sum of digits in multiples of 3 is also a multiple of 3
• Counting by 3s: This is the same as multiplying by 3
Multiplying by 4 pattern: This is the sequence where each number is 4 more than the previous one. All results are even numbers.
We see that each number is 4 more than the previous one
16 + 4 = 20, then 20 + 4 = 24, then 24 + 4 = 28
4, 8, 12, 16, 20, 24, 28
4, 8, 12, 16, 20, 24, 28
• Pattern rule: Each number increases by the same amount (4)
• Even numbers: All results are even numbers
• Counting by 4s: This is the same as multiplying by 4
Power of 2 pattern: Each number is multiplied by 2 to get the next number. This is called exponential growth.
We see that each number is doubled to get the next one
16 × 2 = 32, then 32 × 2 = 64, then 64 × 2 = 128
2, 4, 8, 16, 32, 64, 128
2, 4, 8, 16, 32, 64, 128
• Pattern rule: Each number is multiplied by 2 to get the next
• Exponential growth: Numbers grow quickly
• Power of 2: Each number is 2 raised to a power
Multiplying by 6 pattern: This is the sequence where each number is 6 more than the previous one. All results are even numbers.
We see that each number is 6 more than the previous one
24 + 6 = 30, then 30 + 6 = 36, then 36 + 6 = 42
6, 12, 18, 24, 30, 36, 42
6, 12, 18, 24, 30, 36, 42
• Pattern rule: Each number increases by the same amount (6)
• Even numbers: All results are even numbers
• Counting by 6s: This is the same as multiplying by 6
Multiplying by 9 pattern: This is the sequence where each number is 9 more than the previous one. The digits of each multiple add up to 9.
We see that each number is 9 more than the previous one
36 + 9 = 45, then 45 + 9 = 54, then 54 + 9 = 63
9, 18, 27, 36, 45, 54, 63
9, 18, 27, 36, 45, 54, 63
• Pattern rule: Each number increases by the same amount (9)
• Digit sum property: Sum of digits in multiples of 9 is also a multiple of 9
• Counting by 9s: This is the same as multiplying by 9
Multiplying by 7 pattern: This is the sequence where each number is 7 more than the previous one.
We see that each number is 7 more than the previous one
28 + 7 = 35, then 35 + 7 = 42, then 42 + 7 = 49
7, 14, 21, 28, 35, 42, 49
7, 14, 21, 28, 35, 42, 49
• Pattern rule: Each number increases by the same amount (7)
• Counting by 7s: This is the same as multiplying by 7
• Arithmetic sequence: Each term differs by a constant amount
Multiplying by 8 pattern: This is the sequence where each number is 8 more than the previous one. All results are even numbers.
We see that each number is 8 more than the previous one
32 + 8 = 40, then 40 + 8 = 48, then 48 + 8 = 56
8, 16, 24, 32, 40, 48, 56
8, 16, 24, 32, 40, 48, 56
• Pattern rule: Each number increases by the same amount (8)
• Even numbers: All results are even numbers
• Counting by 8s: This is the same as multiplying by 8
- Sequence: 2, 4, 6, 8, 10, 12, 14...
- Rule: Add 2 to get the next number
- All results are even numbers
- Sequence: 5, 10, 15, 20, 25, 30...
- Rule: Add 5 to get the next number
- All results end in 0 or 5
- Sequence: 10, 20, 30, 40, 50, 60...
- Rule: Add 10 to get the next number
- All results end in 0
- Look at the first few numbers in the sequence
- Find the difference between consecutive numbers
- Verify that the difference is the same throughout
- Identify the multiplication factor (the common difference)
- Continue the sequence by adding the common difference
- By 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20...
- By 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...
- By 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...
- By 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50...
- Remember that multiplication patterns are arithmetic sequences
- Count by the multiplication factor to continue the pattern
- Check your work by verifying the differences between terms
- Notice special properties of each pattern (ending digits, sums, etc.)
- Forgetting that all multiples of 2 are even
- Missing that multiples of 5 always end in 0 or 5
- Confusing addition patterns with multiplication patterns
- Not recognizing that the common difference equals the multiplication factor
- "Patterns repeat in a predictable way"
- "The difference between terms equals the multiplication factor"
- "Multiples of 2 are always even"
- "Multiples of 5 end in 0 or 5"
- "Multiples of 10 end in 0"
Difference between consecutive terms = multiplication factor
• Even numbers only
• Difference of 2
• Counting by 2s
• Ends in 0 or 5
• Difference of 5
• Counting by 5s
• Ends in 0
• Difference of 10
• Counting by 10s
| Multiplication | Pattern | First 5 Terms |
|---|---|---|
| ×2 | Add 2 | 2, 4, 6, 8, 10 |
| ×3 | Add 3 | 3, 6, 9, 12, 15 |
| ×4 | Add 4 | 4, 8, 12, 16, 20 |
| ×5 | Add 5 | 5, 10, 15, 20, 25 |
| ×6 | Add 6 | 6, 12, 18, 24, 30 |
| ×7 | Add 7 | 7, 14, 21, 28, 35 |
| ×8 | Add 8 | 8, 16, 24, 32, 40 |
| ×9 | Add 9 | 9, 18, 27, 36, 45 |
Questions & Answers
Question: How do I know what the pattern is when I see a sequence of numbers?
Answer: To find the pattern in a sequence of numbers:
- Look at the first two numbers and find the difference between them
- Check if that same difference exists between the next pair of numbers
- If the difference is the same throughout, that's your pattern!
For example: in 3, 6, 9, 12... the difference is always 3, so it's the ×3 pattern.
Question: My child is having trouble with multiplication patterns. How can I help them practice?
Answer: Try these fun activities to practice multiplication patterns:
- Count by 2s, 5s, and 10s out loud together
- Use manipulatives like blocks or coins to group items
- Create visual patterns with colored dots or stickers
- Play pattern games where you say the next number in the sequence
The key is making it visual and hands-on so the patterns become clear!
Question: Why do some patterns have special rules, like multiples of 5 always ending in 0 or 5?
Answer: These special rules happen because of how our number system works! Our number system is based on 10, so when we multiply by 5, we're essentially multiplying by half of 10.
- When you multiply an even number by 5, you get a multiple of 10 (ends in 0)
- When you multiply an odd number by 5, you get a number that ends in 5
These patterns are shortcuts that help you recognize and verify your answers!