Multiplying by 2: This is the same as doubling a number or adding the number to itself. For example, 7 × 2 = 7 + 7 = 14.
- Take the original number (7)
- Add it to itself (7 + 7)
- The result is 14
We have 7 as our number
When multiplying by 2, we double the number (add it to itself)
7 + 7 = 14
7 × 2 = 14
• Rule of 2: Multiplying by 2 means doubling the number
• Pattern recognition: All results are even numbers
• Addition connection: n × 2 = n + n
Multiplying by 5: When you multiply any number by 5, the result always ends in 0 or 5. For even numbers, it ends in 0; for odd numbers, it ends in 5.
We have 6 as our number
We can think of 6 × 5 as half of 6 × 10
6 × 10 = 60
60 ÷ 2 = 30
6 × 5 = 30
• Rule of 5: Results always end in 0 or 5
• Pattern recognition: Even numbers × 5 end in 0, odd numbers × 5 end in 5
• Connection to 10: n × 5 = (n × 10) ÷ 2
Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number, shifting all digits one place to the left.
We have 8 as our number
When multiplying by 10, we add one zero to the end of the number
8 with a zero added at the end gives us 80
8 × 10 = 80
• Rule of 10: Adding a zero to any number multiplies it by 10
• Place value: Each digit moves one place to the left
• Pattern recognition: All multiples of 10 end in zero
Multiplying by 2: This is the same as doubling a number or adding the number to itself. For example, 12 × 2 = 12 + 12 = 24.
We have 12 as our number
When multiplying by 2, we double the number (add it to itself)
12 + 12 = 24
12 × 2 = 24
• Rule of 2: Multiplying by 2 means doubling the number
• Pattern recognition: All results are even numbers
• Addition connection: n × 2 = n + n
Multiplying by 5: When you multiply any number by 5, the result always ends in 0 or 5. For odd numbers, it ends in 5.
We have 7 as our number
We can think of 7 × 5 as half of 7 × 10
7 × 10 = 70
70 ÷ 2 = 35
7 × 5 = 35
• Rule of 5: Results always end in 0 or 5
• Pattern recognition: Odd numbers × 5 end in 5
• Connection to 10: n × 5 = (n × 10) ÷ 2
Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number.
We have 15 as our number
Add one zero to the end of 15
15 with a zero added at the end gives us 150
15 × 10 = 150
• Rule of 10: Adding a zero works for any number
• Place value: Each digit shifts one place left
• Pattern recognition: Result ends in zero
Multiplying by 2: This is the same as doubling a number or adding the number to itself.
We have 18 as our number
When multiplying by 2, we double the number (add it to itself)
18 + 18 = 36
18 × 2 = 36
• Rule of 2: Multiplying by 2 means doubling the number
• Pattern recognition: All results are even numbers
• Addition connection: n × 2 = n + n
Multiplying by 5: When you multiply any number by 5, the result always ends in 0 or 5. For odd numbers, it ends in 5.
We have 9 as our number
We can think of 9 × 5 as half of 9 × 10
9 × 10 = 90
90 ÷ 2 = 45
9 × 5 = 45
• Rule of 5: Results always end in 0 or 5
• Pattern recognition: Odd numbers × 5 end in 5
• Connection to 10: n × 5 = (n × 10) ÷ 2
Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number.
We have 23 as our number
Add one zero to the end of 23
23 with a zero added at the end gives us 230
23 × 10 = 230
• Rule of 10: Adding a zero works for any number
• Place value: Each digit shifts one place left
• Pattern recognition: Result ends in zero
Multiplying by 2: This is the same as doubling a number or adding the number to itself.
We have 14 as our number
When multiplying by 2, we double the number (add it to itself)
14 + 14 = 28
14 × 2 = 28
• Rule of 2: Multiplying by 2 means doubling the number
• Pattern recognition: All results are even numbers
• Addition connection: n × 2 = n + n
- n × 2 = n + n (doubling)
- All results are even numbers
- The fastest way to double any number
- n × 5 = (n × 10) ÷ 2
- Results always end in 0 or 5
- Even numbers × 5 end in 0
- Odd numbers × 5 end in 5
- n × 10 = n with a zero added at the end
- Each digit moves one place to the left
- All multiples of 10 end in zero
- Take the original number
- Add it to itself (double it)
- The result is the answer
- Take the original number
- Multiply it by 10
- Divide the result by 2
- That's your answer
- Take the original number
- Add a zero at the end
- The new number is the answer
- 3 × 2 = 6 (3 + 3 = 6)
- 7 × 2 = 14 (7 + 7 = 14)
- 12 × 2 = 24 (12 + 12 = 24)
- 18 × 2 = 36 (18 + 18 = 36)
- 4 × 5 = 20 ((4 × 10) ÷ 2 = 40 ÷ 2 = 20)
- 7 × 5 = 35 ((7 × 10) ÷ 2 = 70 ÷ 2 = 35)
- 6 × 5 = 30 ((6 × 10) ÷ 2 = 60 ÷ 2 = 30)
- 9 × 5 = 45 ((9 × 10) ÷ 2 = 90 ÷ 2 = 45)
- 5 × 10 = 50
- 8 × 10 = 80
- 15 × 10 = 150
- 23 × 10 = 230
- For multiplying by 2: Just add the number to itself
- For multiplying by 5: Think of it as half of multiplying by 10
- For multiplying by 10: Always add one zero to the end
- Remember: multiplying by 5 always ends in 0 or 5
- Remember: multiplying by 2 always gives an even number
- Confusing the ending digits for multiples of 5 (0 vs 5)
- Forgetting that multiplying by 2 always results in an even number
- Mixing up the rules for 2, 5, and 10
- Not properly shifting place values when multiplying by 10
- "Times 2 means double" - helps remember that n × 2 = n + n
- "Times 5 ends in 0 or 5" - even numbers end in 0, odd numbers end in 5
- "Times 10 adds a zero" - always add one zero to the end
- "5 is half of 10" - use this to calculate 5s easily
Double the number: n × 2 = n + n
Ends in 0 or 5: n × 5 = (n × 10) ÷ 2
Add a zero: n × 10 = n0
• Doubles the number
• Always even result
• Same as adding to itself
• Ends in 0 or 5
• Half of ×10
• Even×5→ends in 0
• Odd×5→ends in 5
• Add one zero
• Digits shift left
• Always ends in 0
| Multiplication | Pattern | Result |
|---|---|---|
| 1 × 2 | Double | 2 |
| 2 × 2 | Double | 4 |
| 3 × 2 | Double | 6 |
| 4 × 2 | Double | 8 |
| 1 × 5 | Ends in 5 | 5 |
| 2 × 5 | Ends in 0 | 10 |
| 3 × 5 | Ends in 5 | 15 |
| 4 × 5 | Ends in 0 | 20 |
| 1 × 10 | Add zero | 10 |
| 2 × 10 | Add zero | 20 |
| 3 × 10 | Add zero | 30 |
| 4 × 10 | Add zero | 40 |
Questions & Answers
Question: Why does multiplying by 5 always end in 0 or 5? It seems like magic!
Answer: It's not magic, it's math! When you multiply by 5, you're essentially counting groups of 5. Let's look at the pattern:
- 1 × 5 = 5 (ends in 5)
- 2 × 5 = 10 (ends in 0)
- 3 × 5 = 15 (ends in 5)
- 4 × 5 = 20 (ends in 0)
Every other multiple of 5 ends in 0 because you're combining pairs of 5s, which make 10s. When you have an odd number of 5s, there's always one left over, making the result end in 5.
Question: My child is struggling with multiplying by 5. What's the easiest way to explain this?
Answer: The easiest way to explain multiplying by 5 is to relate it to multiplying by 10:
- First, multiply the number by 10 (just add a zero)
- Then divide that result by 2
For example: 6 × 5
- 6 × 10 = 60
- 60 ÷ 2 = 30
So 6 × 5 = 30!
You can also teach them to notice that results always end in 0 or 5.
Question: How come multiplying by 2 always gives me an even number? Why can't it be odd?
Answer: That's a great observation! When you multiply by 2, you're actually doubling the number, which means you're adding it to itself:
- 3 × 2 = 3 + 3 = 6 (even)
- 7 × 2 = 7 + 7 = 14 (even)
- 9 × 2 = 9 + 9 = 18 (even)
Since you're pairing up identical numbers, you'll always have pairs with nothing left over. That's what makes a number even - it can be divided into pairs with nothing left over. That's why multiplying by 2 always results in an even number!