• The factors
• The product
• Is 30 a multiple of 10?
Factor: Numbers being multiplied together.
Product: The answer to a multiplication problem.
Multiple: The result when a number is multiplied by another whole number.
- Look at the numbers on either side of the multiplication symbol
- These are the factors
- The number after the equals sign is the product
- Check if the product can be divided evenly by one of the factors
Look for the × symbol in the expression
These are the factors: 3 and 10
This is the product: 30
Yes, because 10 × 3 = 30, so 30 is a multiple of 10
Factors: 3 and 10, Product: 30, Yes, 30 is a multiple of 10
• Factors: Numbers multiplied together
• Product: Result of multiplication
• Multiple: Product of a number and a whole number
\(1 \times 10 =\) _____
\(2 \times 10 =\) _____
\(3 \times 10 =\) _____
\(4 \times 10 =\) _____
What pattern do you notice in the products?
Pattern: A repeated arrangement following a rule.
10s Facts: Multiplication facts where one factor is 10.
\(1 \times 10 = 10\)
\(2 \times 10 = 20\)
\(3 \times 10 = 30\)
\(4 \times 10 = 40\)
Notice that each product ends in 0
To multiply by 10, add a zero to the other factor
\(1 \times 10 = 10\), \(2 \times 10 = 20\), \(3 \times 10 = 30\), \(4 \times 10 = 40\). Pattern: Add a zero to the other factor.
• 10s Rule: Add zero to factor when multiplying by 10
• Pattern Recognition: Look for consistent changes
• Factors: 10 is always one factor
15, 20, 30, 35, 40, 50, 55, 60
Explain how you know.
Multiple: A number that can be divided evenly by another number.
Multiple of 10: A number that ends in 0 and can be divided by 10.
20, 30, 40, 50, 60 all end in 0
20 ÷ 10 = 2, 30 ÷ 10 = 3, etc.
All multiples of 10 end in 0
20, 30, 40, 50, 60 are multiples of 10
20, 30, 40, 50, and 60 are multiples of 10 because they end in 0 and can be divided evenly by 10.
• Ending in 0: All multiples of 10 end in 0
• Divisibility: Can be divided evenly by 10
• Pattern: Consistent ending digit
Factor: Numbers being multiplied together.
Product: The answer to a multiplication problem.
Multiple: A number that results from multiplying a number by a whole number.
- Look for the 10: Identify when 10 is a factor
- Apply the rule: Add a zero to the other factor
- Check the product: Verify it ends in 0
- Confirm multiple: Check if it can be divided by 10
Factor: A number that divides another number evenly.
Product: The result when two or more numbers are multiplied.
Multiple: The result when a number is multiplied by another whole number.
- Identify the factors: Look for the numbers being multiplied
- Locate the product: Find the answer to the multiplication
- Check for 10s pattern: See if 10 is one of the factors
- Apply the rule: Use the "add zero" pattern
- Verify multiple: Confirm the product is a multiple of 10
- Check answer: Does it make sense?
• Any number × 10 = that number with 0 added to the end
• All products of 10s facts end in 0
• The tens digit in the product equals the other factor
• All products of 10s facts are multiples of 10
• The factor 10 appears in every 10s fact
Factor: Numbers being multiplied together
Product: Answer to a multiplication problem
Multiple: Result of multiplying by a whole number
• 10s facts always have 10 as a factor
• Products of 10s facts end in 0
• Multiples of 10 end in 0
• Pattern: Add zero to other factor
1. Identify the factors in the multiplication
2. Recognize if 10 is one of the factors
3. Apply the 10s rule (add zero)
4. Identify the product
5. Confirm it's a multiple of 10
Simple: \(4 \times 10 = 40\) (factors: 4,10; product: 40; multiple: yes)
Pattern: \(1 \times 10 = 10, 2 \times 10 = 20, 3 \times 10 = 30\)
Multiple: 20, 30, 40 are all multiples of 10
• Add zero to multiply by 10
• All multiples of 10 end in 0
• Count by 10s to recognize patterns
• Check by dividing by 10
• 10s facts follow a clear pattern
• Vocabulary helps understand relationships
• Patterns make calculations easier
• Multiples of 10 always end in 0
Questions & Answers
Question: Why do all the 10s facts end in 0? It seems like a magic trick!
Answer: It's not magic, it's place value! Here's why:
- When you multiply by 10, you're essentially shifting the digits one place to the left
- The ones place gets filled with a 0
- For example, 3 × 10 means 3 tens, which is 30
- This happens because our number system is based on tens
So when you see 4 × 10 = 40, you're saying "4 tens" which is 40. The 0 shows there are no extra ones!
Question: My child understands that 10s facts end in 0, but sometimes confuses which numbers are multiples of 10. How can I help?
Answer: Here's a simple approach:
- Teach that multiples of 10 ALWAYS end in 0
- Use the divisibility rule: if a number ends in 0, it's divisible by 10
- Practice with lists of numbers - circle those ending in 0
- Connect to real life: money (dimes, dollars) often shows multiples of 10
For example, 25 ends in 5, so it's not a multiple of 10. But 30 ends in 0, so it is a multiple of 10.
Question: What's the difference between a factor and a multiple? They seem similar.
Answer: Great question! Here's the difference:
- Factor: Numbers you multiply together (parts of multiplication)
- Multiple: The result of multiplication (the answer)
In 3 × 10 = 30: 3 and 10 are factors, 30 is the product and also a multiple of both 3 and 10. So factors are the numbers you start with, and multiples are the results!