Relating 9s division to 10s facts: A 3rd grade strategy.

➕ Relating 9s Division to 10s Facts

Understanding the relationship between 9s division and 10s facts provides a helpful strategy for solving division problems. This method leverages the ease of working with multiples of 10 to simplify division by 9.

📜 History and Background

The connection between 9s and 10s has been observed for centuries, often used as a mental math trick. It relies on the proximity of 9 to 10 and how their multiples relate.

📌 Key Principles

• 🔢 Understanding the Pattern: When dividing by 9, the difference between 9 and 10 (which is 1) plays a key role. This difference helps us relate multiples of 9 to nearby multiples of 10.
• ➖ Subtraction Strategy: To divide a number close to a multiple of 9, think of the nearest multiple of 10. Then, adjust by subtracting the difference.
• ➗ Division Connection: Recognize that dividing by 9 is closely linked to how many times 9 'fits' into a number, which can be easier to visualize using 10s facts.

💡 Practical Examples

Let's explore practical examples to illustrate how 9s division relates to 10s facts:

🧮 Example 1: 63 ÷ 9

• 🎯 Think: What times 10 gets close to 63? We know that $6 \times 10 = 60$.
• ➖ Adjust: Since we're dividing by 9, we need to account for the difference. $63 - 60 = 3$, and $6 + (3 \div 3) = 7$
• ✅ Therefore: $63 \div 9 = 7$

➕ Example 2: 45 ÷ 9

• 🎯 Think: What times 10 gets close to 45? We know that $5 \times 10 = 50$.
• ➖ Adjust: Since we're dividing by 9, we need to account for the difference. $50 - 45 = 5$, and $5 = 5$
• ✅ Therefore: $45 \div 9 = 5$

➖ Example 3: 27 ÷ 9

• 🎯 Think: What times 10 gets close to 27? We know that $3 \times 10 = 30$.
• ➖ Adjust: Since we're dividing by 9, we need to account for the difference. $30 - 27 = 3$, and $3 = 3$
• ✅ Therefore: $27 \div 9 = 3$

✍️ Practice Quiz

Solve the following division problems using the 10s fact strategy:

1. $18 \div 9 = ?$
2. $36 \div 9 = ?$
3. $54 \div 9 = ?$
4. $72 \div 9 = ?$
5. $81 \div 9 = ?$
6. $90 \div 9 = ?$
7. $99 \div 9 = ?$

🔑 Answer Key

1. $18 \div 9 = 2$
2. $36 \div 9 = 4$
3. $54 \div 9 = 6$
4. $72 \div 9 = 8$
5. $81 \div 9 = 9$
6. $90 \div 9 = 10$
7. $99 \div 9 = 11$

📝 Conclusion

Relating 9s division to 10s facts provides a mental math shortcut, simplifying division by leveraging familiar multiples of 10. This strategy enhances understanding and speed in problem-solving.