How to fix errors when making 10 to add numbers

📚 The 'Make Ten' Strategy: A Comprehensive Guide

The 'Make Ten' strategy is a mental math technique used to simplify addition problems, especially when adding numbers that are close to ten. Instead of adding the numbers directly, you break down one of the numbers to create a ten, making the rest of the addition easier. This strategy builds a strong foundation for mental math and number sense.

📜 History and Background

The concept of using benchmarks like ten is deeply rooted in the development of number systems. Early mathematicians recognized the importance of grouping numbers in powers of ten, which led to the decimal system we use today. The 'Make Ten' strategy is a practical application of this understanding, helping children visualize and manipulate numbers more effectively. It leverages our inherent understanding of place value, making calculations simpler.

🔢 Key Principles

• 🎯 Identify Numbers Near Ten: Look for numbers that are close to 10 (e.g., 8, 9). These are ideal candidates for the 'Make Ten' strategy.
• ✂️ Decompose Numbers: Break down one of the addends into two parts. One part will combine with the other addend to make ten. For example, in 8 + 5, you would break down 5 into 2 + 3 since 8 + 2 = 10.
• ➕ Add to Ten: Add the first part of the decomposed number to the other addend to make ten. This simplifies the problem.
• ✅ Add the Remainder: Add the remaining part of the decomposed number to ten. This gives you the final answer.

⚠️ Common Errors and How to Fix Them

• 🤯 Misunderstanding Decomposition: Error: Incorrectly breaking down numbers. Example: In 7 + 5, breaking 5 into 1 + 3 instead of 3 + 2. Fix: Practice number bonds to 10. Use manipulatives like counters to visualize the decomposition.
• 🧮 Incorrect Addition to Ten: Error: Making mistakes while adding to form ten. Example: 6 + 5 = (6 + 3) + 2 but student incorrectly adds 6+3. Fix: Reiterate basic addition facts. Use number lines to visually add and subtract to/from 10.
• ➖ Forgetting the Remainder: Error: Adding to ten but forgetting to add the remaining part of the decomposed number. Example: 8 + 6 = (8 + 2) + 4 = 10, but student forgets to add the 4. Fix: Encourage students to write down the decomposed numbers and the remainder clearly. Use visual cues.
• 😵‍💫 Applying the Strategy to Unsuitable Problems: Error: Trying to use the strategy when it's not efficient. Example: 2 + 3. Fix: Teach students to recognize when the 'Make Ten' strategy is helpful (when one number is close to 10) and when direct addition is simpler.

💡 Practical Examples

Example 1: 8 + 5

1. 🎯 Identify: 8 is close to 10.
2. ✂️ Decompose: Break 5 into 2 + 3 (because 8 + 2 = 10).
3. ➕ Add to Ten: 8 + 2 = 10.
4. ✅ Add the Remainder: 10 + 3 = 13. Therefore, 8 + 5 = 13.

Example 2: 6 + 7

1. 🎯 Identify: 6 is close to 10.
2. ✂️ Decompose: Break 7 into 4 + 3 (because 6 + 4 = 10).
3. ➕ Add to Ten: 6 + 4 = 10.
4. ✅ Add the Remainder: 10 + 3 = 13. Therefore, 6 + 7 = 13.

✍️ Practice Quiz

• ❓ Solve: 9 + 4 = ?
• ❓ Solve: 7 + 5 = ?
• ❓ Solve: 8 + 3 = ?

📈 Conclusion

The 'Make Ten' strategy is a powerful tool for building number sense and improving mental math skills. By understanding the principles and practicing regularly, students can overcome common errors and confidently solve addition problems. Mastering this strategy not only simplifies calculations but also lays a strong foundation for more advanced mathematical concepts.