Why students struggle with making a ten to subtract

📚 Why 'Making a Ten' Can Be Tricky

Many students find the 'make a ten' strategy challenging when subtracting because it requires a strong understanding of number sense and place value. Let's break down the core reasons and how to overcome them.

🔢 The Core Concept: Making a Ten

The 'make a ten' strategy is a mental math technique used to simplify subtraction, especially when borrowing is involved. The general idea is to manipulate the numbers to create a ten, making the subtraction easier.

📜 A Brief History

The 'make a ten' strategy isn't tied to a specific inventor or date. It evolved organically as educators sought more intuitive ways to teach subtraction. It's rooted in number bonds and understanding how numbers relate to each other, predating modern math curricula.

🔑 Key Principles

• ➕ Number Bonds: Understanding how numbers can be broken down and combined. For instance, knowing that 7 can be broken down into 5 and 2.
• 🔟 Place Value: Recognizing the value of each digit in a number (ones, tens, hundreds, etc.).
• 🔄 Decomposition: Breaking down a number into smaller, more manageable parts.
• 🤝 Compensation: Adjusting numbers to make the calculation easier while maintaining the correct difference.

🤔 Common Challenges

• 🧱 Lack of Number Sense: A weak foundation in number bonds makes it difficult to see how numbers can be manipulated.
• 📍 Place Value Confusion: Not understanding the value of each digit leads to errors when borrowing.
• 🧮 Working Memory Overload: The multiple steps involved can overwhelm some students.
• ⛔ Difficulty Visualizing: Some students struggle to visualize the process of breaking down and regrouping numbers.

💡 Tips and Tricks

• 🧱 Build Number Sense: Use manipulatives like counters or base-ten blocks to help students visualize number relationships.
• 📍 Reinforce Place Value: Practice identifying the value of each digit in a number.
• ➕ Practice Number Bonds: Use games and activities to help students memorize number bonds.
• 📝 Break it Down: Explicitly show each step of the 'make a ten' strategy.
• 🗣️ Verbalize the Process: Encourage students to talk through their thinking as they solve problems.

➕ Real-World Examples

Let's say we want to solve $15 - 7$:

1. Break down 7 into $5 + 2$.
2. Subtract 5 from 15 to make 10: $15 - 5 = 10$.
3. Subtract the remaining 2 from 10: $10 - 2 = 8$.

Therefore, $15 - 7 = 8$.

Another example: $32 - 5$:

1. We can re-write this problem as $32 - 2 - 3$
2. $32 - 2 = 30$
3. $30 - 3 = 27$

Therefore, $32 - 5 = 27$

📝 Practice Quiz

Try these problems using the 'make a ten' strategy:

1. $12 - 4 =$ ?
2. $16 - 8 =$ ?
3. $11 - 3 =$ ?
4. $14 - 6 =$ ?
5. $13 - 5 =$ ?
6. $17 - 9 =$ ?
7. $18 - 9 =$ ?

✅ Conclusion

Mastering the 'make a ten' strategy requires a solid foundation in number sense and place value. By addressing the common challenges and practicing regularly, students can develop the skills they need to subtract with confidence. Keep practicing!