Break Apart Ones To Make A Ten

This foundational math strategy,often called "making a ten" or "decomposing to add," transforms how students approach addition, especially with larger numbers. It moves beyond rote memorization, fostering deeper number sense and mental math fluency. On top of that, mastering this technique empowers learners to break complex problems into manageable, intuitive steps, building confidence and laying the groundwork for more advanced mathematical concepts. Let's explore this powerful method in detail.

The Core Concept: Breaking Apart Ones to Make Ten At its heart, "breaking apart ones to make ten" is a mental math strategy used primarily for addition. It involves taking one addend (the number being added) and splitting it into two parts: one part that exactly combines with the first addend to make ten, and the remaining part. Once ten is formed, adding the remaining part becomes straightforward Easy to understand, harder to ignore..

Imagine you need to solve 8 + 5. Instead of counting up from 8 five times (8, 9, 10, 11, 12), you recognize that 8 needs just 2 more to reach ten. So, you "break apart" the 5 into 2 and 3. You add the 2 to the 8 to make ten (8 + 2 = 10). So naturally, then, you add the remaining 3 to the ten (10 + 3 = 13). Also, the answer is 13. This process leverages the powerful anchor of ten, a number children often grasp intuitively And it works..

Why This Strategy Matters

1. Builds Number Sense: It moves beyond counting, helping students understand the relationships between numbers and the composition of numbers (e.g., 5 is 2 + 3, 8 is 2 + 6 or 3 + 5).
2. Strengthens Mental Math: It provides a reliable, efficient method for performing calculations mentally, reducing reliance on finger counting or written algorithms for simpler problems.
3. Facilitates Larger Calculations: The principle extends to larger numbers. As an example, adding 27 + 5 becomes 27 + 3 + 2 = 30 + 2 = 32. It breaks down the problem into steps involving making tens.
4. Supports Place Value Understanding: It reinforces the idea that numbers can be decomposed into their place values (e.g., 27 is 20 + 7, so 20 + 7 + 3 + 2 = 20 + 10 + 2 = 32).
5. Reduces Cognitive Load: By focusing on the manageable task of making ten, it simplifies the overall addition process.

Applying the Strategy: A Step-by-Step Guide Mastering "breaking apart ones to make ten" involves a clear sequence of steps:

1. Identify the Addends: Look at the addition problem. Identify the two numbers you need to add (e.g., 8 + 5).
2. Find the "Make Ten" Partner: Determine what number, when added to the first addend, makes ten. For 8, it's 2 (8 + 2 = 10).
3. Break Apart the Second Addend: Split the second addend into two parts: the "make ten" partner (the amount needed to reach ten from the first addend) and the remaining part. For 5, it's 2 and 3.
4. Add the "Make Ten" Part: Add the "make ten" partner to the first addend to reach ten.
5. Add the Remaining Part: Add the remaining part to the ten.
6. State the Sum: The result of step 5 is the sum of the original problem.

Example 1: 8 + 5

• Step 1: Addends: 8 and 5.
• Step 2: What makes 10 with 8? 2.
• Step 3: Break 5 into 2 and 3.
• Step 4: 8 + 2 = 10.
• Step 5: 10 + 3 = 13.
• Step 6: Sum is 13.

Example 2: 27 + 5

• Step 1: Addends: 27 and 5.
• Step 2: What makes 10 with 7? 3 (since 7 + 3 = 10).
• Step 3: Break 5 into 3 and 2.
• Step 4: 27 + 3 = 30.
• Step 5: 30 + 2 = 32.
• Step 6: Sum is 32.

The Science Behind the Strategy This technique leverages several cognitive principles. First, it exploits the human brain's strong association with the base-ten system. Ten is a natural anchor point. Second, it engages working memory effectively by focusing on the manageable task of reaching ten before adding the remainder. Third, it promotes conceptual understanding over procedural memorization, leading to deeper learning and better retention. Research in math education consistently shows that strategies like this significantly improve students' computational fluency and problem-solving abilities compared to purely rote methods Most people skip this — try not to..

Addressing Common Questions (FAQ)

• Q: What if the first addend is already ten or more? The strategy still applies. As an example, adding 10 + 7: You recognize 10 is already ten. You "break apart" the 7 into 3 and 4. Add the 3 to the 10 to make 13, then add the remaining 4 to get 17. Alternatively, you might think of it as 10 + (3 + 4) = 10 + 7 = 17.
• Q: Does this only work for addition? While primarily used for addition, the underlying concept of decomposing numbers is fundamental to many other operations and concepts, like subtraction (e.g., "making ten" for subtraction), place value, and even multiplication (e.g., breaking numbers into tens and ones).
• Q: My child struggles to find the "make ten" partner. How can I help? Practice with concrete manipulatives like ten frames, counters, or blocks is highly effective. Have them physically place counters to show how many more are needed to fill a ten frame. Using number bonds (visual diagrams showing how numbers split into parts) is also very helpful. Start with smaller numbers and gradually increase difficulty.
• Q: Is this faster than counting on fingers? For many students, especially with practice, "making ten" is significantly faster and more efficient than counting on fingers,

which can be slow and error-prone for larger numbers. It also builds a stronger number sense.

• Q: How can I make this strategy more engaging for my child? Turn it into a game! Use dice, cards, or online apps that focus on "making ten." Create real-life scenarios, like sharing snacks or toys, where they need to figure out how many more are needed to make ten. The more fun and relevant it is, the more likely they are to internalize the concept That alone is useful..

• Q: My child can do it with manipulatives but struggles to do it mentally. What should I do? This is a common step in the learning process. Continue practicing with manipulatives, but gradually reduce their use. Encourage them to visualize the ten frame or number bond in their mind. Verbalize the steps together, then have them try independently. Consistent, short practice sessions are more effective than long, infrequent ones.

Conclusion: Empowering Young Mathematicians The "make ten" strategy is far more than a simple addition trick; it is a powerful cognitive tool that builds a strong foundation for mathematical thinking. By leveraging the natural anchor of ten, it simplifies complex calculations, enhances number sense, and promotes flexible problem-solving. This approach transforms addition from a rote procedure into an engaging exercise in logical reasoning and decomposition. As students master this technique, they gain not only computational fluency but also a deeper understanding of how numbers interact, setting them on a path to becoming confident and capable mathematicians. The "make ten" strategy is a testament to the idea that effective math education is about understanding, not just memorization, and it empowers young learners to approach numbers with curiosity and confidence.