Break Apart Ones To Make A Ten

Breaking Apart Ones to Make a Tens: Mastering a Crucial Math Concept

Understanding the concept of "breaking apart ones to make a ten" is a cornerstone of early elementary math education. This strategy, also known as the "making ten" strategy, significantly simplifies addition and subtraction problems, paving the way for more complex mathematical concepts. This comprehensive guide delves deep into this crucial skill, exploring its application, benefits, and various teaching methods. We'll equip you with the knowledge and tools to confidently teach or learn this fundamental mathematical concept.

Why "Breaking Apart Ones to Make a Ten" Matters

The ability to decompose numbers strategically is paramount in developing strong number sense. This strategy isn't just about memorizing addition facts; it's about fostering a deep understanding of number relationships. By mastering this skill, children:

Develop fluency in addition and subtraction: Instead of relying solely on rote memorization, they can solve problems efficiently and accurately, even with larger numbers.
Build a strong foundation for future math: This strategy is a building block for more advanced concepts like regrouping in multi-digit addition and subtraction, and even multiplication and division.
Enhance problem-solving skills: It encourages flexible thinking and the ability to approach problems from different angles, fostering critical thinking skills.
Improve mental math abilities: Regular practice with this method strengthens mental computation skills, reducing reliance on calculators and enhancing overall mathematical confidence.

Understanding the Concept: A Visual Approach

Imagine you have 8 single units (ones) and you need to add 5 more. Instead of counting all 13 units individually, the "making ten" strategy encourages you to "borrow" two units from the 5 to make a ten with the 8. This breaks the problem into two easier steps:

8 + 2 = 10 (Making a ten)
10 + 3 = 13 (Adding the remaining units)

This seemingly small adjustment transforms a potentially challenging problem into two simple addition facts. This visual representation is extremely helpful, especially for visual learners. Using manipulatives like counters, blocks, or even drawings can solidify this understanding.

Practical Applications: Addition and Subtraction

Let's explore how this strategy works in both addition and subtraction:

Addition Examples:

Problem: 7 + 6 = ?
- Solution: Break apart the 6 into 3 and 3. 7 + 3 = 10. Then, 10 + 3 = 13.
Problem: 9 + 5 = ?
- Solution: Break apart the 5 into 1 and 4. 9 + 1 = 10. Then, 10 + 4 = 14.
Problem: 18 + 7 = ?
- Solution: Break apart the 7 into 2 and 5. 18 + 2 = 20. Then 20 + 5 = 25. This demonstrates scalability to larger numbers.

Subtraction Examples:

Subtraction benefits from the "making ten" strategy, particularly when dealing with numbers close to multiples of ten. Instead of directly subtracting, we can add to reach a ten, making the subtraction simpler.

Problem: 15 - 8 = ?
- Solution: Think: "What do I add to 8 to make 10?" The answer is 2. Add 2 to both numbers: 17 - 10 = 7.
Problem: 12 - 5 = ?
- Solution: Think: "What do I add to 5 to make 10?" The answer is 5. Add 5 to both numbers: 17 - 10 = 7.
Problem: 23 - 9 = ?
- Solution: Think: "What do I add to 9 to make 10?" The answer is 1. Add 1 to both numbers: 24 -10 = 14

Teaching Strategies and Activities

Effective teaching involves diverse methods catering to different learning styles. Here are some proven strategies:

1. Manipulatives:

Use physical objects like counters, blocks, or ten-frames. Visually breaking apart and regrouping the objects helps children grasp the concept concretely.

2. Number Lines:

A number line provides a visual representation of number relationships. Children can use hops to show the process of making a ten and adding or subtracting the remaining amount.

3. Games and Activities:

Engaging games make learning fun and memorable. Simple card games, dice activities, or even online games focusing on making tens can reinforce the concept through playful interaction.

4. Real-World Examples:

Relate the concept to everyday situations. For example: "You have 8 apples, and your friend gives you 5 more. How many apples do you have in total?" This contextualization makes learning more meaningful and relevant.

5. Differentiated Instruction:

Recognize that children learn at different paces. Offer varied levels of support, starting with simple problems and gradually increasing the complexity. Provide extra practice for students who need it, and challenge advanced learners with more complex problems.

Addressing Common Challenges and Misconceptions

Even with the best teaching methods, some students might encounter difficulties. Here's how to address them:

Difficulty understanding the concept of decomposition: Use manipulatives to visually demonstrate breaking apart numbers. Repeated practice with smaller numbers before moving to larger ones is crucial.
Trouble visualizing the "making ten" strategy: Use visual aids like ten-frames and number lines to illustrate the process. Encourage children to draw pictures to represent the problem.
Struggling with mental math: Start with simpler problems and gradually increase the difficulty. Provide ample practice opportunities for building mental computation skills. Regular practice with timed activities (but in a non-stressful way) can help speed up mental calculations.
Reliance on finger counting: While finger counting can be a useful tool initially, encourage children to transition to the "making ten" strategy as they become more comfortable. Emphasize the efficiency and speed of this method.

Extending the Concept: Beyond Basic Addition and Subtraction

The "making ten" strategy is not limited to simple addition and subtraction. Its principles can be extended to:

Multi-digit addition and subtraction: The concept of regrouping (carrying and borrowing) in multi-digit operations relies heavily on the understanding of making tens.
Mental math strategies: Mastering this strategy significantly enhances mental math capabilities, allowing for quick and efficient calculations.
Multiplication and division: Understanding number relationships and decomposition is helpful in developing strategies for multiplication and division. For example, breaking down multiplication problems into smaller, manageable parts.

Conclusion: A Powerful Tool for Mathematical Success

The ability to break apart ones to make a ten is a fundamental skill that lays the groundwork for a strong mathematical foundation. By understanding this concept, children develop fluency in addition and subtraction, enhance their problem-solving abilities, and build confidence in their mathematical capabilities. Through effective teaching strategies, diverse activities, and addressing common challenges, educators and parents can empower children to master this crucial skill and unlock their mathematical potential. Remember, consistent practice and a supportive learning environment are key to success. The journey towards mathematical proficiency is a marathon, not a sprint. Embrace the process, celebrate small victories, and watch your students (or yourself!) blossom in their mathematical understanding.