Make A Ten To Find The Sum

Have you ever watched a child struggle to add 8 + 5, counting on their fingers and taking forever? It’s a common sight, but what if I told you there’s a simple, effective strategy that can transform this struggle into a moment of confident calculation? This technique, known as "make a ten," is a game-changer for young learners. It's not just about getting the right answer; it's about building a deeper understanding of numbers and how they work together.

Imagine you’re teaching a group of first graders. They’re learning to add, but some are finding it tough to grasp. You introduce "make a ten" with colorful blocks and a story about how friendly numbers like 10 can help us add faster. As they start to visually break down numbers and combine them to reach that magic number 10, their faces light up. It’s like unlocking a secret code to math. This article will explore the "make a ten" strategy, showing you why it works, how to teach it, and how it can benefit children in the long run.

Mastering the 'Make a Ten' Strategy for Addition

The "make a ten" strategy is a mental math technique used to simplify addition problems, particularly those that involve adding numbers to 7, 8, or 9. The core idea is to manipulate the numbers in the problem to create a sum that includes the number 10, which is easier to work with. This method transforms what might seem like a difficult addition into a more manageable one, fostering a stronger number sense and improving mental calculation skills.

The foundation of this strategy lies in understanding number bonds – how numbers can be broken down and combined to form other numbers. For example, a child needs to recognize that 7 can be decomposed into 5 and 2, or 8 into 5 and 3. This understanding of number composition is crucial for effectively applying the "make a ten" strategy. By mastering this technique, children not only learn to add more efficiently but also develop a deeper intuitive understanding of how numbers relate to each other. This skill is beneficial for more advanced mathematical concepts later on.

Comprehensive Overview of the 'Make a Ten' Strategy

At its core, the "make a ten" strategy is about leveraging our understanding of the number 10 to simplify addition. It's based on the principle that adding to 10 is easier for most people, particularly children. The strategy involves breaking down one of the addends (the numbers being added) to "make" a 10 with the other addend, and then adding the remaining amount.

Definitions and Scientific Foundations

The "make a ten" strategy is rooted in cognitive psychology and mathematics education. Psychologically, it utilizes the concept of chunking, where information is organized into manageable parts. By breaking down numbers and creating a group of ten, the brain can process the addition more efficiently. Mathematically, it's based on the associative property of addition, which states that the way numbers are grouped in an addition problem does not change the sum (e.g., (a + b) + c = a + (b + c)).

History and Essential Concepts

While the exact historical origins are difficult to pinpoint, the "make a ten" strategy has been a staple in elementary mathematics education for decades. It aligns with the shift towards teaching number sense and mental math strategies, rather than rote memorization of facts.

The essential concepts include:

1. Number Bonds: Understanding how numbers can be broken down into smaller parts (e.g., 7 = 5 + 2).
2. Decomposition: Breaking a number into its component parts.
3. Composition: Combining numbers to form a larger number.
4. The Associative Property of Addition: Understanding that the grouping of numbers doesn't change the sum.
5. Fluency with Numbers to 10: Having a strong sense of how numbers relate to 10 (e.g., knowing that 8 + 2 = 10).

To illustrate the strategy, let's consider the problem 8 + 5:

1. Identify the number closer to 10: In this case, it's 8.
2. Determine how much 8 needs to reach 10: 8 needs 2 to become 10.
3. Decompose the other number (5) into the required amount (2) and the remainder: 5 can be broken down into 2 + 3.
4. Combine the first number (8) with the decomposed part (2) to make 10: 8 + 2 = 10.
5. Add the remaining part (3) to 10: 10 + 3 = 13.

Therefore, 8 + 5 = 13.

This might seem like a lot of steps, but with practice, it becomes a quick and intuitive process. The key is to help children visualize the process, often using manipulatives like blocks or drawings.

Trends and Latest Developments

The "make a ten" strategy is not a static method; its application and teaching methods are constantly evolving. Here are some current trends and developments:

• Integration with Visual Aids: Educators are increasingly using visual aids like ten frames (a rectangular frame divided into ten equal parts) to help children visualize the "make a ten" process. These visual aids provide a concrete representation of the numbers and make the concept more accessible, especially for visual learners.
• Technology Integration: Educational apps and interactive games are now available that reinforce the "make a ten" strategy. These digital tools often provide immediate feedback and make learning more engaging for children.
• Emphasis on Conceptual Understanding: There's a growing emphasis on ensuring children understand why the strategy works, rather than just memorizing the steps. This involves explaining the underlying mathematical principles and encouraging children to explain their reasoning.
• Differentiation: Teachers are recognizing the need to differentiate instruction to meet the needs of all learners. This might involve providing extra support for students who struggle with the concept or offering more challenging problems for students who have mastered it.
• Connection to Place Value: Some educators are using the "make a ten" strategy as a stepping stone to understanding place value. By understanding how to compose and decompose numbers to make 10, children can better understand how numbers are structured in the base-ten system.

Professional insights suggest that the "make a ten" strategy is most effective when it's introduced after children have a solid understanding of number bonds and number composition. It's also important to provide plenty of opportunities for practice, both with concrete materials and with abstract problems.

Tips and Expert Advice

Here's some practical advice and real-world examples to effectively teach and implement the "make a ten" strategy:

1. Start with Concrete Materials: Use manipulatives like counters, blocks, or ten frames to introduce the concept. This allows children to physically manipulate the numbers and visualize the process of making a ten. For example, when teaching 9 + 4, have the child place 9 counters on a ten frame and then add 1 counter to fill the frame, making 10. The remaining 3 counters then represent the answer: 10 + 3 = 13.
2. Use Storytelling: Create stories or scenarios that involve making a ten. For instance, "There are 8 apples in a basket, and we need to have 10. How many more apples do we need to add?" This makes the concept more relatable and engaging for children.
3. Break it Down: Decompose the steps into smaller, more manageable chunks. Don't rush the process. Ensure the child understands each step before moving on to the next.
4. Practice Regularly: Consistent practice is key to mastering the "make a ten" strategy. Use a variety of activities, such as worksheets, games, and real-life problem-solving situations.
5. Encourage Verbalization: Have the child explain their thinking process aloud. This helps them solidify their understanding and allows you to identify any misconceptions. For example, ask them to explain why they chose to break down a particular number or how they knew how many to add to make ten.
6. Connect to Real-World Situations: Relate the strategy to everyday situations. For example, "You have 7 stickers, and your friend gives you 5 more. How many stickers do you have in total? Let's use 'make a ten' to figure it out."
7. Use Games: Incorporate games like "Go Fish" or "Memory" with number bonds that add up to 10. This makes learning fun and engaging.
8. Introduce Ten Frames: A ten frame is a simple visual tool that can help children understand how to make a ten. It's a rectangle divided into two rows of five squares, which can be filled with counters or dots to represent numbers. Using ten frames helps children visualize the process of adding to ten.
9. Use Number Lines: A number line can also be a helpful tool for teaching the "make a ten" strategy. Children can start at one number and then "jump" to 10, and then jump the remaining amount to find the answer.
10. Provide Feedback: Give children specific and positive feedback on their work. This helps them stay motivated and encourages them to continue practicing.

By implementing these tips and expert advice, educators and parents can effectively teach the "make a ten" strategy and help children develop strong mental math skills.

FAQ

Q: What age is the "make a ten" strategy appropriate for?

A: The "make a ten" strategy is typically introduced in first grade, around ages 6-7, when children are developing their understanding of addition and number bonds. However, it can be adapted for older students who struggle with basic addition facts.

Q: Is "make a ten" just a trick, or does it build real understanding?

A: It's not just a trick. When taught correctly, it builds a deep understanding of number relationships, decomposition, and the associative property of addition. It helps children develop number sense and mental math skills that are beneficial for more advanced math concepts.

Q: What if a child struggles to decompose numbers?

A: Spend more time on number bonds and number composition. Use concrete materials and visual aids to help them understand how numbers can be broken down into smaller parts. Start with smaller numbers and gradually increase the difficulty.

Q: How can I make it fun for my child?

A: Use games, stories, and real-life scenarios to make the strategy more engaging. Incorporate manipulatives and visual aids. Celebrate their successes and provide positive feedback.

Q: Can this strategy be used for subtraction?

A: While primarily used for addition, the concepts of number bonds and decomposition can be applied to subtraction as well, particularly when teaching related facts. However, there are other subtraction strategies that might be more effective.

Conclusion

The "make a ten" strategy is a powerful tool for building number sense and improving addition skills in young learners. By understanding the underlying principles and using effective teaching strategies, educators and parents can help children master this technique and develop a lifelong love of math. It's not just about memorizing facts; it's about fostering a deep understanding of how numbers work together.

Ready to help your child or students master the "make a ten" strategy? Start by using concrete materials and visual aids, and gradually move towards abstract problem-solving. Share your experiences and ask questions in the comments below! Let's work together to make math fun and accessible for all learners.