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? Or perhaps you remember the frustration of timed math tests, where simple addition felt like climbing a mountain? There's a better way to approach these calculations, a technique that transforms addition from a chore into a mental playground. It's called "Make a Ten," and it's a powerful strategy for building number sense and making math more intuitive.

Imagine turning that 8 + 5 problem into something much easier. What if we could magically transform the 8 into a 10? Suddenly, the problem becomes 10 + 3, which is a breeze to solve. That's the essence of "Make a Ten" – a clever strategy that leverages our natural comfort with the number 10 to simplify addition problems. This isn't just a trick; it's a fundamental building block for mathematical fluency and confidence. In this comprehensive guide, we'll explore the "Make a Ten" strategy in detail, uncovering its benefits, practical applications, and expert tips for mastering this invaluable technique.

Mastering the 'Make a Ten' Strategy: A Comprehensive Guide

The "Make a Ten" strategy is a cornerstone of early math education, designed to help children (and adults!) develop a stronger understanding of number relationships and improve their addition skills. It’s a mental math technique that simplifies addition by decomposing one number in a problem to create a 10 with the other number. This leverages the human brain's natural affinity for the number 10, making calculations faster and more intuitive. It's especially helpful when dealing with addition problems that involve numbers close to 10, such as 6, 7, 8, and 9.

At its heart, the "Make a Ten" strategy is about recognizing that numbers can be broken down and recomposed to make addition easier. Instead of relying on rote memorization or counting, this method encourages students to visualize numbers and manipulate them strategically. This approach not only speeds up calculations but also fosters a deeper understanding of number sense and lays a solid foundation for more advanced mathematical concepts.

Deeper Dive: Understanding the Foundations of 'Make a Ten'

The "Make a Ten" strategy isn't just a random trick; it's rooted in several fundamental mathematical concepts:

Number Decomposition: This refers to the ability to break down a number into its component parts. For example, understanding that 7 can be decomposed into 5 + 2 or 3 + 4 is crucial for the "Make a Ten" strategy. It allows us to see numbers as flexible entities that can be manipulated.
Number Bonds: Number bonds are pairs of numbers that add up to a specific total. In the context of "Make a Ten," we focus on number bonds that make 10. For example, 6 + 4 = 10, 8 + 2 = 10, and so on. Knowing these bonds by heart significantly speeds up the "Make a Ten" process.
Commutative Property of Addition: This property states that the order in which we add numbers doesn't change the sum (a + b = b + a). This allows us to choose which number to decompose based on what's most convenient for making a 10. For example, when adding 3 + 8, we can choose to decompose the 3 or the 8, depending on which feels easier.
Associative Property of Addition: The associative property states that the way numbers are grouped in an addition problem doesn't change the sum: (a + b) + c = a + (b + c). This property is at play when you regroup the numbers to form the ten.
Base-Ten System: Our number system is based on powers of 10. Understanding this system makes it easier to work with 10 as a benchmark and to see how numbers relate to each other in terms of tens and ones.

A Historical Perspective

While the "Make a Ten" strategy might seem like a modern invention, its roots can be traced back to ancient number systems and calculation methods. Early civilizations relied on various tools and techniques to perform arithmetic, and many of these implicitly involved the idea of grouping and regrouping numbers to simplify calculations.

The development of the decimal system, with its base-ten structure, further solidified the importance of 10 as a fundamental unit in mathematics. As math education evolved, educators recognized the value of teaching strategies that leverage this base-ten understanding. The "Make a Ten" strategy, in its modern form, became a popular and effective way to help students develop number sense and master addition.

Step-by-Step Guide to Using 'Make a Ten'

Here's how to use the "Make a Ten" strategy to solve addition problems:

Identify the Number Closer to 10: Look at the two numbers you're adding and identify the one that is closer to 10. This is the number you'll want to "build up" to 10.
Determine What's Needed to Make 10: Figure out how many you need to add to the number you identified in step 1 to reach 10. This is where knowing your number bonds to 10 comes in handy.
Decompose the Other Number: Take the other number in the addition problem and decompose it into two parts: one part that you need to make 10, and the remaining part.
Make 10: Add the first part of the decomposed number to the original number to make 10.
Add the Remaining Part: Add the remaining part of the decomposed number to 10. The result is the answer to your original addition problem.

Example: Let's solve 7 + 5 using the "Make a Ten" strategy.

7 is closer to 10 than 5.
We need to add 3 to 7 to make 10 (7 + 3 = 10).
Decompose 5 into 3 + 2.
Add 3 to 7 to make 10 (7 + 3 = 10).
Add the remaining 2 to 10 (10 + 2 = 12).
Therefore, 7 + 5 = 12.

Visual Aids: Tools to Help Visualize 'Make a Ten'

Visual aids can be incredibly helpful for understanding and applying the "Make a Ten" strategy, especially for younger learners. Here are some effective tools:

Ten Frames: A ten frame is a rectangular grid with two rows of five squares each. You can use counters or drawings to represent numbers within the ten frame. To use it with "Make a Ten," represent one addend in the ten frame, then fill in the remaining spaces to make 10. The number of counters you added, plus the number of counters left over, represents the other addend and visually shows the decomposition.
Number Lines: A number line is a straight line with numbers marked at equal intervals. To use it with "Make a Ten," start at one addend and "jump" to 10. Then, make the remaining jumps to reach the final sum.
Manipulatives (e.g., Counters, Blocks): Physical objects can help children visualize the process of decomposing and recomposing numbers. For example, you can use different colored counters to represent the two parts of the decomposed number.
Drawings: Simple drawings, such as circles or dots, can also be used to represent numbers and illustrate the "Make a Ten" strategy.

Current Trends and Developments

The "Make a Ten" strategy remains a popular and effective tool in modern math education. Here are some current trends and developments:

Emphasis on Conceptual Understanding: There's a growing emphasis on teaching the "Make a Ten" strategy not just as a procedure, but as a way to build conceptual understanding of number relationships. Educators are focusing on helping students understand why the strategy works, rather than just memorizing the steps.
Integration with Technology: Interactive apps and online games are being developed to help students practice the "Make a Ten" strategy in a fun and engaging way. These tools often provide visual representations and immediate feedback, which can enhance learning.
Differentiation: Educators are recognizing that students learn at different paces and in different ways. They're using differentiated instruction to tailor the "Make a Ten" strategy to meet the individual needs of each student. This might involve providing more visual aids for some students, or more challenging problems for others.
Focus on Fluency: While conceptual understanding is important, there's also a focus on developing fluency with the "Make a Ten" strategy. This means that students should be able to apply the strategy quickly and accurately, without having to think about each step in detail. Fluency is developed through practice and repetition.
Connection to Higher-Level Math: Educators are increasingly emphasizing the connection between the "Make a Ten" strategy and more advanced mathematical concepts, such as algebra. By understanding the underlying principles of number decomposition and recomposition, students are better prepared for success in higher-level math courses.

Expert Tips and Practical Advice

Here are some expert tips and practical advice for mastering the "Make a Ten" strategy:

Master Number Bonds to 10: This is the single most important thing you can do to improve your "Make a Ten" skills. Practice number bonds to 10 until they become automatic. Flashcards, games, and online resources can be helpful.
Practice Regularly: Like any skill, the "Make a Ten" strategy requires practice to master. Set aside time each day or week to practice addition problems using this method.
Use Visual Aids: Don't be afraid to use visual aids, especially when you're first learning the strategy. Ten frames, number lines, and manipulatives can help you visualize the process and understand the underlying concepts.
Start with Smaller Numbers: If you're struggling with larger numbers, start with smaller numbers and gradually work your way up. This will help you build confidence and develop a stronger understanding of the strategy.
Break It Down: If you're having trouble with a particular problem, break it down into smaller steps. For example, instead of trying to do the entire "Make a Ten" process in your head, write down each step.
Turn It into a Game: Make learning fun by turning the "Make a Ten" strategy into a game. You can create your own games or use online resources.
Teach Someone Else: One of the best ways to learn something is to teach it to someone else. Explain the "Make a Ten" strategy to a friend or family member. This will help you solidify your own understanding and identify any areas where you need more practice.
Be Patient: Learning the "Make a Ten" strategy takes time and effort. Don't get discouraged if you don't master it right away. Just keep practicing, and you'll eventually see results.
Connect to Real-World Situations: Applying the "Make a Ten" strategy to real-world situations can make it more meaningful and engaging. For example, you can use it to calculate the total cost of two items at the store, or to figure out how many more pieces of candy you need to have a total of ten.

Frequently Asked Questions (FAQ)

Q: At what age should children learn the "Make a Ten" strategy?
- A: The "Make a Ten" strategy is typically introduced in first grade, when children are learning basic addition facts. However, some children may be ready to learn it earlier, while others may need more time to develop the necessary skills.
Q: Is the "Make a Ten" strategy only useful for addition?
- A: While the "Make a Ten" strategy is primarily used for addition, it can also be helpful for subtraction. For example, to solve 13 - 8, you can think of it as "What number do I need to add to 8 to get to 13?" You can then use the "Make a Ten" strategy to figure out that 8 + 2 = 10, and 10 + 3 = 13, so 8 + 5 = 13. Therefore, 13 - 8 = 5.
Q: What if both numbers are far from 10?
- A: The "Make a Ten" strategy is most effective when at least one of the numbers is close to 10. If both numbers are far from 10 (e.g., 4 + 3), other strategies, such as counting on or using number bonds, may be more efficient.
Q: How does "Make a Ten" relate to other addition strategies?
- A: "Make a Ten" is just one of several addition strategies that students can use. Other strategies include counting on, using number bonds, and doubling. The best strategy to use depends on the specific problem and the individual student's preferences and strengths.
Q: Is it okay to use fingers to help with "Make a Ten"?
- A: While the goal is to eventually perform the "Make a Ten" strategy mentally, it's perfectly fine to use fingers or other manipulatives to help visualize the process, especially when first learning the strategy. As you become more comfortable with the strategy, you'll gradually rely less on these aids.

Conclusion

The "Make a Ten" strategy is more than just a trick for solving addition problems. It's a powerful tool for developing number sense, building mathematical fluency, and fostering a deeper understanding of number relationships. By mastering this strategy, you can transform addition from a chore into a mental playground, making math more intuitive and enjoyable. Whether you're a student struggling with basic addition, a teacher looking for effective teaching strategies, or simply someone who wants to improve their mental math skills, the "Make a Ten" strategy is a valuable asset to have in your mathematical toolkit.

Ready to put your "Make a Ten" skills to the test? Try solving some addition problems using this strategy and see how quickly and easily you can find the answers. Share your experiences and tips in the comments below, and let's continue to explore the fascinating world of mathematics together!