Make A 10 To Subtract

Mastering Subtraction: A Deep Dive into Making Ten to Subtract

Subtraction, a fundamental arithmetic operation, often presents challenges for young learners. While seemingly simple, mastering subtraction requires a strong understanding of number relationships and efficient strategies. So this article explores the powerful technique of "making ten to subtract," a method that simplifies subtraction problems, particularly those involving subtracting from numbers less than 20. Day to day, we will get into the underlying principles, illustrate the process with various examples, and explore its application in real-world scenarios. This thorough look will empower you to not only understand this method but also effectively teach it to others.

Understanding the "Make a Ten" Strategy

The "make a ten" strategy, also known as the "ten-frame strategy," leverages the ease of subtracting from ten. This approach fosters a deeper understanding of number composition and decomposition, strengthening a child's number sense. Now, instead of directly subtracting, this method decomposes the larger number into ten and a smaller part, making the subtraction process significantly easier. It's particularly useful when subtracting a single-digit number from a teen number (numbers between 11 and 19). The core principle lies in recognizing that subtracting from ten is often simpler than subtracting from other numbers.

Step-by-Step Guide: Making Ten to Subtract

Let's break down the "make a ten" subtraction strategy step-by-step, using examples to clarify each stage. We will focus on subtracting single-digit numbers from teen numbers initially.

1. Decompose the Teen Number:

The first step involves breaking down the teen number into ten and the remaining units. Because of that, for instance, consider the problem 13 - 5. We decompose 13 into 10 + 3.

2. Subtract from Ten:

Next, we subtract the smaller number (the number being subtracted) from ten. In our example, we subtract 5 from 10: 10 - 5 = 5.

3. Add the Remaining Units:

Finally, we add the remaining units from the decomposition of the teen number to the result from step 2. In this case, we add the 3 (from 10 + 3) to the 5 (from 10 - 5): 5 + 3 = 8.

4. The Solution:

Because of this, 13 - 5 = 8.

Let's illustrate with another example: 16 - 8.

1. Decompose: 16 = 10 + 6
2. Subtract from Ten: 10 - 8 = 2
3. Add Remaining Units: 2 + 6 = 8
4. Solution: 16 - 8 = 8

Visualizing with Ten Frames

Using ten frames is a highly effective visual aid for understanding the "make a ten" strategy. A ten frame is a 2x5 grid that visually represents the number ten. To subtract using a ten frame:

1. Represent the Teen Number: Fill the ten frame with counters to represent the ten part of the teen number. Then add counters outside the ten frame to represent the remaining units. For 13 - 5, you'd have a full ten frame (10 counters) and 3 counters outside.

2. Remove the Smaller Number: Remove the number of counters that represents the number being subtracted (5 in this case). Remove 5 counters from the full ten frame, leaving 5 counters.

3. Count the Remaining Counters: Count all the remaining counters, both inside and outside the ten frame. This will give you the answer: 8.

This visual approach helps children conceptualize the decomposition and recombination process, making the abstract concept of subtraction more concrete and easier to grasp.

Extending the "Make a Ten" Strategy: Beyond Teen Numbers

While the "make a ten" strategy is primarily associated with subtracting from teen numbers, its underlying principle – decomposing numbers to simplify subtraction – can be extended to larger numbers. Let's look at an example involving numbers greater than 20:

Example: 23 - 9

1. Decompose: We can think of 23 as 20 + 3. On the flip side, we can also strategically decompose it as 10 + 13.

2. Subtract from Ten: 10 - 9 = 1

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3. Add Remaining Units: 1 + 13 = 14

4. Solution: 23 - 9 = 14

This shows that the fundamental principle of making ten, or more generally, making a friendly number (a number that makes subtraction easier), can be applied even with larger numbers. The key is to choose the decomposition that best facilitates easy subtraction.

The "Make a Ten" Strategy and Number Bonds

The "make a ten" strategy is intrinsically linked to understanding number bonds. Number bonds represent the different combinations of numbers that add up to a given total. Now, mastering number bonds strengthens a child's number sense and makes the decomposition required for "make a ten" subtraction intuitive. Take this: understanding that 7 + 3 = 10 allows a child to easily decompose 17 as 10 + 7 for subtraction problems. Regular practice with number bonds lays a solid foundation for effective subtraction using this method.

Real-World Applications of the "Make a Ten" Strategy

The "make a ten" subtraction strategy isn't just a classroom exercise; it finds practical application in various everyday situations. Consider these examples:

• Shopping: If you have $12 and buy an item costing $7, using the "make a ten" strategy (10 + 2 - 7) quickly calculates your remaining money ($5).

• Baking: If a recipe calls for 14 strawberries and you've already used 6, the method helps determine how many are left (8).

• Games: Many games involve tracking scores or resources. The "make a ten" strategy streamlines quick calculations during gameplay.

These examples demonstrate the practical relevance of this mathematical technique, highlighting its value beyond the confines of the classroom.

Frequently Asked Questions (FAQ)

Q: What if the number being subtracted is larger than the units digit of the teen number?

A: This is a common misconception. In practice, the "make a ten" strategy only works if you can decompose the teen number in a way that allows you to subtract from ten. If the number being subtracted is larger than the units digit, you would need to use a different subtraction method, such as counting back or using a number line. Take this: 12 - 8 cannot be done directly using this strategy as the 'make a ten' methodology is not applicable here.

Q: Is this strategy suitable for all subtraction problems?

A: No, this strategy is most effective for subtracting single-digit numbers from teen numbers or when strategically decomposing larger numbers to create easier subtractions involving 10. For other subtraction problems, other methods like the standard algorithm or using number lines are more appropriate.

Q: How can I help my child master this strategy?

A: Consistent practice is key. Use manipulatives like ten frames and counters. Here's the thing — start with simpler problems and gradually increase difficulty. Focus on understanding the concept of decomposition and recombination. Make it fun by incorporating games and real-life examples.

Q: Why is this strategy considered superior to other subtraction methods?

A: While not inherently superior to all methods, "make a ten" provides a strong foundation in number sense and decomposition, crucial skills for more advanced mathematical concepts. It simplifies subtraction by leveraging the ease of subtracting from ten, making it particularly intuitive for young learners.

Conclusion: Empowering Learners through Understanding

The "make a ten" strategy is a valuable tool for mastering subtraction, particularly for young learners. The "make a ten" strategy doesn't just teach subtraction; it cultivates a stronger number sense, a vital asset in future mathematical endeavors. Remember that consistent practice and a focus on conceptual understanding are crucial for mastering this valuable mathematical skill. Which means by breaking down the method into manageable steps and utilizing visual aids like ten frames, educators can effectively teach this technique, empowering students to solve subtraction problems with confidence and efficiency. Its emphasis on number decomposition and the strategic use of ten simplifies the subtraction process, fostering a deeper understanding of number relationships. This approach, therefore, represents more than just a method; it is a pathway to building a dependable foundation in arithmetic.