Show The Tens Fact You Used. Write The Difference

The aroma of freshly baked cookies wafted through the kitchen as 8-year-old Lily meticulously arranged them on a plate. She needed to put 17 cookies in total, and she knew that her mom had already placed 7 of them. How many more did she need? Lily paused, her brow furrowed. Numbers sometimes seemed like a jumbled puzzle. Suddenly, she remembered her teacher's words: "Think of your tens facts! They can solve so many problems!" A smile spread across her face as she realized she could use this trick to quickly figure out the solution.

Later that day, a group of friends were playing a game of tag. There were 12 kids in total, but 5 had to go home for dinner. How many children were left to play? Young Ethan, usually quick to answer, hesitated. He knew he could count on his fingers, but he wanted a faster way. He recalled the lesson from earlier that week: learning to "show the tens fact you used" and then "writing the difference." With a bit of thought, he cleverly applied the strategy and confidently announced the correct number.

Main Subheading: Unlocking Math Proficiency with "Show the Tens Fact You Used"

These seemingly simple scenarios highlight a powerful yet often overlooked strategy in early math education: using tens facts to solve subtraction problems. The approach not only builds a strong foundation in number sense but also encourages mental math agility and problem-solving skills. It leverages children's natural understanding of the number 10 as a benchmark to simplify complex calculations. The process involves breaking down numbers to make a ten, subtracting, and then adjusting the answer. Teaching children to "show the tens fact you used" makes their thinking visible and provides a valuable tool for both educators and learners. By explicitly demonstrating the steps, students solidify their understanding of place value, decomposition, and the relationship between addition and subtraction.

Comprehensive Overview

The strategy of "show the tens fact you used" is deeply rooted in the principles of number sense and place value, both crucial components of early mathematical development. It is based on the idea that numbers can be broken down and rearranged to facilitate easier calculations.

At its core, this method builds upon the understanding that 10 is a friendly number, a benchmark that most children become comfortable with early on. They readily recognize combinations that make 10 (e.g., 6 + 4, 8 + 2) and can visualize quantities in relation to 10. This familiarity forms the basis for extending these concepts to larger numbers and more complex subtraction problems.

The approach encourages children to see subtraction not just as "taking away," but as a process of finding the difference between two numbers. This shift in perspective promotes a deeper understanding of the relationship between addition and subtraction.

The key steps involved in this strategy typically include:

1. Identifying the nearest ten: Recognize which multiple of ten is closest to the number being subtracted from (the minuend).
2. Decomposing the subtrahend: Break down the number being subtracted (the subtrahend) into two parts: one that will bring the minuend down to the nearest ten, and the remainder.
3. Subtracting to ten: Subtract the first part of the subtrahend to reach the nearest ten.
4. Subtracting the remainder: Subtract the remaining part of the subtrahend from ten.
5. Writing the difference: State the result of the final subtraction.

For instance, consider the problem 13 - 5.

1. The nearest ten to 13 is 10.
2. We can break down 5 into 3 (to get to 10) and 2 (the remainder).
3. 13 - 3 = 10
4. 10 - 2 = 8
5. Therefore, 13 - 5 = 8

The historical context of this strategy is intertwined with the development of mathematics education. While the specific phrase "show the tens fact you used" might be a more recent pedagogical tool, the underlying principles of number decomposition and using benchmarks have been employed for centuries. Ancient mathematicians relied on similar techniques to simplify calculations before the advent of modern calculators. As math education evolved, educators sought more intuitive and accessible methods to help children grasp abstract concepts. Breaking down problems into smaller, manageable steps, and leveraging the familiarity of the number 10, proved to be a highly effective approach. Today, the method aligns with the Common Core State Standards and other modern math curricula that emphasize number sense, place value, and problem-solving strategies.

Trends and Latest Developments

Recent trends in mathematics education highlight the importance of building a strong foundation in number sense and mental math strategies. There's a growing recognition that rote memorization of facts is not sufficient for developing true mathematical proficiency. Instead, educators are focusing on helping students understand the underlying concepts and develop flexible problem-solving skills.

The "show the tens fact you used" strategy aligns perfectly with this trend. It encourages students to think critically about numbers, to decompose and recompose them in meaningful ways, and to develop a deeper understanding of the relationships between operations.

Furthermore, there's an increasing emphasis on making mathematical thinking visible. Educators are encouraging students to explain their reasoning, to show their work, and to articulate their problem-solving strategies. This not only helps students solidify their own understanding but also allows teachers to identify misconceptions and provide targeted support. The explicit act of demonstrating how tens facts are used directly addresses this need for visible thinking.

Popular opinions among math educators and researchers generally support the use of benchmark numbers like 10 to facilitate mental math calculations. Research consistently demonstrates that students who have a strong foundation in number sense are more successful in later math courses. They are better able to understand abstract concepts, solve complex problems, and apply their knowledge in real-world situations.

Newer teaching resources and methodologies often incorporate visual aids and manipulatives to help students understand the "show the tens fact you used" strategy. These resources might include ten frames, number lines, or base-ten blocks, which allow students to physically represent the numbers and the subtraction process. This hands-on approach can be particularly helpful for visual learners and students who struggle with abstract concepts.

Moreover, technology is playing an increasingly important role in math education. Interactive apps and online games can provide students with opportunities to practice the "show the tens fact you used" strategy in a fun and engaging way. These tools can also provide personalized feedback and track student progress, allowing teachers to tailor their instruction to meet individual needs.

Tips and Expert Advice

Implementing the "show the tens fact you used" strategy effectively requires careful planning and thoughtful execution. Here are some practical tips and expert advice for educators and parents:

1. Start with concrete examples: Begin by using physical objects, such as counters or blocks, to represent the numbers and the subtraction process. This hands-on approach helps children visualize the concept and make the connection between the concrete and the abstract.

   • For example, if you're teaching 12 - 4, have the child arrange 12 counters. Then, guide them to remove 2 counters to reach 10. Next, have them remove the remaining 2 counters from the 10. This visual representation makes the process more tangible and easier to understand.

2. Use ten frames: Ten frames are a powerful visual tool for teaching number sense and the benchmark number 10. They consist of a 2x5 grid, which can be filled with counters or dots to represent numbers.

   • When teaching subtraction with tens facts, have the child represent the starting number in a ten frame. Then, guide them to remove counters to reach 10, and then remove the remaining counters. The ten frame provides a clear visual representation of the decomposition process.

3. Encourage verbalization: Have students explain their thinking process aloud. This verbalization helps them solidify their understanding and identify any misconceptions. It also allows you, as the educator, to assess their understanding and provide targeted feedback.

   • For example, when solving 15 - 7, encourage the child to say, "First, I need to take away 5 to get to 10. Then, I need to take away 2 more because 7 is 5 and 2. So, 15 - 7 is 8."

4. Practice regularly: Like any skill, proficiency in using tens facts for subtraction requires consistent practice. Provide students with ample opportunities to practice the strategy in a variety of contexts.

   • Use worksheets, games, and real-world scenarios to provide engaging practice opportunities. For example, you might ask, "You have 14 stickers, and you give 6 to your friend. How many stickers do you have left?" Encourage the child to use the "show the tens fact you used" strategy to solve the problem.

5. Differentiate instruction: Recognize that students learn at different paces and have different learning styles. Differentiate your instruction to meet the individual needs of your students.

   • For students who are struggling, provide additional support and scaffolding. Use concrete examples and visual aids to help them understand the concept. For students who are ready for a challenge, provide more complex problems and encourage them to explore different strategies.

6. Connect to real-world scenarios: Help students see the relevance of math by connecting it to real-world scenarios. This makes the learning more engaging and meaningful.

   • For example, you might ask, "You have 11 candies, and you want to share them with your 3 friends. How many candies will each friend get?" Or, "You need to bake 16 muffins, and you've already baked 9. How many more muffins do you need to bake?"

7. Foster a growth mindset: Encourage students to embrace challenges and view mistakes as opportunities for learning. This helps them develop resilience and persevere in the face of difficulty.

   • Praise effort and progress, rather than focusing solely on correct answers. Emphasize that math is a skill that can be developed through practice and hard work.

FAQ

Q: What age group is this strategy most suitable for? A: This strategy is typically most effective for children in the early elementary grades (first through third grade) as they are developing their number sense and place value understanding.

Q: Is this strategy only useful for subtraction problems? A: While it's primarily taught for subtraction, the underlying principles of number decomposition and benchmark numbers can also be applied to addition problems.

Q: What if a child struggles to decompose numbers? A: Provide additional support with concrete materials like counters or ten frames to help visualize the decomposition process. Break down the steps into smaller, more manageable chunks.

Q: How can I make this strategy more engaging for students? A: Use games, real-world scenarios, and visual aids to make the learning more interactive and fun. Incorporate technology, such as interactive apps and online games, to provide engaging practice opportunities.

Q: Is this strategy aligned with Common Core Standards? A: Yes, this strategy aligns with Common Core State Standards that emphasize number sense, place value, and problem-solving strategies.

Conclusion

Mastering subtraction through the "show the tens fact you used" strategy is more than just learning a mathematical trick; it's about cultivating a deeper understanding of number relationships and fostering mental math agility. By breaking down numbers, leveraging the benchmark of 10, and explicitly demonstrating their thinking, children gain confidence and competence in their mathematical abilities. This approach lays a strong foundation for future success in more advanced mathematical concepts.

We encourage you to try these techniques with your students or children. Share your experiences and insights in the comments below. What are some challenges you've encountered, and what strategies have you found most effective? Let's collaborate to help all learners unlock their mathematical potential!