Week 8 Assignment 4using Reasoning Strategies To Learnb ✓ Solved
Using Reasoning Strategies to Learn Basic Addition and Subtraction: In the weekly reading, you learned that it is common for teachers to move too quickly from counting strategies to memorizing basic facts. Instead, teachers should spend time developing students’ reasoning strategies that lead students to memorization. This assignment explores a variety of reasoning strategies through guided intervention, or purposefully designed tasks and problems that help children (or adults in your case) notice and use specific reasoning strategies. Complete the tasks and reflection questions for each reasoning strategy.
Reasoning Strategy 1 - One More One Less
In grades K-1, students learn the counting sequence and practice counting on from a given number. These skills provide a foundation for finding “one more” and “one less” (e.g., 5+1 and 5-1). The hundreds chart can be a useful tool for visualizing number relationships when working with these addition and subtraction facts. It can also support students when they begin finding “ten more” and “ten less”.
Use the interactive hundred chart to answer questions: On your hundred chart, mark each starting number in yellow. Then, mark each sum or difference in pink.
- Starting number 3. Add 1.
- Starting number 6. Subtract 1.
- Starting number 8. Add 1.
- Starting number 10. Subtract 1.
- Starting number 25. Add 1.
- Starting number 37. Subtract 1.
Further tasks include marking starting numbers of 22 with operations of adding/subtracting 10, followed by a reflection on how the structure of the hundreds chart supports understanding the number system, noticing patterns, and aiding in addition and subtraction and the counting sequence.
Reasoning Strategy 2 - Doubles
Students tend to learn their doubles facts quickly (0+0 through 9+9). These facts can then serve as anchors for other facts (e.g., knowing 3+3 helps a student add 3+4). Teachers should provide ample “doubling” activities. This can be done with read alouds, story problems, or picture cards.
Watch the video of the book Two of Everything and answer the related questions regarding coin counts and button totals. Reflect and write a “doubling” word problem for the expression 4+4.
Reasoning Strategy 3 - Combinations of 10
In the early grades, students work with ‘both addends unknown’ problems to explore combinations of ten. As students solve these problems by decomposing and composing ten, they begin to commit these facts to memory using a virtual rekenrek.
Use a rekenrek to solve a specific problem and reflect on various components of the activity, including combinations started with, reasoning for tool selection, and understanding the concept of '4 and 6' being the same as '6 and 4'.
Reasoning Strategy 4 - Anchoring 10/Making 10
The making 10 strategy builds from students’ knowledge of combinations of ten and is most useful when one addend is close to 10. Watch a related video and reflect on the addition facts represented in the video and the similarities and differences present.
Create a video demonstrating how to add 9+6 using the making 10 strategy.
Reasoning Strategy 5 - Near Doubles
Students tend to easily remember their double facts. Teachers can help students use what they know about doubles to solve closely related facts. Play the online math game Break Apart and reflect on how it applies students’ knowledge of doubles facts to solve near doubles facts and explain the approach for solving 7+8.
Reasoning Strategy 6 - Properties of Operations
When students understand the properties of operations, they can efficiently and flexibly add and subtract. Focus on making observations rather than memorizing property names.
Watch the provided videos, reflect on your observations and queries, and assist a peer in understanding the commutative property through visual explanations or video demonstrations.
Paper For Above Instructions
The concept of reasoning strategies in mathematics education is pivotal for developing early numeracy skills. As emphasized throughout this assignment, moving from counting strategies to reasoning strategies allows for a deeper understanding of basic arithmetic, especially addition and subtraction. A strong foundation in these areas leads to more effective memorization of basic facts and better problem-solving skills.
Reasoning Strategy 1: One More One Less
The first reasoning strategy, “One More One Less,” employs the hundreds chart effectively for visualization. Through the process of marking starting numbers and their sums or differences, students learn the pattern inherent in our number system. For instance, when adding one, the student moves to the next sequential number, while subtracting one brings them back to the previous number. This foundational understanding significantly enhances their counting skills while establishing relationships between numbers.
Furthermore, adding or subtracting ten allows students to see the larger jumps and understand these relationships visually on the hundreds chart. Patterns emerge, strengthening their ability to manipulate numbers in their head and rely less on memorization alone.
Reasoning Strategy 2: Doubles
The use of doubles, such as the foundational facts of 0+0 to 9+9, establishes strong anchors for students to build upon. Understanding that knowing 3+3 can help solve 3+4 is essential in developing their addition skills. Activities like reading related stories or engaging with visual materials can enhance this learning process. For instance, the book “Two of Everything” reminds students of doubling in various contexts, solidifying their understanding through creative storytelling.
Reasoning Strategy 3: Combinations of 10
Exploring combinations of ten remains a cornerstone of addition strategies. The use of tools like the rekenrek allows students to physically manipulate and visualize numbers. By decomposing ten to find unknown addends, students solidify their comprehension of basic facts. This strategy not only encourages students to play with numbers but also promotes an understanding of the concept that both '4 and 6' and '6 and 4' yield the same total.
Reasoning Strategy 4: Anchoring 10
The anchoring 10 strategy further emphasizes the utility of known facts in addition. By recognizing how numbers relate closely to ten, students can efficiently compute sums like 8 + 6 by transforming it into 10 and adjusting accordingly. Creating videos to illustrate this method promotes both understanding and creativity in the learning process.
Reasoning Strategy 5: Near Doubles
Using the knowledge of doubles to address near doubles is a powerful concept in addition. Games like “Break Apart” facilitate the application of learned facts to new situations. For example, guiding students through solving 7 + 8 by using their knowledge of 7 + 7 strengthens their fluency and confidence. These strategies build a comprehensive toolkit for addition.
Reasoning Strategy 6: Properties of Operations
Lastly, understanding the properties of operations allows students to approach addition and subtraction with a flexible mindset. The commutative property serves as an essential example, enabling students to see the equivalence in addition facts. Engaging in discussions and visual explanations helps students deepen their understanding and overcome misconceptions, ensuring a robust knowledge base for future learning.
Conclusion
By emphasizing reasoning strategies over mere memorization of facts, we equip students with lasting mathematical skills. These strategies promote understanding, encourage exploration, and foster confidence in their ability to manipulate numbers effectively. As educators, we must commit to teaching these reasoning strategies, ensuring our students develop the necessary foundation to succeed in mathematics.
References
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