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Please see attached DQ questions 200 words each. Attachments for supplemental information is also provided.
1,1- In your own words, describe the four-step problem-solving process. Explain why each step is important. Create a simple problem that could be used in a classroom and demonstrate how you would use each of the four steps to solve this problem. How would you teach this process in the classroom?
1,2- Identify at least five different problem-solving strategies. Discuss when and how you would use each of these strategies to solve a problem. Create a problem, then select an appropriate strategy and describe how you would teach a student to use this strategy to solve the problem.
2,1- In your own words, explain the concept of a numeration system. Describe some of the properties that give meaning to a numeration system. How would you teach the importance of numeration systems to a class?
2,2- Explain, in your own words, how the concepts of equivalent sets, one-to-one correspondence, equal sets, and subsets have applications in everyday life. Why is it important for students to have a basic understanding of these fundamental concepts?
3,1- Discuss various methods you might use to teach the commutative property and the associative property of addition. Explain how these properties are used in everyday life and why they are important to understand.
3,2- Discuss the divisibility rules for the numbers 2 through 10. What is the value of knowing and understanding these rules? Give an example of how you would use these rules.
4,1- Discuss various models for integer multiplication and division. What are the advantages and disadvantages of each method? Which method would you use to teach this topic?
4,2- What are equivalent fractions? Explain how two fractions can be equivalent. Give practical examples of fractions that are equivalent. How would you teach this concept to a class?
5,1- Explain how the base 10 number system works. How would you teach the notion of place value to a class? How are decimal numbers related to rational numbers? When is a decimal number also a rational number?
5,2- Explain the process of decimal multiplication and division. Explain the mathematical justification for moving the decimal point when performing decimal division.
6, 1- In your own words, explain the concept of a variable. Discuss how you can teach a class about the use of variables and how they can be used to create an algebraic expression.
6, 2- How would you teach students to translate English statements into algebraic expressions? Discuss some of the common words and phrases used to represent mathematical operations.
7,1- Out of the concepts you have studied in this course, choose one that you feel would be particularly difficult for students to understand. Provide a concrete real-world situation or example to help illustrate this concept.
7,2- It is necessary to have a good understanding of mathematics in order to teach it. Who do you think would make a better math teacher: a person who has natural mathematical talent and understands concepts easily without making mistakes, or a person who had to struggle to gain their understanding of math and learn to avoid making mistakes?
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