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?

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.

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.

In your own words, explain the division algorithm. Pick two examples that you would use in class to explain this algorithm. Why did you pick those examples?

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?

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.

How would you teach the concept of multiplication of fractions? If a student doesn’t understand it this way, what alternate method can you use?

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?

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?

Explain the process of decimal multiplication and division. Explain the mathematical justification for moving the decimal point when performing decimal division.

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.

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.

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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