1. Provide two examples of each rounding and truncation (four total examples) to illustrate mental math skills.

B. Primes and Composites: There are 20 boys and 24 girls in an Algebra I class. The class is so large that the teacher wants to divide the students by gender into cooperative groups composed of the same number of students.

1. Explain the process the teacher will use to determine how many students will be in each group using appropriate mathematical terms from number theory.

2. Determine the largest number of students that can be placed in a group, showing all work.

3. Given your answer in B2, determine how many groups will be created from the Algebra I class, providing support (i.e., showing all work or, if you use mental math, explaining your answer).

4. Explain how to prove that there is an infinite number of primes.

C. Modular Operations: You want to explain the concept of modular operations to a middle school mathematics classroom, starting with a demonstration from clock arithmetic. Your explanation should include the following support:

• Appropriate examples for modular addition using positive integers

• Appropriate examples for modular addition using negative integers

• Appropriate examples for modular multiplication using positive integers

• Appropriate examples for modular multiplication using negative integers

• A sentence or two about the use of modular operations in real-world scenarios

1. Explain how you would discuss the following (suggested length of 1–2 pages) in the classroom setting:

a. Modular arithmetic and its relation to time

b. What is meant by 10 mod 6

c. How to add or multiply in mod 7

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