Lesson+C

You will have 5 days to complete this assignment. Please refer to the rubric attached for grading.


 * Your team must make a wiki page.


 * Your team's final presentation has to be in a PowerPoint.

Part I: "Hi Mike! Let me tell you about the Fundamental Theorem of Arithmetic!"

The fundamental theorem of arithmetic states that every natural number greater than one is either prime or can be written as a unique product of prime factors. What does this mean? Refer to the work you did in previous problems to help you explain the fundamental theorem of arithmetic to your friend, Mile, who has been absent. Be sure to include the following terms: factor, multiple, divisible, prime, composite, prime factorization and exponents.

Part II: Secret Number

Juanita has a secret number. Read her clues and then answer the questions that follow: Juanita says, "Clue 1" My secret number is a factor of 60." 1. Can you tell what Juanita‟s secret number is? Explain your reasoning. 2. Daren said that Juanita‟s number must also be a factor of 120. Do you agree or disagree with Daren? Explain your reasoning. 3. Malcolm says that Juanita‟s number must also be a factor of 15. Do you agree or disagree with Malcolm? Explain your reasoning. 4. What is the smallest Juanita‟s number could be? Explain. 5. What is the largest Juanita‟s number could be. Explain. 6. Suppose for Juanita‟s second clue she says, " Clue 2: My number is prime." 7. Can the class guess her number and be certain? Explain your answer. 8. Suppose for Juanita‟s third clue she says, "Clue 3: 15 is a multiple of my secret number." 9. Now can you tell what her number is? Explain your reasoning. 10. Your secret number is 36. Write a series of interesting clues using factors, multiples, and other number properties needed for somebody else to identify your number.

Part III: Slammin‟ Lockers

Georgia Middle School has 100 students with lockers numbered 1 through 100. One day, Sally walks down the hall and opens all the lockers. Eric goes behind her and closes all the lockers with an even number. Then, Jane changes the situation of the lockers with numbers that are multiples of 3. This means that a closed locker is opened and an open locker is closed. If this pattern continues FOR ALL 100 STUDENTS, which lockers will remain open after the 100th student walks down the hall? Explain your thinking giving details, and using both appropriate mathematical models and language. What if there were 500 students and 500 lockers? What if there were 1000 students and 1000 lockers? Can you find a rule for any number of students and lockers? Explain why your rule works.