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SECTION 1 - INTEGERS Integers 2. Suppose there are 100 lockers. Which lockers are changed exactly twice? Explain your DAILY ACTIVITY: FLUENCY reasoning. 1. Let b = all multiples of 3. Is 8b a multiple of 6? Justify. 2. Let p = all multiples of 3 and q = all multiples of 4. Is pq - 20 a multiple of 2? Why? 3. David noticed that or 7x7 (1.e. a product of a prime number with itself), and there are exactly three factors of 49 namely 1, 7, and. What other numbers between 1 and 100 have exactly three factors? Explain. Activity 1-A-2 4. Alana noticed that a number like 8 = (i.e. ) has exactly four factors: 1, 2, , and . What other numbers of this form have exactly four factors? Do all the perfect cubes have exactly four Extensions to the Locker Problem factors? Is it true that all numbers that have exactly four factors are perfect cubes? Explain. 1. Suppose there are 200 lockers and 200 students. Kayla reasons that since there are 10 lockers opened in the first 100 lockers (i.e. between 1 and 100) there must be 10 lockers opened in the next 100 (i.e. between 101 and 200). Is Kayla's reasoning correct? Explain why or why not