Critical Thinking Math, Math, Math! I will actually let you work together on this one. I will give you Five minutes. A good combination of math.

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Presentation transcript:

Critical Thinking Math, Math, Math! I will actually let you work together on this one. I will give you Five minutes. A good combination of math and logic will help you get this within six minutes. All of you could do it if given enough time. All the Talking you want. Work with a partner, a group, or the whole class.

The Problem Suppose you're in a hallway lined with 100 closed lockers. You begin by opening every locker. Then you close every second locker. Then you go to every third locker and open it (if it's closed) or close it (if it's open). Let's call this action toggling a locker. Continue toggling every nth locker on pass number n. After 100 passes, where you toggle only locker #100, how many lockers are open?

The Solution Answer: 10 lockers are left open: Lockers #1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Each of these numbers are perfect squares. This problem is based on the factors of the locker number. Each locker is toggled by each factor; for example, locker #40 is toggled on pass number 1, 2, 4, 5, 8, 10, 20, and 40. That's eight toggles: open-closed-open-closed- open-closed-open-closed. The only way a locker could be left open is if it is toggled an odd number of times. The only numbers with an odd number of factors are the perfect squares. Thus, the perfect squares are left open. For example, locker #25 is toggled on pass number 1, 5, and 25 (three toggles): open-closed-open.

Goals for the Day I can improve my understanding of AP Multiple Choice Questions.

Vocabulary Quiz #27 Open Socrative and log in with: Bauer2016 When you finish come up and get a copy of the AP MC exam and your scantron sheet (perhaps the first one done could help pass out the scantrons – thanks!)

Practice AP Exam – Multiple Choice Meet with a partner or small group of 3 – NO MORE THAN 3! Get a copy of the MC test booklet and your scantron sheet. Determine the correct answer for EVERY question that you or your partner(s) missed. Then write an explanation of why the correct answer is correct OR why all other answers are incorrect. Aim to work with your group only. The only exception to this is if your group is absolutely stumped on a question. Have someone explain it to you – this is an absolute last resort! If you get completely finished, turn in your answers and the exam. If you don’t turn in everything at the end of the period – try to get done! There are 5 Albert assignments up on Google Classroom – your homework is to complete at least three by Thursday, but you may do the last two for extra credit. Your growth on the MC portion was outstanding!! Keep working to get better – I’m very proud of you!