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Sixth Grade Math January 30 , 2012

Sixth Grade Math January 30 , 2012. Sixth Grade Math January 30 , 2012. EQ: How do I use probability?. Warm-Up #9.

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Sixth Grade Math January 30 , 2012

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  1. Sixth Grade MathJanuary 30, 2012

  2. Sixth Grade MathJanuary 30, 2012 EQ: How do I use probability? Warm-Up #9 Twenty people are seated around a circular table. Each person is either a knight, who always tells the truth, or a knave, who always lies. If each person at the table says, “The person on my right is a knave," how many knaves are seated around the table? Answer

  3. Sixth Grade MathJanuary 30, 2012 Lesson Plans • If you were gone on Friday, do the lesson plans. If you were here on Friday, you may play Yahtzee, but everyone make sure your worksheet is done by tomorrow. • Take notes on permutations (next slides). • For homework, work on the back side of your worksheet from yesterday. • Also for homework, go to Khan Academy and practice probability. • Also, watch the video on permutations. It is under precalculus, you smart kids!

  4. Sixth Grade MathJanuary 30, 2012 Lesson Plans • If you were gone on Friday, do the lesson plans. If you were here on Friday, you may play Yahtzee, but everyone make sure your worksheet is done by tomorrow. Yahtzee sheets are here. • Tomorrow you will all take notes on combinations and have homework that will be practice of everything we have learned in probability so far. • On Wednesday you will have a quiz on permutations and combinations. • I will come by school tomorrow to bring you graded papers that I have. If something is missing, I will e-mail your parents.

  5. Sixth Grade MathJanuary 30, 2012 Notes on Permutations (copy only what is in purple) • A permutation is the total number of arrangements of objects or numbers. • For example, the total number of arrangements of books on a shelf are , or 24. • This is written in mathematics as 4!, read as “four factorial.” • You can also use a tree diagram to find a permutation of 4 books on a shelf, but using the factorial is much easier. • This permutation can also be written as 4P4, or the permutation of four items taken four at a time.

  6. Sixth Grade MathJanuary 30, 2012 Notes on Permutations • An example of a permutation problem would be “How many different ways could I ask you to line up for pictures?” • Since there are 25 students in this class, the answer would be 25!, or 1.5 x 1025, a very big number! • Another problem would be “How many ways could I choose four of you to win first, second, third, and fourth place for a math award?” • This is written as 25P4, or the permutations of 25 students taken four at a time. • The math looks like this: 25 x 24 x 23 x 22, because we have a choice of 25 students for first place, then 24 students for second, and so on. • Mathematically, we would figure it out like this: 25P4 = 25! = 303,600. Write it out and see how the factors (25-4)! cancel.

  7. Sixth Grade MathJanuary 30, 2012 25 25 25+10 10 10 Notes on Permutations • The big idea: nPr = n items taken r at a time = • Isn’t math fun? And yes, Ben, this is on your calculator, but do it by hand first!! • So what does this have to do with probability? A lot in computer programming, sets, insurance . . . • An example would be “What is the probability that my license plate is BEB-123 given that O’s cannot be used as a letter, and digits cannot be used twice? 25 x 25 x 25 x 10 x 9 x 8 = 11,250,000! Solution

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