Dinner Party___

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					Dinner Party!!!




           By Becky Rose
      7th Grade Math Teacher
  Western Peaks Elementary School
   Dysart Unified School District
       Materials Needed:
• 2 color counters (10 for each small
  group)
• 1 dry erase marker for each group
• pencil to record answers
• paper to write out questions
            Directions:
• Put your class into groups of 2-3
  students each.
• Distribute materials to each group.
• Have students label the 2 color
  counters using the dry erase marker.
  Labels should be as follows:
     yellow – seats A-E
     red – 5 different guests names
              (student selected)
      Dinner Party Dilemma…
   Imagine that you have five dinner
guests coming over for a dinner
party. While you are thinking about
seating arrangements, you realize
that there are many different ways
you could seat your guests. But is
there a way to figure out exactly how
many arrangements are possible?
Remember, people are “available”
until they are assigned a seat.
       What to do…
• Use the labeled color counters and
  follow the directions for each step.
• Record your results after each
  question.
• Remember, people are “available”
  until they are assigned a seat.
• Once a person has been assigned a
  seat, they can no longer be
  “available” for any other seat around
  the table.
Pick a person to sit in seats A, B, C, D, and E one at a time
and in order. Answer the following questions one at a time as
you fill in the number and name you have picked for each seat.

1.   How many people are available      to sit in seat A?
     ___________________
2.   How many people are available      to sit in seat B?
     ___________________
3.   How many people are available      to sit in seat C?
     ___________________
4.   How many people are available      to sit in seat D?
     ___________________
5.   How many people are available      to sit in seat E?
     ___________________
   Write the mathematical
        expression…
In questions 1-5 you counted the
  number of persons available to fill
  each seat.
How could you figure out the total
  number of ways there are to fill all of
  the seats?
Write this out as a mathematical
  expression.
       Extension Activity
• Using the mathematical expression
  you wrote, answer the following:
     How many ways is it possible to
     arrange 5 people in 5 seats?
         6 people in 6 seats?
         7 people in 7 seats?
            Key Terms
• Permutations: a category of
  probability in which a series of things
  can be put in order
• Factorial: the product of all positive
  integers less than or equal to a given
  positive integer
• Probability: the likelihood of an
  event to occur; the odds of
  something happening
                Solutions:
• 1: 5
• 2: 4
• 3: 3
• 4: 2
• 5: 1
• Expression:    5 * 4 * 3 * 2 * 1 or 5!
     This could also be written out as follows:
           n * (n-1) * (n-2) * (n-3) * 1
     when n = total number of options available
• Extension:     5!    =      120
                 6!    =      720
                 7!    =      5040

				
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posted:8/9/2012
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