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Possible Outcomes

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					                                  Possible Outcomes
Materials:
 Flip chart paper
 Pens
 Grids
 Die faces
 Dice
 Bag with blue marbles only
Objectives:
D-1 acquire data through a) surveys, questionnaires
D-21 list the possible outcomes of an event occurring in an experiment
D-22 identify favorable outcomes among the possible outcomes
D-23 use a fraction to describe the probability of an event happening
D-29 calculate the probability of a single event using concrete materials
D-30 list the possible outcomes and favorable outcomes for a random experiment
involving compound events
D-31 calculate the probability of a compound event happening
Description:
1. Using a tally chart, investigate how students in the class get to school (adapt the chart
   according to the class data – perhaps car, SUB, truck might be relevant)
 Transport
                    Car           Truck            Van             SUV        Other
   Mode
Frequency
 While creating and completing the chart, use the appropriate language from
   probability. For example: Let’s talk about the event of your coming to school. What
   are some of the ways, or outcomes, of how you might get to school? What is the
   entire list of possible outcomes for this particular event?
 Once the chart has been completed, have the students create questions that they could
   ask about the data that they have collected. Some examples of questions might be
   “What is the most common way for getting to school in our class?” “If we had a new
   student or visitor enter our classroom, how do you think they would have come to
   school? Why?” Gradually, have the students consider the chance of getting to school
   in a certain way. Have the students verbalize how they are determining this
   probability. This should be done to lead to a formula definition for the experimental
   probability of an event happening being created by the students. It may take a few
   tries, and even more discussion before they can reach a definition that captures the
   difference between these experimental trials and the theoretical outcomes
   Experimental: P(A) = number of trials that gave a favorable result
                                    total number of trials conducted
   Theoretical: P(A) = number of possible favorable outcomes
                            total number of all possible outcomes
 The students can also be asked to consider whether a theoretical probability is
   possible in this scenario.
2. Provide each pair of students with a grid, and two dice (of different colours). Begin
   by having them roll the two dice and then record them on the grid in the appropriate
     location (they will need to designate horizontal and vertical each to a particular roll
     colour). After the first 6 rolls, have the students complete the grid and to record the
     total possible number of outcomes. Next, have the students answer a few questions
     such as: How many different ways are there to roll a total of 5? What are the chances
     of rolling a sum of 5? What are the chances of rolling at least one 5? Give them a
     few minutes to create their own questions appropriate for their particular grade
     level(s) and share.
3.   Ask the students to state the possible outcomes of tossing a single coin, then of
     tossing two coins. Ask the students to come up with different ways of representing
     the all possible outcomes (for example a tree or a list). Have the students generate
     questions that could be asked about the information found in the possible outcomes
     and have them answer the questions. Some questions that they might not bring up
     are: How many different events involve exactly 2 heads? How many different events
     involve at least 1 head? How are you defining different? Would your answers
     change if you used two different coins?
4.   This activity should be done with the group as a whole, selecting individual people to
     make draws or give the answers.
    Start with a bag that you put two marbles in. Have someone draw one marble that
     they keep in a closed hand. Ask the students what the probability is that the particular
     marble drawn is blue. Ask the students if it is possible to have a probability greater
     then that. On an overhead sheet, draw a line and mark 1 (100%, 1/1) at the far right.
     Ask the students to give another example where the probability of an event is 1.
    Return the blue marble to the bag, have another student draw a marble that they keep
     in the closed hand. Ask the students what the probability is that the marble drawn is
     red. Ask the students if it is possible to have a probability less than 0. Mark the 0 at
     the other end of the number line and discuss the importance of students understanding
     that probability is a descriptive number between 0 and 1 (or 0% and 100%). Students
     need a variety of experiences where they experience and work with these values for
     probabilities as well as others. Ask the students to give another example where the
     probability of an event is 0. Also ask the students if there are any probability
     questions that could be asked about drawing from a bag with two blue marbles that
     would not have an answer of either 0 or 1? What could they do with the situation to
     allow for other possible answers?
5.   Have the students write out the possible outcomes for each of the following
     situations, then create or use manipulatives and questions for a partner to solve.
     a) Two containers each contain one each of a red, green and yellow marble. If one
         marble is drawn from each container, what are the possible outcomes?
     b) A drawer contains 9 pairs of socks – three black, three white and three pink. The
         socks have been put in the drawer as single socks. If two socks are being drawn
         out of the drawer, what are the possible outcomes for the draw?
     c) A local restaurant has a take out meal deal. The deal is that for $6.99 you can get
         a lasagna or 3 slices of pizza, a salad (tossed, Greek, or Caesar), and a drink
         (coffee or pop). What are all the possible outcomes for this deal?
     d) Discuss the use of probability in chance events in the news and everyday life –
         what are the possible outcomes for the event? For example: the Boston Bruins
      are favoured to win the Stanley cup; Regina has a 75% POP (what happens if you
      hear this while it is raining); 5 chances to win $1 000 000.
6. Conclude by having the students generate a set of definitions (with or without
   examples) for the terms: possible outcomes, events.
Adaptations:
   Different manipulatives or numbers of manipulatives could be used in many of these
    problems – three coins, double-sided counters, spinners,… In the third task set, students
    could be asked how their answers would differ if they had tossed three rather then two coins
    but were looking for the same trial to occur (1 head or 2 heads).

                                         Rolling Dice



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