VIEWS: 31 PAGES: 3 POSTED ON: 4/30/2010 Public Domain
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 1 2 3 4 5 6 1 2 3 4 5 6