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									                                                 Carmen Manoil(100334505, Section 1A), Oct 2/2007

                                     PROBABILITY KIT

Description - The “Probability Kit” is a comprehensive kit that includes:
        a deck of cards
        didactic coins
        color and number spinners
        transparent spinners
        few polyhedral dice (with 4,8,10,12,20 faces)
        six sided cube dice
        activity cards
        teacher’s notes

        The media is full of predictors and students should understand how these numbers are
        determined and how to interpret them
        Probability concepts are pretty abstract and the manipulative included in this kit help
        students visualize these abstract concept
        Probability experiments are an important step in beginning to understand probability
        concepts and predictions
        The latest research have showed that hands-on activities are very important for learning
        The manilupatives are suitable for cooperative learning, individual learning, as well as
        whole class instruction. + They are FUN!!!

In grades 7-8 all students should:
         perform simple probability experiments involving two independent events
         design studies, collect and record data
         select, create, and use appropriate graphical representations of data (histograms, stem-
         and-leaf plots, box plots, and scatterplots)
         find, use, and interpret measures of center and spread, including mean, median, mode;
         distinguish between the experimental probability and the theoretical probability of a
         specific outcome etc.
Many other mathematical concepts such as factor, multiple, prime number, composite number,
divisors, etc. can be incorporated in probability questions and activities.

The kit contains:
1. A deck of cards

Examples of activities:
      P(4)=? – probability to get a 4 (after removing all the face cards and considering ace=1).
      P( heart )=?
      P(any heart and any 4)=?
      Students can be asked to calculate the theoretical probabilities of different events, and
      then to calculate the experimental probability by drawing cards without looking, recording
      the outcomes, and analyzing their results

2. Didactical coins (quarters, dims, nickels, pennies)

Examples of questions and activities:
Consider flipping a coin.
       How many possible outcomes are there?
       Without flipping the coin, P(H)=?, P(T)=?. What kind of probability is this, theoretical or
       Use a quarter. Flip the coin 20 times and record all the outcomes in a frequency table.
       Find out P(H). What kind of probability is this? Why?

3. Number Dice

Examples of questions and activities:
      Introducing tree diagrams (draw a tree diagram that illustrates all the possible/favorable
      outcomes)-for 2 dice
      P (two even numbers)=?
      P (an odd, and an even number)=?
      P (a prime number, a composite number)=?
      P (6, a factor of 4)=?

4. Color spinners

Examples of questions and activities:
Using 2 color spinners
        How many possible outcomes are there?
        Draw a tree diagram.
        Decide on a way to represent your data, spin both spinners 20 times, and record your
        results using tally charts.

5. Number spinners

Examples of questions and activities using a color spinner and a number spinner:
      Draw the tree diagram for the possible outcomes.
      P ( a multiple of 2, and blue )=?
      P (a prime number, and not get yellow)=?

6. Transparent spinners

        A set consisting of 5 spinners, each with a transparent base and a metal arrow.
        The transparent base of the spinner allows the teacher to use them on the overhead
        Students can place the spinners over colorful drawn circular, spinners bases found on
        textbooks, and worksheet to complete probability experiments.
        They can be customized to fit any situation.

7. Polyhedral Dice (with 4,8,10,12,20, faces)

Examples of questions and activities:
         P (a prime number)=?
         P (3, 5 or 7)=?
         P (a factor of 4)=?
Activities for the die with 3 numbers on a face:
         P (the sum of the numbers is a multiple of 2)=?
         P (a number greater than 3 is on the side)=?
         P (the sum of the numbers on the side is a factor of 24)=?

8. Probability Activity Cards

        The probability activity cards have two sides. The “activity side” of the card asks the
        student to conduct an experiment and suggest ways of recording data.
        The “problem side” of the card poses questions concerning the mathematics of an
        Students are expected to use their knowledge of mathematics and probability to
        formulate the answers to the questions

Virtual Probability Kit:

Activity 1 – “Target Mean”
Activity 2 - “Roll And Roll”

see handouts bellow

                                                                        Carmen Manoil, Oct 2/2007

                Target Mean (or Median)
        Ideal for consolidation after teaching measures of central tendency (mean, median)
        Number of players: 2 or more
        The goal of the game is to make 4 numbers (or 5, 6 if enough time is available and the
        students’ competence allows) that, when averaged, equal or are close to a target mean.
   1. The students have to decide on a target number between 11 and 66, for example 35.
   2. Each player gets 2 dice and the table from “handout 1”.
   3. Each time they role the dice, the players will get 2 numbers. One of the two numbers will
       be the tens’ digit, and the other number will be the ones’ digit. The players can decide
       which number will be the tens’ digit, and which one will be the ones’ digit. For example,
       if a player gets a 4 and 5, the player can choose 45 or 54.
   1. Each player records his numbers in the table from “handout 1”.
   4. Players take turn rolling the two dice and deciding on the result number (45 or 54).
   5. After four turns, each of the players has to calculate the mean of the four numbers, and to
       round it to the closest integer. The player whose mean is closest to the target number
       wins one round - 1 point.
   6. The Ss can play 3 rounds and the player who reaches 3 points first is the winner.

For example if Stefan and Dave play together:
    - Let’s say Stefan got a 4 and a 2, and he decided to form the number 24 (not 42, although
       he could).
    - Let’s say Dave got a 3 and a 6, and he decided to form the number 36 (not 63)
    - Let’s say that for the second, third, and forth rolls they got:

Round 1: Stefan
                         Tens    Units   The Mean
First number                2   4            34,5
Second number               1   6        Rounded to the
                                         closest integer is
Third number                6   2        35.
Forth number                3   6

Round 1: Dave
                         Tens    Units   The Mean
First number                3   6
Second number               3   5            34
Third number                4   1
Forth number                2   4

So Stefan won round 1.
   1. Instead of using dice, 2 spinners (number spinners) can be used.
   2. If the teacher wants to make the game more complicated, or if he/she wants to use the
       game to reinforce the concept of “median”, students can be asked to calculate the median
       of the 4 numbers.

                                          Handout 1


Round 1:
                  Tens Units   The Mean
First number
Second number
Third number
Forth number

Round 2:
                  Tens Units   The Mean
First number
Second number
Third number
Forth number

Round 3:
                  Tens Units   The Mean
First number
Second number
Third number
Forth number

                                                                   Carmen Manoil, Oct 2/2007

                                    Roll and Roll

   Work in groups.
   Consider the four sided die and the six sided cub die.
   One die will have sides labelled 123, 124, 134, 234, and one will have sides with the
   numbers 1, 2, 3, 4, 5, 6.

   1. How many outcomes are there? _________________
   2. What is the probability of getting 3 and 134?_________________
   3. P (5, 234) = _______________
   4. P (2, 123) =______________
   5. P (an even number, 234) = _____________
   6. Roll both dice 24 times and record your findings as tally charts, in the table given
   7. Use your data to calculate the experimental probability of each outcome.
   8. Compare the theoretical probability of each outcome from steps 2,3, and 4 with
      the experimental probability calculated at step 7. What do you notice? Why is

Group: ___________________________________________________

                        123               124                234                 134







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