Probability:   Study of  Chance

Designed by: Tammy B. Hester  

Grade Level:  7th      Subject:  Math

1) Core Curriculum Objective:  Predict simple possible future outcomes,  and determine the number of possible combinations or permentations of a set of objects.    (7SP2-2)   [III.D]   [VI.A.1]

Restatement:  Predict outcomes , and determine if a game is fair and the number of possible outcomes.

2) Overview:   The students will conduct experiments to determine if a game is fair.  Students will discuss how the data can be displayed and interpreted using range, mode and median.

3) Focus Question: Can math be used to determine the outcome of a game?

4) Time Frame:   2 fifty minute class periods

5) Resources:  

Glencoe course 2  pages 492-495

Spinners divided in half

Spinners divided in thirds

Markers

Overhead grid

Graph paper

6) Assessment:  

Day One

Activity One

Describe a situation where you buy one raffle ticket and 100 were sold to win a new bike. Ask students what would be their probability of winning.  Make sure students understand the meaning of probability. 

Probability -  The ratio of the number of ways an event can occur to the number of possible outcomes; how likely it is that an event will occur.

Students will work with a partner of their choice.  Students will use the spinners divided in half.  One student will spin twice --Player one scores 1 point if the spinner lands on the same side twice.  Player two scores 1 point if the spinner lands on different sides.

Students should play 50 rounds tallying the scores as they go.  The winner is the player with the most points.  Students should play 3 or 4 times -- 50 rounds each.

*** Depending on time you may choose less rounds per game, but each game must be the same number of rounds.

( Give each group tally sheets for each game.  See attachment I.)  Give an example of how to make tally marks on the board or overhead.

Activity Two

After completing the games in activity one, ask the students if they thought the games were fair.   Students should explain what they think would make a game fair.

Make sure students come to the understanding that if each player has a fifty-fifty chance then the game is fair.  In some games, even though players have equal skill there may be other factors that would cause players not to have an equal chance of winning.  This is when a game becomes unfair.

Follow the same rules as Activity one, except use a spinner divided into thirds.  Based on the data you record on your tally sheets determine if each activity is fair.

The teacher should circulate and monitor groups to check for understanding during all activities.

Day Two

Activity One

Introduce activity with a demonstration of game:  paper, rock, scissors

Ask if anyone knows how to play.  Pick a volunteer to play with the teacher to model the game for any one that does not know how to play.

Review the rules:

Paper covers rock   --- paper wins

Rock crushes scissors --- rock wins

Scissors cut paper --- scissors win

You may want to write these rules on the board while the students are playing.

Divide the class into pairs (player A and player B)  and have them play the game 18 times.

Use overhead graph grid to graph the wins of player A in red ( how many A players won one game, two games, etc.)  do the same for all B players in a different color.

Help students determine range, mode and mean for each set of data.  Compare the results.

Range --The difference between the greatest number and the least number in a set of data.

Mode --The number or item that appears most often in a set of data.

Mean--The arithmetic average; the sum of the numbers in a set of data divided by the number of pieces of data.

Answer the following questions to determine if the game is fair.

a. How many outcomes does the game have?

b. Label each possible outcome as to win for A, B, or tie.

c. Count wins for A

d. Find probability A will win in any round ( 3/9 = 1/3 ) Explain what probability means.

e. Count wins for B.

f. Find probability B will win in any round.

g. Is game fair?  Do both players have an equal probability of winning in any round?

Compare the mathematical model with what happened when the students played the game.

The teacher should circulate at all times to monitor groups to check for understanding.

This is a good activity to use as an introduction to probability.

Follow up with how probability is used in the world.

For articles or other media pertaining to this topic, look up the following in Encarta Encyclopedia:    Probability

Attachment I