Introduction | Learners l Standards | Process | Variations | Resources |Evaluation | Conclusion | Credits | Student Page | Home
Introduction | Learners l Standards | Process | Variations | Resources |Evaluation | Conclusion | Credits | Student Page | Home
This lesson was adopted from Life by the Numbers, "Chances of a Lifetime." The purpose of this lesson is to introduce students to probability.
This lesson is designed to give students the opportunity to investigate odds both experimentally and theoretically.
This lesson is designed to be used by high school students . It integrates math and technology and requires that students work in cooperative groups.
This lesson will be completed in four class blocks (approximately 45 min. each). Students should be put in groups of three or four. During the first class block, the teacher will ask students to choose a number from 2 through 12 which they think will come up most often as the sum of two dice when they are rolled repeatedly. The students will record and explain their prediction. The students will then be asked to test their predictions by rolling a pair of dice 250 times and recording the number of times each result occurs. At the end of the first class, each group will hand in their results along with their guess and explanation.
During the next class, the teacher will ask students to complete the student worksheet which is a table that shows every possible roll of the dice. The table has 6 columns, one for each number on the first die, and 6 rows, one for each number on the second die. The students should fill in the table by adding the numbers from each die together. The students will hand in a group paper answering which number comes up most often and to compare the results of the table with the dice-rolling experiment.
On the third day, the students should be asked to create a histogram, using graph paper, to represent the results of their experiment and of the data in their table.
On the final day, students will use their experimental and theoretical data to develop definitions of the following terms with teacher guidance:
- Random experiment
- Outcome
- Event
- Sample Space
- Probability
The teacher can use the examples on the follow-up exercise page for student practice.
Students can test their predictions by using the random number function on a graphing calculator instead of actually rolling the dice 250 times. Calculators make the activity much more efficient if students have access to graphing calculators and proficiency in their use.
This lesson works well in a one teacher classroom if your students are testing predictions by rolling a pair of dice. If the calculator is going to be used, it is often helpful to have another teacher in the classroom to help with calculator gliches.
Each group will receive a grade for each days' work as outlined below:
This lesson is a great introduction to probability for students. It helps students to develop their own definition of "probability" and related terms. The lesson allows students to see the difference between theoretical and experimental results first hand. If the students use the graphing calculator, they can see how integrating technology can facilitate the process.
Life by the Numbers Teaching Guide, "Chances of a Lifetime" p.16 and p.19
Exercises taken from: Precalculus with Trigonometry Functions and Applications, Paul A. Foerster, p237.