Overview

Investigate the odds of rolling a certain number on a six - sided die.

Background Information

Probability can be determined in one of two ways: theoretical and experimental.

Concepts

1. A six sided die has a one in six probability for each (A die has six sides).
2. A fair die has equal probability for each side (Each number appears only once).
3. (Generalization) The probability of an outcome is the number of specific outcomes out of the total number of all possible outcomes of one event.
4. Theoretical probability is determined with reasoning.
5. Experimental probability is determined by repeating a certain event a number of times and collecting numerous results to determine the probability.

Misconceptions

I can cause a certain number to be rolled (blowing, throw hard, throw a certain way, wishing for it...). It is magic.

Generative Assessment

1. Have students predict the probability for a die with a different amount of sides than six.
2. Use a spinner with equal partitions and predict the probability for each section to be selected.
3. Create problems with equal numbers of socks of different colors in a drawer.

Bloom’s Taxonomy If students have never experienced the concept and derive the concept on their own it would be application or possibly synthesis. If they have conceptualized the concept before it is comprehension.

Objective

Students predict what will happen if they roll one die 36 times, record predictions, roll one die 36 times, record data, organize data onto a graph, analyze the data, and explain the pattern they found and predict what would happen with different sided die.

Materials

Die, pencil, paper

Beginning

Ask the students to predict what the outcome would be if they rolled a die 36 times. Ask them how they made their prediction. Record all answers on the board. Ask them what makes them believe they are right. Have the students roll the die and collect the data.

Middle

Ask students how to display date. If students do not know how to arrange data have them chart the number of rolls for each roll 1 - 6 (1 - 6 horizontal axis, # rolls verticle axis). Students put their data on the board. Analyze the data. Possible questions:

1. What number turned up most?
2. What number would you predict would turn up most if you did it again?
3. What are the odds of a certain number turning up?
4. What did you discover from the data?

Have students communicate the concept in several ways.