This unit introduces students to the concept of probability by using a 6-sided dice.  (The lesson could be enhanced by also using a 10, 12, or 20-sided dice.)  The students will predict what the probability of rolling a number and then graph the number of rolls in Microsoft Excel to see that after many rolls the probability of rolling 2 is the same as rolling a 6.

• Mathematics Outcomes:
  • Listing all possible outcomes of a simple event. 
  • Using the term .sample space. to denote all possible outcomes eg for tossing a fair die, the sample space is 1, 2, 3, 4, 5, 6 .
  • Assigning probabilities to simple events by reasoning about equally likely outcomes eg the probability of a 5 resulting from the throw of a fair die is 1:6.
  • Recognising that the sum of the probabilities of all possible outcomes of a simple event is 1.
  • Uses spreadsheets to represent odds and probabilities.

• Microsoft® Excel 2003

1. Introduce the activity by explaining that probability is a mathematical description of the chances a certain event will occur.  Show the class a dye.  Explain that there are 6 sides to the dye and that the chances of rolling one number aren’t any different than rolling  another number.  Have the class come up with the probability of rolling a 6.  Ask them what the probability of rolling a 1 is.

2. Download and the Microsoft® Excel file 'Probability' and save to the school server for students to access:

Probability

3. Pair the students off and give them each a dye. Students open the 'Probability' Excel file.  At this point the students should see an Excel spreadsheet with a row of numbers from 1s to 6s.  These columns will represent the number of time the students rolled a certain number.  Have one student roll the dye and another tally the numbers.  For instance, the first round of rolling may come up with two 4s, three 1s, and one 6.  The student tallying the rolls will put 2 in cell E3, 3 in cell B3, and a 1 in cell G3.  The students can then switch tasks.  There will be 4 rounds in total.

    

4. Once the students are done they are now able to analyze the data.  The students will begin by graphing each of the rounds and then move on to graphing the sum of the rounds by using the Chart Wizard.

5. View the results and explain to the students that in order to show the probability of rolling a certain number many events have to be recorded. Ask the students what they think a graph of the entire classes data would look like.  Would it be more uniform than any one team’s graph?  If so, why?   

1. Is there such a thing as luck? In this activity you will examine the theory of probability. Choose a partner to work with, grab a dye from your teacher and open the Microsoft® Excel document called 'Probability'.

2. Your task is to roll the and record the results. You have six throws per round with four rounds in total so take turns of being both the roller and the recorder. Tally your results for each round in your Excel spreadsheet.

3. Let's turn your numerical data into a graph:

Creating a Graph in Microsoft® Excel 2003

1. Highlight the cells B3 to G3.

2. Click the Chart Wizard button on the menu bar.

3. Select a Column graph to suit and click Next.

4. We don't need to make any changes to the data range or series information, so click Next.

5. Provide a title for your graph and name the axis. Click Next.

6. Select Place chart: As new sheet and click Finish. Your graph will now be imported as a new sheet in your Excel workbook: 

 

4. Continue creating graphs for each round. Are the graphs uniform in shape or not?  Do they represent the prediction that the probability for rolling a 6 is the same as that for rolling a 1?

5. Now graph the sum row cells B11 and G11. 

6. Is this a better graph then the previous 4 at showing the probability?  Is there a more uniform shape to the graph?

7. What do you think a graph of the entire classes data would look like?  Would it be more uniform than any one team’s graph?  If so, why? In order to show the probability of rolling a certain number many events have to be recorded. Why do you think this is?

Explain to the students that it is possible to calculate the probability by taking the number of times a certain number was rolled and divide this by the total rolls.  Do this in Microsoft® Excel with the data that students have recorded.  Show that the more data one has to work with the better the outcome.  Ask the students to create there own study using a deck of cards.

Assessment Tracking Sheet