Online Cereal Toy Investigation Simulator

This applet, designed by Erin Mulder, allows students to conduct multiple simulations and collect data on a larger sample.   Students may run 20-30 trials more quickly than the dice toss.   The applet is probably best used following the class data collection simulation with 6-sided dice. 

In this simulation, students will need to collect data on the total number of boxes bought to get all 6 toys so they must decide how best to record that data.   The class must also decide on a method of recording the class data (e.g. adding to the class line plot using a different color marker would facilitate comparison of the results).   Discussion should center around how well the small class sampling results matched the larger computer-generated results. 

Directions for Cereal Applet:

• Once the Applet is loaded, click on "Next Box" to buy a box of cereal.
• A box of Cheerios and a toy will be added to the screen.
• Click "Next Box" again to buy another box of cereal and get a free toy.
• Keep clicking "Next Box" until you get all six toys.
• The applet will stop at this point and tell you how many boxes you had to buy to get all six toys.
• Students can then see how many of each toy they got.
• When students have recorded this information for the trial, they click on "Reset" to begin a new trial.
• Students should add these computer simulations to the class data for discussion. 

Run the online Cereal Toy Investigation Simulator.  [Java applet requires Java-enabled browser.]

Data Collection: Tossing Two Dice

Students LOVE working with dice, almost forgetting that they're doing math.  While standard probability lessons ask students to calculate the probability of tossing an even number, a sum of 10, etc., students are more highly motivated when they generate their own experimental data.

The Mathwire collection contains many examples of both one-die toss activities and two-dice toss activities.  These data investigations begin with a game but make data collection an integral part of the activity, so that students begin to examine the underlying probability of the game and can use appropriate strategies in future play.

Students will generate their own small set of data, which should be combined with the whole class data for a larger set.  Teachers may ask questions to help students draw conclusions and make generalizations about the probability of dice tosses.

After this initial hands-on data collection and analysis, extend the activity by asking students to use online dice simulators to generate even more data to test their hypotheses and generalizations.  This option allows students to quickly generate large sets of random data.  It is helpful to pair students for this activity:  one student at the computer keyboard and the other student recording the results of each simulated dice toss.  Again, ask students to post their results to a class data collection display (e.g. tally chart, graph, etc.) so that the class is able to analyze the larger sample.

Check out these online dice-toss simulators:

• Coins & Dice:  A Probability Simulator records the results of each dice toss, making it easy for students to record the result of each dice toss
• Dice Roll displays the results in a bar graph so that students visually see the results of extended dice tosses

This data collection and data anaylsis approach provides students with hands-on data collection activities that generate real-life data for analysis.  Students then take advantage of technology to simulate the activity, quickly collecting larger sets of random data.  It's the best of both worlds!