Making predictions is an important step in all data collection activities. After a brief explanation of the problem or experiment, students are asked to think about what they expect the results to be and make a prediction. The teacher leads a discussion of the predictions and the reasoning behind them, often posting these on chart paper for future reference during the data analysis phase.
I recently read a study on this very subject. It found that having students make predictions about new math situations or problems did indeed foster deeper mathematical thinking and understanding in students. Additionally, this practice also increased student engagement in the task, as they were invested in the results.
One data collection activity I have used with students from kindergarten through middle school, is the Cheerios Investigation. Students are told about an advertising campaign in which Cheerios randomly includes one of six toys in each box of Cheerios. They hope that this will prompt families to buy more boxes of Cheerios trying to get all six toys. Students are asked to think about this and predict how many boxes of Cheerios the average family would need to buy to get all six toys.
The teacher then leads a discussion about the predictions, including the reasoning behind them. In my experience, there's always the eternal optimist (or naive person) who says six. Then there's the off-the-cuff response of 100 or some other large number. The most popular response is 36, although I've yet to hear an adequate mathematical reason for that number. Nonetheless, the teacher accepts all predictions and reasoning, posting them on a chart for later reference.
Students then conduct the simulation, using a die and tallying the results until they have indeed gotten each of the six toys (each toy represented by a number 1-6 on the die). They post their results on the class line plot, then repeat the experiment as time allows.
The class line plot is the basis for the data analysis. Students may compare their small sample to the larger class sample. Discussion may include mean, median, mode, range, outliers, etc., as appropriate for the class level. Finally, students are asked to write an analysis of the data, this time in a letter to Mr. (or Mrs.) Oats, explaining why the plan to include toys will increase the number of boxes of Cheerios families will buy.
It's a simple activity but it leads to rich mathematical discussion and students are actively involved and engaged in the results from beginning to end. Additionally, if several classes in the school conduct this experiment, classes can share results to generate an even larger sample.
See Mathwire's Cereal Toy Investigation to view a lesson plan and download handouts.
Mathwire also offers the Cereal Toy Investigation applet, designed to allow students to quickly generate larger samples, extending the die-toss experience. Students simply click the Next Box button to buy another cereal box. The applet is designed to stop when the student has accumulated all six toys so that students may record this number before running another trial. [Note: This app requires Java.]