Probability is best learned through lots of discussion, game playing and experimenting -- an approach that fosters both enjoyment and success. Unlike many other math topics, performance in probability is enhanced by creativity and personal connections. Basic probability concepts are typically taught in elementary grades.

### Probability in Words

Young students often have difficulty with the basic vocabulary of probability. Words such as "possible," "impossible," "likely" and "certain" are routinely used colloquially, yet incorrectly. Students will understand these concepts best by making connections to real events, such as whether snow is unlikely tomorrow, if a school holiday is possible next week, or if a new baby is sure to be a boy or girl. New learners should explore the idea that some probabilities can depend on circumstance. For example, tornadoes are more likely in certain areas and seasons.

### Probability in Numbers

Next, students begin to use the number zero to refer to impossible events and the number one to represent events that are certain to occur. Events with two equally likely outcomes, such as a coin toss, have a probability of one-half, or 50 percent. For events that are possible or very likely, beginners should learn to use phrases like "less than half" or "almost one." This new use of numbers can be reinforced with matching games, number lines and plenty of partner work and discussion. Students can also create their own games of chance, and for a challenge, they can make their game favor one player over another.

### Predict Probabilities

Once students understand how to describe probabilities using words and numbers, they can begin to make predictions. Before rolling a number cube, they may be able to determine that the chance of rolling any preselected number is one-sixth, the chance of rolling an odd number is one-half, and the chance of rolling a seven is 0. A more basic task is to compare probabilities. Students may enjoy matching events that are equally likely as part of a game. In order to accurately predict, students must be able to identify all possible outcomes for a given event.

### Describe Experimental Probabilities

Beginning students often have difficulty with the idea that an experiment can provide a different result than a correct prediction. For example, a coin toss has a theoretical probability of one-half every time. Yet if tasked to flip a coin 10 times, some students will flip 10 heads in a row. Through experimenting and combining their results with others, students will recognize that larger amounts of data usually trend closer to the prediction.

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