Immediately after introducing the basics of probability, you can teach students real-life applications of probability. Connecting the mathematics of probability to a student's life will help the student internalize the meaning and value of probability. An easy example of applied probability is giving students options with probabilities attached and asking them to make a choice. Specifically, tell students that if they take the bus to school, the probability of being late is five percent whereas taking a car to school yields a 10 percent probability of being late. Explain to them that they need to take a test in the morning, and ask them which method of transportation is the better option.
Card games are another way to introduce students to probability calculations via division. Any card game with a set of poker cards works; Crazy Eights is an example. Tell the students to play with their hands shown. Before turning over a new card, have students calculate the probability of turning over they card they want. For example, if a student wants an eight and he sees that two other players have eights, he would know there are two eights remaining in the deck. The teacher can tell the student the total number of remaining cards in the deck (for example, 30), and the student can calculate his chance of getting an eight -- in this case, it's a one-in-15 chance.
Dice games allow a teacher to introduce probability before or after students have a strong foundation in division. It should be immediately clear to students that rolling one die gives a one-in-six chance of getting a certain number. Present new problems to the students, such as the chance of getting an even number. Use counting methods to help the students calculate the answers without using division.
Subjective probability is one of the three main forms of probability and is frequently used in daily decisions. Students have an implicit knowledge of subjective probability already. You can formalize this knowledge by providing problems related to subjective probabilities and eliciting answers from students. Some interesting questions are "What is the chance of the sun rising tomorrow?" and "What is the chance of you winning the lotto?"