Provide a metaview, lifting students into a wider view of the concept. Use another medium (not reading or writing) to connect students' personal knowing to the concept (i.e. visual arts, music, movement, metaphor, etc.) Involve learners in reflective production that blends the emotional and the cognitive.

Birthdates and numbers 1 to 50 experiment.

Objective: To have the students experience the inaccuracy of their guesses as to the likelihood or unlikelihood of certain events.

Activity: Ask the students to guess the probability of at least two students in the class sharing the same birthday. It would appear that this is a very unlikely event. However, in a normal sized class of twenty-five students, it is almost certain (nearly 100% probability) that there will be a pair who share a birthday. Ask each student to call off his/her birthday. If another student hears his/her birthday called, s/he should raise her/his hand. Of 365 days which are possible birthdates, we are considering pairs of birthdates. With one person, there are no pairs. With two persons, there is one pair. With three persons, there are three pairs. For each additional person in the group, another pair is added for each person already in the group. Therefore, to determine the number of pairs for a group of n members, you must add the sum of all numbers from 1 through n-1. As you can see, there are certainly more opportunities for a matching pair than appeared at first. Now try another activity. Ask students to jot down a number between 1 and 50. If you have a group of up to 15 students there will be a 90% probability that two students will select a pair of matching numbers. Students will usually assume that it is fairly unlikely for a pair of students to select the same number. Have students call out their numbers as with the birthdays to see if any pairs exist. For larger classes, extend the range. Now ask the students what these two examples demonstrate about probability. There is likely to be a variety of responses. If no one makes the point that we must have some standard procedures to determine the probability of certain events, the teacher should stress this, and tell the students that the purpose of this unit is to learn about these concepts and procedures. Probability is a ratio comparing the frequency of events to the total number of events. The underlying problem in most cases is to determine these numbers.

Assessment: Quality of discussion and accuracy of understanding.