0 to 1, or Never to Always

Intent In this activity, students work with probabilities expressed as fractions, percentages, and decimals.

Mathematics Students continue to focus on the distinction between probability based on a theoretical model and probability based on observed results and on measuring probability using a real-number scale from 0 to 1.

Progression Earlier in the unit, students estimated the probability of given events. In this activity, they invent situations that match a given probability.

Approximate Time 5 minutes for introduction 25 minutes for activity (at home or in class) 10 minutes for class discussion

Classroom Organization Individuals or pairs, followed by whole-class discussions

Doing the Activity Clarify that students are to invent two situations for each question, one based on theoretical probability and the other on observed results. Let's test a link to Keypress.com by clicking here. Here is an equation with a non-breaking space: x + y = z Here is a test of subscripts and superscripts: x2 + y2 = z1 + z2

Discussing and Debriefing the Activity If students have worked individually, ensure that there is time for them to compare their invented situations. Question 5 is included to give students an opportunity to consider an impossible situation.

Key Questions Does it matter whether probabilities are written as fractions, decimals, or percents? Why is the smallest probability 0? Why is the largest probability 1? What does a probability of 2.3 imply?