**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:
*x*2 +*y*2 =*z*1 +*z*2

**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?