Perceptions of Likeliness

Overview and Objective

Many words and phrases are used to describe the chances of certain events occurring:

• It is likely to rain today.
• There is little chance for the team to win the game.
• The chances are very good that my phone's battery will last through the day.

In this lesson, students will explore a variety of these phrases and rank them according to their perceived likeliness of the event occurring. Then, students will explore Box and Whisker plots of the responses of the entire class.

Warm-Up

To begin the lesson, share the phrases listed above and ask students to share other similar examples they have heard. For a few of them, invite them sort the phrases based on which ones they believe are the most likely to happen. For example, using the three phrases above, students might not all agree on which is more likely to happen - raining, or the phone battery lasting through the day. After discussing a few examples, share with students that they will be exploring a number of these phrases in class today.

Main Activity

Students are going to explore a variety of phrases commonly used to describe the likeliness of various events happening. For each phrase, they will enter a number from 0 to 100 corresponding to how likely they think it is for the event to happen. 0 means the event will never happen and 100 means the event will always happen. The phrases are listed alphabetically. While students may use this Polypad canvas or a piece of paper to record their rankings, a Google Form will work best for compiling the class data later in the lesson.

After students have entered their data, compile the data for the class on one Polypad canvas. Below is a video overview of how to sort the data from the Google Form in a Google Sheet and then how to copy the data into a table on Polypad. The first step is to find the median of each data set so the data can be sorted based on the median. The data must be in rows in Polypad but can only be sorted in columns in a Google Sheet, so transposing of the data a few times is needed. All of this is shown in the video below.

If you are not using a Google Sheet with the data, you'll need to enter in the data manually for each student. After creating the data table in Polypad, construct a Box and Whisker chart with the data. Depending on your students' background knowledge of Box and Whisker charts, you may want to spend time reviewing how theses charts are constructed using the median, lower quartile, upper quartile, minimum, and maximum of each data set. Perhaps take one of the columns and go through the specific measures as a class.

Use the "Toggle Outlier" button on Polypad to switch back and forth between showing outliers on the line of the Box and Whisker or not. If necessary, review with students the definition of an outlier. If students have not encountered the definition of an outlier, asking students what they notice and what they wonder when the "Toggle Outlier" button is repeatedly clicked can be a good way to start the conversation.

An outlier is any data point which is more than 1.5 times the interquartile range above the third quartile or below the first quartile. Removing outliers can be helpful in some situations.

After discussing the features of a Box and Whisker chart, facilitate a class discussion on the data:

• Which descriptions have the most class agreement? Why do you think these descriptions result in agreement?
• Which descriptions have the most class disagreement? Why do you think these descriptions result in disagreement?
• What do the outliers tell us about the data? Why do you think some are father from the median than others?
• Do some data sets have multiple outliers?
• Which descriptions are most similar to each other?

Closure

The ideas for this lesson come from this article by Rick Wicklin. Consider sharing parts of the article with your class and see if any of the observations and conclusions shared in the article also appear in the data from your class.

Polypad for This Lesson

To assign these to your classes in Mathigon, save a copy to your Mathigon account. Click here to learn how to share Polypads with students and how to view their work.