Students select a graphical representation to display discrete data and determine a single value to represent a data set.

The purpose of the Day 2 activities is to reinforce key concepts from Day 1. Students will engage in a math talk and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas. 

• There are different types of data;
• Data is often characterized as continuous or discrete;
• Discrete data is often countable and can only take on certain values;
• A measure of central tendency for a data set summarizes all of its values with a single number;
• Mode is the number that appears most often in a data set;
• Mean is the great equalizer; it can be determined by redistributing the data evenly or through partitive division.

Present the following data sets one at a time. Ask students to identify a single number to summarize all the values. Name the measure of central tendency used each time and ask students to justify their answer.

12, 13, 18, 15, 17

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Each set of data should be presented through a context. For example, you might consider leveraging the context of archery as we did in Day 1, or maybe some other olympic sport. Alternatively, you could come up with your own context to help students make connections as they work towards finding the mean, the median and the mode.

Consider leveraging the following Visual Math Talk Prompts to Spark Curiosity and lower the floor on these prompts so all students can enter into each problem. Here, we are leveraging the context of points scored over a series of games in basketball.

For the first set of data, show students the following silent solution math talk visual prompt:

In the video, students will see the number of points that a basketball player scored for the past 5 games this season:

12, 13, 18, 15, 17

Students are then prompted to:

Determine the mean, median and mode for this data set.
Which measure of central tendency do you think best represents the number of points scored by this player over the last 5 games?

After pausing the Visual Math Talk Prompt video to give students an opportunity to think and work through this problem, students can then share their thinking including their models and strategies used to determine the mean, median and mode. 

While students who have experience calculating the mean by simply adding the values together and dividing by the number of values in the data set, others might choose to create a bar graph and “redistribute” the extra points scored in game 3 and 5 to games 1 and 2 to average out the number of points.

This approach is worth highlighting because it truly demonstrates the big idea of the mean as the “great equalizer”.

For the median, rearranging the bars from least to greatest can allow us to easily find the median (or middle) value in the data set.

Finally, with the data set organized from least to greatest, we can easily identify the mode: the value occurring most often. In this case, since the number of points scored in each game was unique, there is no mode.

Login/Join to access two (2) additional Visual Math Talk Prompts as well as the Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access two (2) additional Visual Math Talk Prompts as well as the Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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