• For students who are less familiar with basketball, and to help set the stage for students to solve the paradox, it’s important to describe the difference between 2-point shots (closer to the hoop) and 3-point shots (further from the hoop). In particular, it’s helpful to name that 3-pointers are worth more points because they’re more difficult. Then, when students think about the paradox described in the Key Question, they’ll be able to connect Plum’s overall lower shooting percentage to the fact that a higher share of her shots are in the more difficult category (3-pointers).
• For motivating the lesson context, it’s helpful to emphasize that both players were MVP (Most Valuable Player) contenders in 2022. So, solving the paradox from the Key Question isn’t just an interesting mathematical exercise. The solution could inform how we think about which player should win the award.
• This lesson covers a relatively high number of statistical ideas and methods. Intentionally pointing out connections between them can help students better internalize them. For example, vertically stacking the bars in a side-by-side bar chart would yield a segmented bar chart. In addition, adjusting the bar widths in a segmented bar chart (according to sample sizes) would yield a mosaic plot. So, side-by-side bar charts, segmented bar charts, and mosaic plots are highly interrelated.
• The Discussion Question covers Simpson’s Paradox – a fascinating statistical concept that students should appreciate, but that also isn’t covered in most state standards for high school statistics. If students are struggling with the paradox, you can let them know that the other concepts from this lesson (joint, marginal, and conditional relative frequencies; side-by-side bar charts, segmented bar charts, and mosaic plots) are more important for their course performance.

First, download this lesson's slide deck and handout key to see the prompt and sample responses for the Lesson Starter. Then, check out the additional background notes below.

Instructional routine: Would You Rather. The "Would You Rather” routine provides an opportunity for students to develop their higher-order thinking skills, active listening skills, and ability to communicate arguments, all from a simple binary prompt. Students resistant to choosing just one of the two options can be encouraged to select the option that they can best justify. Generally, there is not one correct answer to the prompt in this routine, allowing the focus to be on justification of the choice made, rather than the choice itself. You can find more background on implementing a Would You Rather here.

Purpose & Background: This lesson starter provides a gentle entry point into the lesson’s basketball terminology, and it provides an opportunity for students to grapple with the pros and cons of shooting 2-pointers vs 3-pointers. Conversation may develop to consider risk (more difficult shots) versus reward (3 points instead of 2), and why some players tend to focus on one type of shot. For example, shorter players may be more likely to take 3-pointers, given that their shots are more likely to get blocked by taller players closer to the hoop. Such discussion positions students to consider Wilson and Plum’s choices and percentages later in the lesson.

First, download this lesson's handout key and read through its Discussion Question section. Then, check out our model discussion norms and the additional background notes below.

• The discussion provides a good opportunity to promote deeper conceptual understanding of mosaic plots. Students can compare the areas of the segmented bar charts and the mosaic plots. Looking at the segmented bar charts, the “shots made” area is greater for Plum, since the height of the white areas in the charts is higher for Plum. However, for the mosaic plots, the “shots made” area is greater for Wilson, since the total area (height x width) of the white areas is greater for Wilson. Because mosaic plots vary their bar widths by sample size, they showcase the fact that most of Wilson’s shots are in the higher accuracy category (2-pointers). This leads to a greater “shots made” area and, therefore, a greater shooting percentage overall.
• This question covers Simpson’s Paradox – a fascinating statistical concept that students should appreciate, but that isn’t prominent in most states’ learning standards. If students are struggling with the paradox, you can let them know that the other concepts from this lesson (joint, marginal, and conditional relative frequencies; side-by-side bar charts, segmented bar charts, and mosaic plots) are more important moving forward in the course.

• The shooting data for this lesson comes from the 2021-2022 seasons. During these seasons, the dynamic duo (A'ja Wilson and Kelsey Plum) hit their prime as teammates, becoming the first two WNBA players on the same team to each score 700 points in a single season (2022). Plum was traded to the Los Angeles Sparks in 2025, so the two players are (unfortunately) no longer teammates.
• Even though Kelsey Plum was the “better shooter,” A’ja Wilson actually won the 2022 league MVP (Most Valuable Player) award. Why? Her superb defense and floor presence made her stand out above the other candidates. She led the league in blocks that season and had more total rebounds than any other player. When evaluating a player’s value, shooting is one consideration among many. Ultimately, Plum finished in 3rd place in MVP voting.
• The shooting percentage paradox (Simpson’s Paradox) in this lesson can be found between other players in the league. This lesson can be modified to showcase players from teams more local to your area. Basketball Reference is a great site for looking up the relevant data for players close to you.
• Recent research about the expected value of 3-point shooting conducted might inform future MVP decisions and be of interest to some students.

• There are multiple ways to make visualizations of categorical data misleading (e.g. truncated y-axes, mislabeled axes, use of overstated colors). Refer back to Lesson 1.1 for examples.
• The paradox explored in the Discussion Question is called Simpson’s Paradox. Although not included in all state’s learning standards, Simpson’s Paradox is a great statistical concept for students to learn more about, as time allows. For example, check out this project, which allows students to explore how Simpson’s Paradox arises in criminal justice, college admissions, medicine, and elections.