Reading Box Plots Lesson Plan

Warm-up

Start off the lesson by displaying slide one of the teacher slideshow to students. Here, students will have the chance to look at a picture and discuss what they notice and wonder.

Give students a few minutes to jot down a few things that they notice, and then a few things they wonder. Come together as a class and discuss what they wrote down.

Look out for what students may answer. Some responses may be:

• Notice:
  • A number line
  • A dot at `2`
  • A dot at `11`
  • A rectangle from `4` to `7`
  • A rectangle from `7` to `8`
  • A line at `7`
• Wonder:
  • Why is `1, 12, 13,` and `14` not being used?
  • What does the dot at `2` represent?
  • What does the dot at `11` represent?
  • Why are there rectangles?

These are just a few examples for what students may say. If they don’t, you can bring up that certain numbers are being “highlighted”. These being the beginning/ends of the lines and/or boxes.

Introducing the `5`-number summary

Explain to students that these are called box and whisker plots and they are a way to capture a lot of information about the data. Ofcourse you want to probe why these are called box and whisker plots. Before you formally introduce the `5`-number summary, ask them what they think the two dots at the end represent. Ask them what they think the box in the middle and the line inside the box represent. This will help students start noticing these elements of the box plot.

Tell them that we will be using the box plots today to find the “`5`-number summary” which is to find the minimum, maximum, median, and `Q1` and `Q3` of the data set these box plots represent. Display slide `2`.

Minimum and maximum

Students will already be familiar with this vocabulary but they should be reminded.

• Minimum: The smallest number in a data set
• Maximum: The largest number in a data set

Allow students to recognize that where the points line up to the number line shows us that the minimum is `2` and the maximum is `11`.

Median

Again, students already know what the median of a data set is, but you should remind them.

• Median: The middle value in a data set

Students will be puzzled as to why the median is not in the middle of the box. This is a good point to have the conversation that if the line is a lot on the right side, the means there are a lot more data points on higher side.

Students need more practice interpreting the median given in the box plot since the data points are not actually listed. What percent of the data points are below `7` (about `50%`)? What percent are above `7` (about `50%`)? Can we figure out using the box plot exactly how many data points are there (no).

Quartile `1` and quartile `3`

You might have already introduced the concept of `Q1` and `Q3` to students in earlier lessons. The box plot is also a great way to introduce and reinforce these concepts. The main ideas that you need to communicate to students are the following:

• `25%` of the data points are between the minimum and the start of the box and another `25%` between the end of the box and the maximum. 
• `25%` of the data points are in the box to the left of the median and `25%` on the right of the box. 

Students should also be familiar with `Q1` and `Q3`, but it is likely that they will be much less familiar with this than they are with minimum, maximum, and median. Remind students of their definitions:

• Quartile `1` `(Q1)`: The median of the lower half of data
• Quartile `3` `(Q3)`: The median of the upper half of the data

Allow students time to recognize that `Q1` is `4` and `Q3` is `8`. 

You should follow up with questions like:

• What percent of the students spend between `2-4` hours?
• `75%` of students did less than how many hours of homework last week? 

Summary

Display slide `6` to summarize the `5` key pieces of information that a box plot shows us about the data set it represents. Consider printing the anchor chart to hang in the classroom or to give students as a reference.

Additional examples

The slideshow contains `4` more example box plots where students can practice finding these `5` key pieces of information. You can go through the examples together as a class or have students work independently or with a partner, before sharing their answers with the class!