Box and Whisker Plots
Lesson 7 of 11
Objective: SWBAT create and compare data using box-and-whisker plots.
Students enter silently according to the Daily Entrance Routine. They receive a handout upon entry that will ask them to find quartiles and ranges. A second question will include multiple choice answers. This do now will be collected, graded and returned to students for feedback before their next quiz.
The feedback provided to students is given as a homework assignment. Students are to write a one paragraph summary on how they used given feedback to complete homework problems. Tonight’s homework assignment will mostly focus on identifying and describing quartiles in box and whisker plots. Thus, I need to make sure students understand where each quartile lies and how to find it. One way I provide feedback is by drawing the representative box and whisker plots for one set of data so that students whom are likely to struggle with the homework can use their Do Now assignment as a resource.
Based on work shown yesterday, students need to spend more time finding quartiles and ranges before we move on to identifying these parts in a box and whisker plot. The most common misunderstanding seems to be value vs quantity of values. Students do not understand that unlike an average (which is a measure of center) we are not ALWAYS adding two numbers and dividing to find the quartiles. This is only done with TWO numbers when the quartile falls between two values.
For example, in the first problem in the Extra Practice sheet, there are 7 total values for the seven countries listed in the table. Identifying the quartiles in this list is simplest because all of the values are readily identifiable. In other words, we do not have to calculate the average of two numbers to find the median. This is a confusing idea because median and average are not exactly the same kind of measure, but are very much related. It is best to circle back to the original essential understanding that quartiles divide a set of data into four equal pieces, where each piece has an equivalent number of values. For additional misunderstandings and errors to look out for, watch the video below:
[video describing students misunderstanding when to include vs not include the median when looking for q1 and q3; how finding the quartiles vs plotting them on a number line yields more information for comparing the data; main idea: always spiral back to the essential understanding, the definition of “quartiles” and what they are meant to do]
Students’ use of MP1 is highly important here as this can be a very frustrating topic to understand. Many examples can be useful so that students begin to see how the number of values affects the process for identifying the quartiles. It is also best to use student helpers to continue explaining these topics in their own words as they may have a better way to explain for some students. Additionally, there are two visual examples displayed at the SMARTboard to help students identify the locations of the quartiles. Lastly, I’ve included an extra example for students who are ready to practice an addition problem that involves comparisons.
As we move into the new topic, box and whisker plots, I continue to emphasize the importance of the diagram. Finding the quartiles is one task in itself that will provide useful information; diagraming the data will aid comparisons as the differences become very visible. Again, it is best to use various distinct examples of box and whisker plots and identify the quartiles with students before they do it on their own.
- Begin by identifying these parts in individual box and whisker plots alone (included in worksheet and ppt).
- Then, move on to comparing two diagrams, noting which has a higher or lower quartile. (included in worksheet and ppt).
- Ask students to discuss what this tells them about the data.
We complete those exercises on red slides together for the first ten minutes of this section. Then, I ask students to work independently on their own problems through the Guided Practice . They are given 10 minutes to work on their own before we break into groups of four to review the answers.
Extra time should be given to this section if possible.
Students receive Exit Tickets which must be completed before the end of class. We have one more day until the next quiz so these exit tickets could provide much needed information about this new topic. I make decisions about what topics to include in the quizzes based on these exit slips. Today’s topic demanded a ton of grit and focus to master. It may be too soon to include it in an assessment as students may need more time to practice and ask questions. I’d like to be able to inform my students the next day about what topics will be covered on the quiz and this exit ticket can help with that task.