Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
- Interpret data and construct an appropriate data plot.
- Analyze data plots to find measures of central tendency and variation.
- Compare two data plots in order to form a conclusion based on data.
Prior Knowledge: What prior knowledge should students have for this lesson?
- Find measures of central tendency
- Find measures of variation
- Construct a box plot
- Construct and read a histogram
- Construct and read a line plot
Guiding Questions: What are the guiding questions for this lesson?
- What are some specific items we should look at in each plot that will help us reach our conclusion? -- The medians, the inner quartile range, and the upper and lower quartiles.
- Why are these data points so helpful when we compare data? -- They help us focus on the data as a whole, and not just specific points in a given set.
- Why did you choose this plot for this data set? -- I thought a person with 17 pets would be too many. I saw that the domain was given as a range of numbers. My friend has 17 pets!
- Could we use any other plots to show this data? -- A bar graph. A pie chart. A line plot and a box plot would work for both of these situations. No other graphical representation would work for the histogram.
- How can we tell which is the better team? We can tell by looking at the median, quartiles, and inner quartile range to help us determine this.
- Is a box plot the best way to prove this? -- A bar graph might be useful, but the box plot is probably the best way to prove who is better.
- Do we have to represent this situation with this specific plot? -- No, other plots can be used. It depends on the data and what we are trying to prove. Each plot has its own strengths and weaknesses. Example-Dot plots and bar graphs are used to compare discreet data, circle graphs compare discrete data as it relates to an entire set, box plots show how the data varies, and scatter plots show how two data sets correlate. Review the data and choose the best plot for each specific question.
Teaching Phase: How will the teacher present the concept or skill to students?
Students should be seated in pairs for this task. To establish a culture of debate, pose non-content questions (example: which is the better ice cream flavor?) and ask students to discuss their opinions in pairs. After the pairs discuss, call on a selected group to share their response. Ensure other groups are listening to the discussion by asking them to comment on the first group's response. After hearing from a few groups and allowing the class to provide feedback to the groups, begin the actual lesson. (~5 min.)
Students will be given two data sets, Florida State football wins and Alabama football wins. Students will also received a previously constructed box plot representing the Florida State football wins. Students will work individually to construct a box plot that represents the Alabama football wins. As students construct their box plots, teacher will monitor that all students are able to find the correct measures of central tendency and construct the plot appropriately. Attached below: (~10 min)
After ensuring that all students are able to construct their box plot, ask students to discuss with their partner at least one thing they can learn by reviewing the two box plots. Students should discuss the differences in the medians and the extremes. Students may also discuss the length of the "box" and of the "whiskers" and what they mean in terms of which team is "better". After students discuss, lead a whole class discussion about the box plots by asking selected pairs to share what they have discussed. Class should discuss median, upper and lower quartiles, and inter quartile range. If no groups mention which is the better team, teacher should lead a discussion about how we can use this data to determine which team performed better over the past ten years. Teacher should discuss consistency as it relates to the quartiles and inter quartile range. Some teams may be inconsistent in that they have longer "whiskers" which indicates an odd upper extreme or lower extreme. Teacher may want to use a software program, like Geogebra to show the dual box plots on a smart board or overhead screen. (~10 min)
Inform the class that today, we will be reviewing three types of data plots: histograms, line plots, and box plots. Ask the students to discuss with their partner at least one thing they know about these three graphs (if time is an issue, just discuss histograms and line plots). Call on selected pairs and create a class list of what we know about these plots. Histograms show us frequency inside a given range, box plots show variation in the data, and line plots show frequency of discrete points. (~5 min)
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Inform the class that they are going to receive three sample data sets. They are tasked with matching one data set to a corresponding data plot, and also a sample situation for which the data may fit. Students may need scissors to complete this activity. Students should work in pairs to complete this activity. As students work, teacher facilitates by asking guiding questions of the pairs. After pairs have worked for 10-12 minutes, ask the pairs to stop working and discuss their progress with each other. One member from each pair should stand up, and one should remain seated. The group member standing will be asked to walk around the room and observe the other pairs matching activity and ask questions of the group member who remained seated. The group member who remained seated should be answering questions from other classmates. Questions should include: "Why did you match your plots this way?" "How did you know that situation went with that data set?" "Why doesn't yours look like mine?",etc. Call the class to return to their original group and discuss some things they observed during their gallery walk. Allow the pairs about 5 minutes to finish the activity. Attached below: (~20 min)
Call on selected pairs to share their final results and state reasons why they chose each plot and each situation. Students should have arguments prepared for why they chose to match situation 2 with their data set and graphical representation and situation 3 with their data set and graphical representation. Allow students to debate their reasons with groups who matched these situations differently. Situation 1 clearly goes with the histogram because the independent variables are given as a range. Situations 2 and 3 can either correspond with the box plot or the line plot depending on each groups own reasons. If all groups agree, question the class if there are any other plots that could correspond to these situations. Discuss with students that box plots and line plots can be used to represent the same data sets, but a line plot should not be used if the data has a large range, and many of the discrete points appear only once. (~10 min)
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will work individually to identify the specific data points on two box plots and write a brief summary comparing the data they obtained. (15 min). As you observe the students working, provide them feedback as needed.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Reinforce to students that the individual data points on a box plot are less important than the data as a whole. A higher median does not necessarily indicate a better performance. Quartiles and inter quartile range must also be considered before a conclusion is formed. (~5 min)
If students chose to represent the summative assessment in a line plot rather than a box plot, reinforce that line plots are used to compare discrete data, and box plots are used to show variability. The use of a line plot to represent a data set with a large range and when many of the individual data points appearing only once will not tell us what we need to know about the data.
To measure students mastery of the learning objectives, students will complete the attached individual task.
Formative assessment will occur during the teaching phase, guided practice, and independent practice. Monitoring is embedded throughout the lesson and opportunities to provide feedback and ensure progress are outlined below.
Task 1 is designed to ensure that all students are, in fact, able to construct a box plot to represent a given set of data.
Task 2 is designed to assess whether or not the students can read a set of data and correctly identify a graphical representation that corresponds to that set of data.
- Students will be given a set of data and asked to construct a box plot. This ensures all students are able to construct a box plot, without analyzation. (Task 1)
- Students will match graphs to given situations involving data to ensure that all students are able to recognize a box plot, histogram, and line plot. (Task 2)
Feedback to Students
- Make sure students organized their data in ascending order. (Task 1)
- Ensure students can find the median, quartiles, and extremes. (Task 1)
- As groups discuss the two box plots, ensure that all data points are being considered, not just the extremes and medians. (Task 1)
- Be sure students are matching the histogram to the data that includes a range of numbers in the domain. (Task 2)
- Ask students for specific reasons why they chose to match situations 2 and 3 the way they did. (Task 2)
All feedback should help students understand when to use each plot appropriately and lead students to be able to analyze two sets of data using plots.