Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
- generate a statistical question and use it to collect data.
- determine and justify the appropriate graph to display their data.
- compare/contrast the strengths and weaknesses of different plots.
- analyze and interpret their data and make valid conclusions.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to:
- model single variable data as a dot plot, histogram, and box plot.
- conduct a survey and record their data.
Guiding Questions: What are the guiding questions for this lesson?
1. What is the difference from a question and a statistical question?
2. What can you use statistics for in your life?
3. How do you determine which graphical representation is the best for a given set of data?
4. What are the strengths and weaknesses of different plots?
Teaching Phase: How will the teacher present the concept or skill to students?
Warm-Up (15 minutes)
The teacher should open the PowerPoint presentation for this lesson and have it on the Warm-Up slide. As students walk into the classroom, have them sit down, open their notebooks, and work on the warm-up. This section should give insight about the students' knowledge and ability to construct dot plots, histograms, and box plots. Give the students about 7-8 minutes to work on the question. While the students work on the warm-up the teacher should walk around and assist students who need help, as well as check for answers that students are giving. As some students finish earlier than others the teacher should have 3 students construct the different graphs on the board. After students are finished with the warm-up the teacher should lead a discussion (If students struggle with the understanding or construction of any of the graphs the teacher should stop and re-teach before moving forward). Questions that should be asked by teacher (Checkpoint Slide):
- Who would you have surveyed to answer the statistical question?
Answer: Answers may vary but students should specify that they would only survey 10th graders that are in Hoover High School. Also, after getting this answer from one of the students ask the rest of the class why you wouldn't be able to survey 11th graders at Hoover High School or some other 10th graders at the High School down the road.
- Which graph best illustrates the data?
Answer: Answers will vary but students should realize that a histogram is not the best option because there is so little data and it doesn't vary too much.
Prior Knowledge (13 minutes)
The teacher should move on to "The Statistical Process…" slide. At this slide, the teacher will just review the statistical process, discussing each step with the students. However, students should already know this information; if they do not, the teacher should stop and take time to re-teach before moving forward. Next, the teacher should move to the "Variables" slide. In this slide, students are asked to read the statistical questions and decide whether the question is categorical or numerical. The teacher should go through each example, giving sufficient time for students to think about their answer. Then discuss the students' answers with the class and explain the correct answer. While the teacher is going through the explanations, the goal is to have students clear up their definitions of numerical and categorical data. At the end they should understand that categorical data consists of statistical data that can be placed in categories (such as color or birth place) and numerical data consists of statistical data that can be measured (such as height or time). Question that should be asked by the teacher (next slide):
- Why is some data that contain numbers, such as the post codes, considered categorical?
Answer: Numerical data is something that can be measured, and since post codes are not measured, then it is not numerical even though it is a number.
Introduction of Lesson (2 minutes)
At this point, the teacher should introduce the lesson to students and explain that they will be learning about advantages and disadvantages of dot plots, histograms and box plots. Also, the teacher should explain that they will be working on a project where they will have to choose a statistical question and go through the statistical process. This will get the students prepared and start thinking about what they will be working on.
Lesson (18 minutes)
Dot Plot Slides:
The first slide is a definition of a dot plot with a picture, this is just an illustration; students should already know what a dot plot is and how to construct it. The teacher discusses the advantages and disadvantages of dot plots. The teacher should be sure that students understand that a dot plot is used to illustrate frequency. Explain that is the only axis that does not need to be labeled because it is the same for every dot plot, but all other aspects of the plot should always be labeled. Also, explain to students that it would not be best to use a dot plot for a large set of data, because who really wants to draw 100 dots on a graph?
The first slide is a definition of a histogram with a picture. This is just an illustration; students should already know what a histogram is and how to construct it. The teacher discusses the advantages and disadvantages of histograms. The teacher should be sure that students understand that histograms can only be used for numerical data. Also, students should understand that a histogram displays the number of values within an interval and not the actual values. The teacher should also emphasize that a histogram is great for large sets of data because they can be grouped within the intervals. Finally, the teacher needs to discuss how the change in intervals of a histogram completely changes the way that it looks, and therefore the way it is perceived.
Box Plot Slides:
The first slide is a definition of a box plot with a picture. This is just an illustration; students should already know what a box plot is and how to construct it. The teacher discusses the advantages and disadvantages of box plots. The teacher should be sure that students understand that box plots display a range and distribution of data. Also, box plots show outliers, and they show some skew-ness and symmetry in the graph. The teacher should also be sure that students understand that in a box plot you cannot clearly identify the original data, and they can only be used for numerical data. Finally, the teacher should discuss how box-plots are great for large sets of data.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Guided Practice (17 minutes)
The teacher should direct students to the "What Graph Would You Choose?" slide in the attached PowerPoint Presentation. Students should read the different scenarios, choose the graphical representation that would best illustrate the data, and explain their reasoning. Students should write these in their notebooks and then the teacher should lead a class discussion, making sure to model proper reasoning techniques. During the guided practice phase of the lesson, teachers should ask students to identify (and justify their selection) the best graphical representation of the following scenarios:
- Comparison of the annual snow fall between two snowboarding resorts over several years.
Answer: Answers may vary. An example of an acceptable answer is that box plots would be the choice to illustrate this information because you could display the data and show the distribution of the two data sets.
The teacher should explain that for this graph a histogram would be acceptable, but two totally different graphs would have to be constructed, and with box plots they would illustrate both box plots on the same graph. Also, the same reasoning applies for dot plots.
- The amount of time spent watching TV, in hours, of 200 participants.
Answer: Answers may vary. An example of an acceptable answer is that a histogram would be the best choice to illustrate this information because you could make intervals to display the large set of data.
The teacher should explain that a box plot would be hard to construct because finding the medians of such a large set of data can be difficult and time consuming. Also, a dot plot would be hard because making and drawing 200 dots on a graph is impractical and may lead to a possible error in the graph.
- Wind speed at a windmill farm in a three-week period.
Answer: Answers may vary. An example of an acceptable answer is that a box plot would be the best choice to illustrate this information because you could show the range and distribution of the data very nicely.
The teacher should explain that a histogram could be used with this data, but there may not be that much range between the numbers, so the intervals would not be that useful. Also, a dot plot would not be a good option because the recordings from the speed for a three week period will not have a high frequency of any given number.
- Students' favorite summer-time activity.
Answer: Answers may vary. An example of an acceptable answer is that a dot plot would be the best choice to illustrate this information because you could use the different categories and display frequency.
The teacher should explain that a box plot would not be used to illustrate this information because this information does not have range. Also, a histogram cannot be used because it cannot be used for categorical data.
At this time, the teacher may administer the attached quiz. An answer key has been provided.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Independent Practice (Homework)
Students are given homework to complete and bring back the following day. The students will be given data regarding the number of on-time flight departures. Students will create a graphical representation of the data and write a short essay analyzing the data and justifying their results. Answers will vary with this homework and as long as they made a valid argument it should be accepted for partial or full credit. An answer key has been provided.
Summary (25 minutes)
At this point the teacher should hand out the homework and instruct students to bring it back next class. This way the teacher has yet another assessment to be sure that the students understand the lesson and re-teach if necessary.
Next, the teacher should hand out the "Graphical Representation Project" handout. Also, the rubric for the project should be handed out so that students may see exactly how they will be graded. The teacher should discuss the project with the students, outlining the step-by-step process, and clear up any questions they may have. Students will be given 25 minutes to complete steps 1-5 in class and have the teacher give them the go-ahead to proceed with the rest of the project. The students will have one week to complete and turn in the project.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Students will share their results from the survey project with the class. Also, students will answer questions from the teacher to justify their conclusions.
Students will complete a project for the summative assessment. Students will create unique and original statistical question that can be answered with a survey. Students will then survey their peers, record the data, and create a graphical representation. Finally, students will analyze the data and present their results to the class and write a small report. A rubric is provided; see the uploaded documents.
Students will be formatively assessed throughout the lesson. There are several formative assessments embedded in the attached PowerPoint, in addition to the attached quiz, that check for student understanding. Students will be required to:
- Model a data set using dot plots, histograms, and box plots and to compare and contrast the advantages and disadvantages of each; and
- Identify the characteristics of a statistical question.
Feedback to Students
The teacher will hold a question and answer session with students, giving them instant feedback. The teacher should circulate around the room as the students complete independent practice and formative assessments to clear up misconceptions. Common mistakes that the teacher should look for include:
- Students may think that any set of data that has numbers is numerical
- Students may place gaps in their histograms
- Students may believe that the lengths of the intervals of a boxplot (min,Q1), (Q1,Q2), (Q2,Q3), (Q3,max) are related to the number of subjects in each interval