Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to:
- Identify the effects of extreme data points on shape, center, and spread, specifically, how the mean is affected by outliers
- Evaluate how different shapes of distributions compare to each other in the context of a data set.
- Draw inferences about the context of multiple sets of data by comparing their shape, center and spread.
Prior Knowledge: What prior knowledge should students have for this lesson?
1. Student should be able to describe patterns such a clustering, outliers, and skewed left/right data.
2. Student should be able to identify an outlier in a data set.
3. Student should be able to calculate mean, median, and IQR (centers) of a data set relative to that data.
4. Students should be able to create box plots, histograms, and dot plots.
5. Remind students that in stem and leaf plots; if there is no value in the leaf; then the stem will not be included in the calculations.
This lesson should be taught as a culminating lesson to compare the various graphical representations.
Guiding Questions: What are the guiding questions for this lesson?
1. What can we tell about the data set in the histogram and box plot by their shapes?
2. What might the mean and median tell about a data set in the context of the data set and its shape?
Teaching Phase: How will the teacher present the concept or skill to students?
Before class: create a number line on the wall or floor that ranges from 0-40 with intervals of 10 (use yarn, tape, write on white board, etc.).
The teacher will begin with short review of data displays (dot plots, histograms, and box plots) in data displays lessons. Some guiding questions for review:
1. What are some ways to display data?
2. What measures of central tendency are most useful?
3. What can help us decide how to display data?
Next, move in to the activity for this lesson:
Students will create a human box plot using the height of each student rounded to the nearest inch. If time is an issue you may want to have them measure their heights the day before. If this doesn't work you might also want to use the DAY of students' birth-the range would be from 1-31.
Have students calculate the median, Q1, Q3, minimum and maximum at their seats. Depending on your students they could do this individually or in groups.
After they have these measures calculated have them begin to form the human box plot. The min. person and max. person should be at opposite ends, median person in the middle. Have students who are Q1, Q3, and median hold signs identifying who they are; and have other students hold the yarn for the box and whisker part of the human box plot.
Ask students to describe the shape of their human box plot. They will need to describe if they are symmetrically distributed, skewed, clustered, if outliers are likely present, etc.
Since this is a warm-up to the lesson and the shape of the human box plot will lead to discussions about shape and spread in the lesson, ask students:
1. Are any of you crowded?
2. Are any of you not near anyone else?
3. Are there the same amount of people in each quartile?
4. Where are most of the people?
Answers to these questions should help remind the students that in each quartile there were the same amount of people, so if they were crowded in one area the spread of the data was different in that quartile, not the amount of data in each quartile.
After students are re-assembled in the classroom, the teacher should pass out the notes and begin the lesson. Students and teacher will complete these together (interactive notes). The teacher should have a copy of the Notes Answer key (in attachments section) as well as the student copy. Have students describe the distribution shape of their human box plot; is it uniform? skewed? left/right? any outliers?
To begin teaching the Interactive Notes section of the lesson plan; display the notes on the document camera.
Identify and discuss the standard and learning objectives with students.
Ask students: when describing data distributions what are three things that should always be included?
Proceed to discussion on shape, center and spread with students. As you are teaching, have students fill in notes. Discuss the human box plot students completed-which words would they use to describe their box plot? Invite students to come to the board to answer/explain/justify their responses.
Formative assessment questions should be going on throughout the lesson so you can check for understanding. Poll students: could you explain this to someone? Do you understand only parts? Are you struggling with this lesson? Review any topics students are struggling with.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will complete interactive notes with teacher during the lesson. The formative assessment will take place throughout the lesson.
Practice problems; have students discuss these aloud and be able to answer the questions in the context of the data. What do the mean and median represent for that particular data?
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will complete a homework assignment (independent practice) on this lesson which is included in the attachments.
When you are ready to wrap up the lesson phase; ask the students if they enjoyed the lesson and then do another check for understanding.
Inform students that they will have a short homework assignment on the lesson so they can show their understanding independently. Pass out and collect the next day. Review with students in next class period.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher should review the learning goals and do a "check for understanding" Level 0 being I do not understand this at all, Level 1- I get this a little, Level 2-I get this and can do it with help, Level 3- I get this and can do most of it alone, Level 4 -I get this and can do it independently, and Level 5-I can do this independently, apply it to other situations and teach someone else how to do it.
Review the homework solutions and clarify any student misconceptions.
Finally, looking ahead to next phase of skill, the teacher should review skills from this lesson (ie describing data distributions) as the curriculum progresses into using standard deviation.
Student will complete a homework assignment (attachment) which will serve as both the independent practice and the summative assessment for this lesson.
The formative assessment will be "check for understanding" in students' notes/questions throughout the lesson.
These are sample questions that can be used throughout the lesson to check and further student understanding.
1. Which shape(s) would you expect to have the same mean and median? Answer: a symmetric/uniform distribution
2. Which shape(s) would you expect to have a different mean and median? Answer: a skewed shape, with an outlier possibly.
3. When the mean is greater than the median, what shape is the distribution? Why? Answer; the shape is skewed right because there is an outlier to the right of the mean.
4. When the mean is less than the median what shape is the distribution? Why? Answer: the shape is skewed left because there is an outlier to the left of the mean.
5. Name the common shapes that distributions have. Answer: Bell, Uniform, Skewed Left, Skewed Right.
6. We have already looked at two different measures of center; what are they? Answer: Mean and Median.
5. Which measure of center best describes the peak of a skewed distribution? Why? Answer: Median, because the mean may be affected by an outlier.
6. Evaluate the effect of an outlier on the mean of a data set. Answer: the mean may be raised or lowered by an outlier depending on its location.
7. What three things should always be included when describing a data set? Answer: Shape, Center, Spread.
8. What is the spread of a data set and what does it tell us about a data set? Answer: Spread is the measure of how far apart the data values are, compared to each other. The spread of the data tells us how the data ranges, if there is/are clustering, and extreme values that affect the data.
Feedback to Students
As students are organized in the Human Box plot-have them describe, compare/contrast how they are distributed. Have them describe the shape, where they believe the center to be; identify any outliers. Have them describe how extreme data points affect the mean and median. They should use the vocabulary of this lesson and the previous lessons: mean, median, range, data, bell, normal, skewed left/right, shape, center, and spread to describe their distribution. Take a picture of them—they love it!
Have students answer formative assessment questions in notes; if the teacher hears any misconceptions, preferably have students discuss them and/or the teacher may dispel them. If students are not able to answer the formative assessment questions, then the teacher should re-teach, review, explain again.