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:
- Properly critique the usage of certain displays and explain general factors that contribute to selecting the most appropriate data display.
- Compare and analyze data.
- calculate outliers and how they affect measures.
Prior Knowledge: What prior knowledge should students have for this lesson?
Prior to the lesson, students should be able to:
- Calculate the 5 number summary. (This is done during the intro activity.)
- Calculate mean, median, mode, and range.
- Students should know how to conduct a survey and collect and arrange data.
Guiding Questions: What are the guiding questions for this lesson?
- What are the similarities and differences of various graphical representations (histogram, box plot, and dot plot)?
- How can we analyze data organized in these graphical representations?
- What are the different uses of the histogram, dot plot, and box plot?
- Because a number seems far out from the other numbers, does it necessarily mean it is an outlier?
Teaching Phase: How will the teacher present the concept or skill to students?
Introduction (5-7 minutes)
The teacher will have the PowerPoint on the board ready to present. The first slide is a warm up reminding the students of the summary vocabulary words. This will hopefully jog their memory of the box plot and its values. During this time, the teacher will walk around and answer questions with the students. The teacher should be making sure children are answering the questions correctly. The five summary is actually a middle school concept, therefore the students should know the answers. Even if there was a bit of a brain freeze on these five questions, the sentences are structured to where the student can figure out the answers are based on other answers. On the second slide the answers will be provided. This section should take no more than 7 minutes.
Middle Phase (15-20 minutes) Under Guided Practice
After the students complete the intro 5 summary vocabulary review activity, now it is time to move on to a dot plot and human box plot activity along with the rest of the PowerPoint presentation. The directions for each slide are located under each slide.
Last Phase (15-20 minutes) Under Independent Practice
Students will complete the summative assessment. The teacher will grade the assessment to better understand who of the students were able to explain the different use of each representation of data.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
After the students complete the intro 5 summary vocabulary review activity, now it is time to move on to a dot plot activity. The directions for this will be located on slide 3.
- Ask the students to gather their shoe sizes.
- Students will look in the tongue or sole of their shoe to gather their shoe sizes.
- Have the students record all the shoe sizes in ascending order on the board.
- The students will take the Smart Board pen and write in the data on the PowerPoint. First they all put their shoe sizes in the white box. After everyone has inputted their shoe size, one person, or the teacher will make a scale and draw a dot plot on the graph below.
- Then move into creating the Human Box Plot and have the class line up in a line at the front of the class from smallest shoe size to largest shoe size.
Note: If there are an odd number of students, use section a. If there are an even number of students, use section b.
- Odd number of students: Tell the student in the very middle to come forward out of the line. Ask the class to tell you what value in a box plot this student represents (the median). Next, have the student in the center of the group to the left to come forward and define them as the lower quartile median and the student in the center of the group to the right step forward and define them as the (have the students answer) ______________ (upper quartile median). Discuss with the students the meaning of each of these values. Ask all the students to step back in line.
Have the student who was the lower quartile median hold one end of a string and have the student who was the upper quartile median hold the other end of a piece of string. Also have the median student hold the piece of string.
- Even number of students: Ask the students what would happen if they have to find the median of a set of data that has an even set of numbers. The students should answer by saying that you would have to add the two middle numbers and divide them by two to find the median. Remind them that since a person can't be split in half (if the number comes to ex. 12.5), we will just divide the whole group in half. Have the student in the middle of the lower group to come forward and define them as the (have students answer) _________ (lower quartile median). Have the student in the middle of the upper group step forward and define them as the (have students answer) ______________ (upper quartile median). Discuss with the students the meaning of each of their values. Ask the students to step back in line.
Have the student who was the lower quartile median hold one end of a piece of yarn and have the student who was the upper quartile median to hold the other end of a piece of yarn. Have the two students in the middle of the entire group hold the piece of yarn where they were standing.
- Discuss with the students that the box represents half the class, and that when the box plot is created, 50% of the data is in the box. Also discuss that 25% of the data is to the left of the box, and 25% of the data is to the right of the box. Have students return to their seat and create the box plot on paper. Students should have taken note that there are the same number of students in each 25% section, but the cluster or spread of where they stood matters and can show the variability of the data.
At this point, you may show slide 7 and 8 to further discuss Box Plot.
Questions to ask students to gain a better understanding of where their perception of box plots are:
- What does the box plot tell you about the class shoe sizes? (ex. Everyone wears between a ___ and a ___ shoe size; the majority of the class wears a size ____); the average shoe size is _____; the lower 25% wear below a ____ shoe size; the upper 25% wear a ____ shoe size.)
- Did the students find it difficult or easy?
- How can you tell where the middle of the class is? (the middle number or vertical line in center of box)
- What is the range of the shoe sizes? (The largest shoe size subtracted from the smallest shoe size)
- What is the range of shoe sizes for the middle 50% of students?
- The horizontal line to the right (or left) of the box is longer than the one to its left (or right). What does this tell you about the spread of the sizes? (The spread of the top 25% of the scores is bigger than the spread of the bottom 25%, or vice versa, depending on which line was longer).
- The median is not in the middle of the box. What does this tell you about the distribution of scores? (the spread of scores of the second quartile is smaller than the range of scores of the third).
The 7th slide has space for the teacher to construct a box plot.
- The students should be able to see the distribution. The teacher should use this time to see if the students can remember how to construct a box plot. If they are having trouble, the teacher may go to Slide 8 to review box plot terms and values.
Now the students can construct a box plot on their papers, with the teacher.
- After the box plot is constructed and questions are answered, then the children can move on to constructing a histogram. The notes for those are on slide 17.
- Slide 9 discusses Measures of Spread.
- Slide 10 discusses Measures of Center.
- Slide 11 and 12 discuss Interquartile Ranges.
- Slide 13 discusses outliers.
Once the slides are all completed, students should know the differences between the dot plot, box plot, and histogram and be able to explain advantages and disadvantages of each.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Slide 12 gives an example for the students to practice finding the Interquartile Range. The steps are given upon manual clicks from the teacher for correct explanation. This is a way for teachers to give instant feedback for students who may not be getting the steps correct.
Slide 14 and 15 has examples of obtaining and determining if a problem has an outlier. The problem is given and then the steps are given upon manual clicks of the teacher for correct explanation.
Students will complete the summative assessment.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher can use this time to have a discussion on what students found interesting, what the students still don't understand, and what can be a quick 5 remediation for the next class period. The teacher can also revisit those guided questions to determine if the students grasped the concept. The students can also have this opportunity to clear up any misconceptions.
- What are the similarities and difference between a box plot, dot plot, and histogram?
- What are the different uses of a histogram, dot plot, and box plot?
- What does range tell us? Is it important?
- How is calculating an outlier useful?
The students will complete a worksheet that will require them to construct different types of graphical representations, as well as compare and analyze them. This will be in the form of short response questions. The teacher should grade these and then distribute them back to the students for immediate feedback.
During the lesson, there will be several examples where the teacher can check for understanding. During the introduction activity, the student can use this opportunity to ask the teacher questions, and the teacher as well can walk around to make sure that calculations are being done properly, the proper scales are being used, and making sure the correct values are being placed in the correct areas. During the group activity is another point in the lesson where the teacher can make sure the students are understanding the lesson by asking the following questions and checking the students' work in the group activities.
What are the different uses of the histogram, dot plot, and box plot?
What does the range tell us? Is it important?
Because a number seems far out from the other numbers, or away from the cluster, does it mean it is an outlier?
In the PowerPoint presentation, there are two slides with outliers of calculating outliers. These two slides can be used as a formative assessment. There is also a slide on interquartile ranges that will also have an example for the students to be formatively assessed on.
On slide 18, there are six questions that can be used as a formative assessment before the summative assessment. The answers are given on slide 19 and 20 for further discussion.
Feedback to Students
During the lesson, the teacher should be engaging the students in question and answer sessions, especially using the formative assessment questions and other questions from the PowerPoint. This will give the students instant feedback. During data collection, the teacher will move around the room as the students complete data gathering, formative assessment and the summative assessment. The PowerPoint slides have examples that the students can be assessed on and given instant feedback.
- Many times students forget to put the data in order before they begin their calculations.
- Students may forget the true calculation of an outlier. There are slides that will go over this section. It is not always based on visual, i.e. just because it is far away from the cluster of numbers it is an outlier. The outlier needs to be calculated using the formula Q1 - 1.5 x IQR and Q3 + 1.5 x IQR. If the value lies below the lower number or above the higher number, it is an outlier.
- Students are unable to select which measure of central tendency is most appropriate for a set of data.