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:
- Interpret standard deviation.
- Use the visual characteristics of a dot plot to estimate standard deviation.
Prior Knowledge: What prior knowledge should students have for this lesson?
In order to successfully teach this lesson, the students must know how to calculate standard deviation. The students should also be familiar with calculating measures of center and spread. Students should be able to create a frequency table and dot plot.
Guiding Questions: What are the guiding questions for this lesson?
Is there more variability in the ages of the students in our classroom or the distance the students live from the school?
Teaching Phase: How will the teacher present the concept or skill to students?
For this lesson, the teacher should draw two frequency tables on the board or on chart paper. The teacher will gather information from the students as they enter the classroom, (i.e., the age of the student and the distance each student lives from school). As the students enter the classroom, the teacher should have each student place a tally mark in the corresponding cell for each table. The data should be entered as whole number values, (e.g., 14 yrs old or 3 miles from school), rounding the distance to the nearest mile. Rounding to the nearest whole will make it easier for students to compare the dot plot representing the data to the standard deviation of the data. Also, the standard deviation will be easier to compute. Each student should determine the distance he or she lives from school prior to class (previous night's homework). The distance between two addresses can be found on mapping websites such as Mapquest.com or Google Maps. If students are unable to gather this information prior to class, a list of sample data, Distances from Home Data worksheet (see attached), may be used instead.
As a warm up, have the students make observations about the data in the frequency table. The observations may be discussed with partners or in group. Encourage the students to include conversations approximations of the mean, median, mode and range. Also, remind the students to consider any outliers and their possible effect on the measures of center and spread. The teacher should encourage the students to also review how to calculate standard deviation. If time allows, the students can share one observation from their group with the class.
As you are working through the lesson and the students are working through the worksheet, do not hesitate to review with a class any topics that are necessary. For example, in the worksheet you may need to review how to create a dot plot.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher should have the students copy the values from the frequency tables onto their lesson Worksheet (see attached). The students may complete the worksheet individually, in pairs, or the teacher may guide the students through its completion as a whole group. The teacher should have the students write important information down. The second question on the worksheet asks students to write down some observations from the frequency table. Students should include the responses mentioned during the warm up (e.g., conversations about the mean, median, mode, range) and add any new observations he or she may have.
The teacher may want to have the whole class, or small groups of students, stop after completing question 6 to have a conversation about their prediction for question 7. Repeating this conversation may be helpful for the second sets of data as well.The students will complete the lesson Worksheet (see attached) in class.
If necessary, the teacher can look over the questions related to frequency table and dot plot, to identify if the students are struggling in that area. You may also need to review how to create a dot plot and the the different distributions or skewness applied to a dot plot.
This worksheet should be used to help guide the students with organization of their data.
It has space for the students to:
- Copy the frequency table.
- Create a dot plot.
- Calculate standard deviation.
- Answer all questions.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
On a separate sheet of paper, students will create two number sets (with 5-10 numbers) that have the same mean but different standard deviation. Then have students create two number set (with 5-10 numbers) that have same standard deviation but different mean. Sample data sets are provided (see attached).
If time is limited, GeoGebra and graphing calculators may be used. Both programs calculate mean and standard deviation very quickly and allow the data to be changed quickly.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Have the students respond to the closure question on the lesson Worksheet (see attached). Make sure the students explain the difference in context. Guide the students in their thinking by asking questions like "Why would the variation of student ages in our classroom be less than the variation in distances that students live from school?"
Refer to the Exit Ticket (see attached).
The Exit Ticket includes matching two dot plots with two standard deviations. The students should be able to match each dot plot to the correct standard deviation then explain their choice. This may be completed with the partner the student had been working with throughout the lesson.
The goal is not only for the students to match the information correctly, but also to be able to provide a thorough explanation that justifies their decision. The explanation should indicate whether or not the students understand standard deviation. The students are also asked to apply this understanding as they estimate the effect that adding points to the data set may have on the standard deviation and the mean of that data. Finally, the students are asked to estimate the standard deviation for a given data set.
During the warm up, the teacher should:
- Ask the students what they know about standard deviation. Lead the conversation to the purpose of each step in the process of calculating standard deviation to activate prior knowledge regarding the calculation of standard deviation. If there are students that are unable to calculate standard deviation, provide these students with a copy of the steps to use as a guide in answering question 6 on the lesson Worksheet (see attached). Depending upon student responses, a review of calculating standard deviation may be necessary with the entire class. If needed, the teacher should model for the class the calculation of standard deviation for a small data set, as he or she reviews each step of the process.
x is a value from the original data set,
- Subtract the value, x, from the mean, , to calculate the list of deviations,
- Square the deviation from the mean,
- Find the sum of the squared deviations,
- Divide the sum of the squared deviations by n,
- Find the square root of the quotient,
- If needed, remind the students that standard deviation is a measure of variation of values about the mean. The value of the standard deviation is close to the average distance of data points from the mean. The larger the spread of distribution of the data points, the larger the standard deviation.
- Walk around the classroom as the students are completing the lesson Worksheet (see attached) to review their responses and listen to their conversations. The students' responses on the worksheet should be used to inform the teacher of the their understanding of standard deviation.
Feedback to Students
Throughout the lesson, the teacher should walk around the room to check student work, listen to conversations, and ask probing questions. During this observation, the teacher should provide feedback regarding students' progress. The teacher should use this opportunity to work individually, or with groups of students, to answer questions and increase their understanding of the lesson objectives.
Student conversations should be about the questions on the worksheet and comparing standard deviation with the dot plot. If the students seem to be off track, ask questions to help guide them. What do you notice about the dot plot? What is standard deviation? Think about the process of finding standard deviation. How can the mean and the range assist you in predicting the standard deviation? Provide feedback for their responses as needed.