Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
The student will interpret the standard deviation of two data sets to determine what brand of soccer ball the school should use in the upcoming soccer season.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students must know statistical terms like mean, median, range, variance, quartiles, and interquartile range.
Guiding Questions: What are the guiding questions for this lesson?
Which brand of soccer ball should we use in our next soccer season?
Teaching Phase: How will the teacher present the concept or skill to students?
Hook: The teacher will ask the students if they watched this year Super Bowl (2015). He or she will lead the conversation to the ball inflation issue in which one of the teams deflated the football to their advantage. The teacher will pass an article extracted from USA Today, NFL, which lays out how Super Bowl footballs will now be inspected. The article will inform the students of what happened at the Super Bowl and the consequences this incident brought. (NFL lays out how Super Bowl footballs will be inspected, guarded).
Begin by discussing variation in data (e.g., the pressure of a football) and how this variation of data can play a roll in sports. Remind the students that range (i.e., the difference between the maximum and minimum value of a data set) can be used to describe variation. Have the students brainstorm some possible limitations of using range to analyze variations within a data set (e.g., range only considers the maximum and minimum value in the data set). Ask the students to consider what does one really need to know when considering the air pressure of footballs (e.g., the difference each football's air pressure is from the desired air pressure). Explain to the students that range will not measure the variation for every value and then introduce the concept of standard deviation by defining it as statistical term that describes how values within the data set vary about the mean of that set. Have the students discuss their understanding of the definition of standard deviation and how it might be more useful than range in the football investigation. Continue to explain, that if the standard deviation of a given data set is low, then data is spread close to the mean (or clustered around the mean). This results in a small variance and the data varies less. On the other hand, if the standard deviation is high, then the data is widely spread around the mean. Consequently, there would be a large variance and the data would vary a lot.
Suggested discussion for the teacher to use is below.
Our objective today is not only calculating standard deviation but to interpret it in order to arrive at plausible conclusions according to the given case scenario. Standard deviation by itself does not mean much. It is crucial to interpret it in order to have meaning. For instance, the NFL referees will receive the footballs two and a half hours prior to the game. They will measure the pressure of the footballs, collect the data, and calculate the standard deviation. Then the referees will arrive at a conclusion and make a decision based on their interpretations. What would a small standard deviation mean? What would a larger one represent?
Guided Practice: Worksheet 1
Independent Practice: Worksheet 2
Guided Practice: What activities or exercises will the students complete with teacher guidance?
At this time, introduce Worksheet 1. Remind the students that standard deviation measures the variation of values within a data set. Continue to explain that the first step in considering standard deviation is calculating the variance (i.e., the average of the squared differences from the mean). Tell the students that standard deviation is the square root of the variance. Depending upon student understanding and prior knowledge, the teacher may want to further explain variance by providing several data sets with varying spread (e.g., 5, 5, 5, 5 and 1, 9, 2, 8) to demonstrate why squaring the difference from the mean, instead of just using the distance, or the absolute value of the distance (mean deviation), provides a value that more accurately represents that spread.
To demonstrate the process of calculating standard deviation, the teacher may choose to use test scores from a previous test or the data provided on Worksheet 1 (see attachment). We will use this data to calculate the standard deviation of the test scores.
The teacher should explain the process of calculating the standard deviation:
- Find the mean of the student scores.
- Find the difference between each test score and the mean.
- Square each difference.
- Find the sum of the squared difference.
- Divide the sum by n (number of test scores)
- Find the square root of the resulting quotient.
The teacher will encourage the students to interpret the standard deviation through the use of the following questions/activities.
- Do you consider the standard deviation to be high or low?
- Discuss with your shoulder partner your interpretations of the standard deviation of the test scores. The teacher will discuss the students’ interpretations in order to check for understanding (formative assessment). It is important to lead a thorough discussion in this section in order to expose good arguments that will facilitate student comprehension. The students need to establish a relationship between the standard deviation in context of the problem in order to create meaning, thus arriving at plausible conclusions.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
At this time, introduce Worksheet 2.
Suggested discussion for the teacher to use is below.
The Soccer Schools Champions League will begin very soon. The STEM School team is always a very serious candidate to win the trophy. Our school will host the home games and we want these games to be played under the best conditions possible. Therefore, our athletic director came to see me last week and mentioned his concern about having compliant soccer balls for the games; apparently he watched the Super Bowl and saw the “deflate gate” too. He wants to know which, of the soccer ball brands that we have at school, is more suitable for the competition. The school has 20 balls (10 Adidas and 10 Nike). You will determine which is the best brand for the competition, Adidas or Nike?. You need to understand the importance of this activity. We cannot afford to make mistakes. We will discuss how to calculate standard deviation through some examples before using the soccer balls. I can only teach you the mathematical process of finding the standard deviation, you have to be critical thinkers and give meaning to the results.
It is time to work on the soccer balls. We have a total of 20 balls and five pressure gauges. Each one of you will get a ball (get more balls if you have more than 20 students). I will model for you how to measure the pressure of a soccer ball. Each one of you will measure the pressure of your ball, pass the pressure gauge to the person next to you, and then use a marker to write your measure in the first column of the chart on the board that corresponds to the brand of your ball (there are 10 spaces for Adidas and 10 for Nike balls). When you have entered your data, begin writing the data from the board in the tables on your worksheet. Like the charts on the board, your worksheet has two tables, one for Adidas and one for Nike.
The students will calculate the standard deviation individually. The teacher will walk around the classroom and monitor student work, asking questions to check for understanding (formative assessment). When the students calculate the standard deviation, the teacher will give them a few minutes to check and correct their answers with their shoulder partner.
Suggested discussion for the teacher to use is below.
Ok, this is the big moment, the most important section of the lesson. You need to interpret your results in order to respond to the essential question of the lesson (Which brand of soccer ball is the most suitable for our next soccer season?) I want you to individually respond to all of the questions on the worksheet. Please reflect back to the test scores example and remember the great insights you offered when you analyzed the standard deviation and its correlation with the mean. Think about the information you deduced from the standard deviation. Logically, every context is different.
Questions to consider:
- Should our school use the Adidas or Nike soccer balls?
- Explain your reasons why we should use Adidas (Nike).
- Explain your reasons why we should NOT use Adidas (Nike).
- Did you find any outliers while collecting the data?
- Do you think that an outlier in one of the data sets (Adidas or Nike) would have made a difference in deciding the most appropriate brand? Justify your answer (increasing rigor).
Ok, before I collect your worksheets, we are going to use a Kagan strategy to increase our understanding and interpretation of the standard deviation that we calculated for the air pressure of the soccer balls. Remember, this is an important decision for our school. I will play the music and you will roam around the room. When the music stops the person next to you will be your partner for the activity.
The students will discuss their answers from their worksheet with their partner and later with the teacher.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
After the students exchanged ideas through the Kagan activity and consider new observations from the discussion lead by the teacher, they will edit their responses to the questions on the worksheet. Finally, they will write a small paragraph responding to the guiding question of the lesson.
Have the students consider the following:
- Could the value of the standard deviation have been zero? Negative?
- What might explain the occurrence of an outlier in this data set? Would that outlier be included in calculating the standard deviation? Why or why not?
- The the air pressure in a regulation ball must be between 8.5 psi and 15.6 psi. If the mean was 9.01 for the Nike Balls and the standard deviation was 1.66, would this affect your response to Question 1 on Worksheet 2?
The students will complete the questions on the back of Worksheet 2: Adidas or Nike? (Answer Key provided)
Students answering questions from Worksheet 1. The students will calculate the standard deviation individually. The teacher will walk around the classroom and monitor student work, asking questions to check for understanding.
Teacher-Student discussion about their interpretations from Worksheet 1.
Students writing to answer the guiding question.
Feedback to Students
The students will receive feedback throughout the entire lesson. They will receive feedback from the teacher when they complete the questions from Worksheet 1 and Worksheet 2. They will also receive teacher feedback from the Teacher Led Discussion sections. Moreover, the students will provide feedback to each other when they participate in the Kagan Cooperative Learning Activity. The students will use feedback to improve their performance by editing their responses from Worksheet 2 and answering the guiding question.