College Freshman Entrance Data

Lesson Content

• 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 be able to identify how mean, median, and standard deviation are used in normal distributions.
  • The student will be to distinguish between appropriate and inappropriate data sets to determine normal distribution and skewness.

• Prior Knowledge: What prior knowledge should students have for this lesson?

  
  

  Students must know how to calculate central tendencies of a data set using technology.

  Students must know that standard deviation is a measure how spread out numbers are in a data set.

• Guiding Questions: What are the guiding questions for this lesson?

  
  

  What does it mean to be normal?

  How can we determine if data has a normal spread?

• Teaching Phase: How will the teacher present the concept or skill to students?

  
  

  Note: This is an introductory lesson to this standard and only informally asses the fit as normal.  Further lessons should include the use of the empirical rule and seeing if the minimum and maximum value actually fall within or outside of 2 standard deviations. Further analyses can be made of the quantile plot as well for how well the data fits a normal distribution using the free software GeoGebra.

  The teacher will present students with the following lesson parts:

  1. Formative Assessment: vocabulary review as outlined above in formative assessment.

  2. Guided Practice:

  The teacher will guide students through attached College Freshman College Entrance Data Whole Class Data Set on pages 1 and 2 of worksheet.

  Students in their groups will study the Whole Class Data Set of the average SAT math scores of the top 36 universities in the country.  

  When guiding students through question 1, the teacher should ask students to clearly state what they believe "normal distribution" is.

  During question 2, students should closely examine the table and determine if the data set is normally distributed based on their personal definition. Students are to predict whether or not the data will be skewed right, skewed left, multi-peaked, or normal distribution.

  For number 3 as a whole class, students should calculate mean and find the median using technology as the teacher models using technology used in the classroom (Excel, Geogebra, or graphing calculators).

  Now number 4 should be answered using the graph. The teacher should guide students through these process and ask students to re-examine their answers to numbers one and two.

  After the class makes their own conclusions, the teacher must discuss what qualifies a data set for normal distribution. Discuss that Normal Distributions should have the following characteristics: Mean = median = mode. This assures that the data is basically symmetric and has an axis of symmetry at the mean (or median or mode). Data also must be unimodal so that it doesn't look like a camel hump or rectangle.

  

  Teach students that data that is skewed left has a long tail to the left, as follows:

  

  A distribution that is skewed right has a long tail on the right:

  

  The teacher should tell students the mean, median, and mode should all be equal in order for data to be considered normal distribution. However as with this data set in real life distributions the graph is normally distributed even though mean and median are close in value but not equal.

  3. Independent Practice:

  After guided practice, each group will be randomly given 1 of the 3 different sets of college data from the worksheet (pages 3-8). They will calculate and predict as a group whether or not their data set is normally distributed. Students in their groups will repeat the steps taken during the guided phase and assist each other with finding the proper conclusion.

  Groups will present their findings using white boards or classroom Elmo when work is completed. Class discussion will compare groups that have the same data as well as groups that have different data. They should understand from the histograms what data appears normal, skewed left or skewed right. Class should discuss why these differences in data distributions.

  Example: Cost of University is skewed left because top colleges mostly have higher tuition and costs.

  Example: College acceptance rates are skewed right because top colleges have many applications but can only accept a few of their applicants to minimize growth of their colleges.

  4. Closure and homework assignment:

  To wrap up the lesson after discussion of the results of the independent practice, the teacher should have students quickly complete the attached performance task. The teacher can use answer to task to review the lesson objectives.

  Students should then be given the attached homework assignment on Florida Colleges' Math SAT scores for student to complete and turn in the next day.

• Guided Practice: What activities or exercises will the students complete with teacher guidance?

  
  

  The teacher will guide students through attached College Freshman College Entrance Data Whole Class Data Set on pages 1 and 2 of worksheet.

  Students in their groups will study the Whole Class Data Set of the average SAT math scores of the top 36 universities in the country.

  When guiding students through question 1, the teacher should ask students to clearly state what they believe "normal distribution" is.

  During question 2, students should closely examine the table and determine if the data set is normally distributed based on their personal definition. Students are to predict whether or not the data will be skewed right, skewed left, multi-peaked, or normal distribution.

  For number 3 as a whole class, students should calculate mean and find the median using technology as the teacher models using technology used in the classroom (Excel, Geogebra, or graphing calculators).

  Now number 4 should be answered using the graph. The teacher should guide students through these process and ask students to re-examine their answers to numbers one and two.

  After the class makes their own conclusions, the teacher must discuss what qualifies a data set for normal distribution. Discuss that Normal Distributions should have the following characteristics: Mean = median = mode. This assures that the data is basically symmetric and has an axis of symmetry at the mean (or median or mode). Data also must be unimodal so that it doesn't look like a camel hump or rectangle.

  

  Teach students that data that is skewed left has a long tail to the left, as follows:

  

  A distribution that is skewed right has a long tail on the right:

  

  The teacher should tell students the mean, median, and mode should all be equal in order for data to be considered normal distribution. However, as with this data set, in real life distributions the graph is normally distributed even though mean and median are close in value but not equal.

• Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?

  
  

  After the guided practice, each group will be randomly given 1 of the 3 different sets of college data from the worksheet (pages 3-8). They will calculate and predict as a group whether or not their data set is normally distributed. Students in their groups will repeat the steps taken during the guided phase and assist each other with finding the proper conclusion.

  Groups will present their findings using white boards or classroom Elmo when work is completed. Class discussion will compare groups that have the same data as well as groups that have different data. They should understand from the histograms what data appears normal, skewed left or skewed right. The class should discuss why these differences in data distributions.

  Example: Cost of University is skewed left because top colleges mostly have higher tuition and costs.

  Example: College acceptance rates are skewed right because top colleges have many applications but can only accept a few of their applicants to minimize growth of their colleges.

• Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?

  
  

  To wrap up the lesson after discussion of the results of the independent practice, the teacher should have students quickly complete the attached performance task. The teacher can use answer to task to review the lesson objectives.

  Students should then be given the attached homework assignment on Florida Colleges' Math SAT scores for student to complete and turn in the next day.

• Summative Assessment

  
  

  The teacher will assess the students on the lesson objectives with the attached homework assignment. It can be collected and checked the next class day.

• Formative Assessment

  
  

  Warm Up: Vocabulary Review

  To review, students will be given 5 minutes to write out definitions of the following terms: line of symmetry, mode, mean, median, and standard deviation.

  Possible definitions:

  1. Line of symmetry is the imaginary line where you could fold the image and have both halves match exactly.
  2. Mode is a number(s) that appears most often.
  3. Mean is the average of the numbers.
  4. Median is the "middle" of a sorted list of numbers.
  5. Standard deviation is a measure of how spread out numbers are.

  
  The purpose of this assessment is to assess whether or not the students have a working understanding of the vocabulary used during lesson. The instructor should reiterate the definition of vocabulary words throughout lesson.

• Feedback to Students

  
  

  When they are completing the warm up definitions and the first part of attached College Freshman Data Class worksheet, the teacher should make sure that students understand the correct responses. This is especially true of number 4 on worksheet since this sets up understanding of normally distributed data.

  Students will partner check each other's responses during work. During the independent practice phase, students will be working on different data sets. The teacher can monitor student work as needed.

  The teacher can also give written feedback on the College Application Distribution Performance Task, which is attached, as well as the homework assignment.