Variability

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Objective

SWBAT calculate range and quartiles and use them to describe the variation of a distribution of data.

Big Idea

Students work independently and in pairs to identify quartiles and interquartile range and use measures of variability to compare data.

Do Now

10 minutes

Students enter silently according to the daily entrance routine. Today they are all greeted at the door with a bright “Good morning!” and I hand them their Do Now worksheet. I make sure I am extra peppy and welcoming Monday mornings, they’re usually rough. I also decide to start today with upbeat music in the background. Inevitably, I know I will have some singers during the first 6 minutes of class. The plan is to turn the music off if most of the class is getting off task due to the tunes, giving the message, “I’m sorry guys, I thought you could handle working and listening to music at the same time. You will get another chance to show me with your actions that you can handle that later in class”. If all goes well though, I will run the first 6 minutes of class with music and a timer displayed on the SMARTBoard counting down.

At the end of 6 minutes, I mute the sound of the music and greet the students once again. I ask one student to tell me what they did over the weekend and then I begin reviewing the Do Now by having one student read the first question. Students raise their hands for A, B, C, or D, as I ask which letter was chosen in order. Most students correctly respond an answer as C, the range. To check for understanding I ask students, “and what does the range describe in this problem?”  I’m looking for the answer, “range describes the variation”. 

Discussion about variation and center are supremely important as these are the central ideas behind 7.SP.B.4. Students must be able to examine the center and variability of data and use these observations to compare two sets. Interquartile range is a measure of variation that we review in this unit. In order for students to be able to calculate the interquartile range, they must be able to identify quartiles. This Do Now is geared toward exploring quartiles by asking students to divide the list of numbers into 4 groups. One common misconception is asking students to split the data into 4 groups. Many students do not understand that it is the amount of values that are being separated into 4 groups. In question 2, I ask students to fill in blanks with values that “fit within the given range”. I want students to come up with their own numbers to illustrate the point that it is not the values themselves that matter – it is the number of values that determines how to divide the list into 4 groups. This is a major understanding for identifying quartiles and this understanding graphs like box-and-whisker plots. MP1 is at work here as we make sense of the purpose of quartiles as well as interpreting the values at each quartiles. 

Check TS

10 minutes

Thinking Skills is a period of the day each morning, from 7:25 – 8 am, where students work independently to complete a worksheet or reading provided by a different 7th grade teacher. On Mondays students' work on Math Thinking Skills. I include material that has already been taught and needs to be spiraled, or I include articles that have some mathematical relevance to what we are studying that week. I usually collect these worksheets, grade them, and return them to students with an opportunity to make up the grade. Since the ELA state test is getting closer, I decided not to grade this Thinking Skills and instead turn it into a game to keep students motivated to continue refining their reading skills. Students are asked to enter their answers to the three questions included in the Thinking Skills into clickers and then give me a thumbs up to let me know when they are ready to see the 4 additional questions to be clicked in. I was fortunate to have help from some reading and writing teachers at my school with the first three questions and then created the last 4 questions myself, attempting to tie in comprehension and math. Once students have clicked in all of their answers I stop the assessment and display the top 3 scores, whom earn homework passes.

The assignment is included in this section and its purpose is to educate students about the census (a real world connection to statistics) while also helping students sharpen their reading comprehension skills before the ELA test.

Class Notes

15 minutes

 

After celebrating the winners of the Thinking Skills check, class notes are distributed. The red font in the resource document is written on the blackboard and students are responsible for copying it down. We begin by filling out the heading and then copying the aim. Then,

  • One student reads the definition of range (written on the board) and how to find it.   
  • Students are asked to discuss and share out the meaning of “measure of variability
  • Student pairs are also asked to complete the example to show that they understand the definition: 
    • Ask “the range is ___. Explain how this is a measure of variability
  • Discuss other types of sample questions that require the range
    • By how much do they vary?
  • Explain that there are other, more detailed ways to analyze variability, or by the amount values vary from each other in a set of data.
  • Review  the definition of quartiles and how to find them
    • To find it: first find the midpoint of the data. If there are an odd number of values, the midpoint, or Q2, will be the middle value. If there is an even number of values, the midpoint is the average of the middle two values.  The first and the third quartiles are located at the midpoints of the first and second halves. This skill often needs lots of review. This is where I would like to spend most of the class notes time with students practicing how to find quartiles in randomly generated data sets. I use a random number generator online to create at least three different lists for students to copy and use to practice this skill.
  • Review examples where range is equivalent and quartiles inform variability a different way:
    • Two 7thgrade classes are surveyed for the number of slices of pizza they would eat for dinner. Each class has 15 students. The dot plot below shows the answers given by each student.
      • Discussing the meaning of equivalent ranges vs. different quartiles and interquartile ranges engages students in MP2, reasoning abstractly bout the meaning of the differing measures of variability and the information they provide about each set of data.

 

Got it?

10 minutes

Next, students are asked to complete the back of their notes page in pairs. It will review how to find interquartile range and ask questions targeted at identifying quartiles in percentage form. Walking around and listening to what students are discussing will inform the topics and misunderstandings I need to review at the closing of class.

I show students the following line plot. One student is selected to review finding the quartiles on the board with the help of multiple students in the class. 

After having a chance to work in pairs and ask questions to review the sample line plot, students will work independently on a task that will assess their ability to complete the same activity on their own. This sheet also includes a self-assessment that will help inform the material I need to review and spiral the next day. 

 

Closing

10 minutes

After all students have completed their “exit” slips (“Got it?” wksht), I review some of the most commonly elected topics in their self-assessment portions.  It is announced that homework will be graded, thus students must understand how to find the quartiles and what they mean in order to earn the best grade possible. If there are no other questions, students may begin the homework sheet.