What's Your Frequency? Analyzing and Creating Frequency Tables and Line Plots

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Objective

The students will be looking at data to create, analyze and describe frequency tables and line plots (dot plots).

Big Idea

The students will be working with frequency tables and turning them in to line plots. They will be describing the data and making observations from the tables.

DO NOW

10 minutes

DO NOW:

The beginning part of this lesson is applying their knowledge of the measures of central tendency.  I choose this problem because I wanted to see what students could identify that the mean would be most affected by the outlier without having to calculate out the measures.  Students who know the mean is most affected by the outlier understand that when you have a number that is far away from the other data values it will affect the mean the most.  These students will not have to use the mean algorithm with and without the data value to understand the concept. A good way to get students talking about this is to do a partner share. (It may not always work on nicely for pairs)  Have students that did not have to do any calculations partner up with students that needed to do the calculations for mean.  This is a good way to let the high achieving students share their knowledge and understanding. 

Analyzing Frequency Tables

55 minutes

The lesson middle focuses on direct guided instruction.  Students will be looking at frequency tables with a variety of data (both numerical and categorical).  They will be required to create their own frequency tables using intervals. Additionally, it will be important to address a few questions to relate this to 6.SP.B.5

  • Students should be able to report how many people were surveyed
  • Students should be able to describe the data (shape, center, and spread)
  • To challenge, have students find the mean, median, mode and range of the data from the line plot

The student will work through a few tables and graphs with the teacher and then they will be given two opportunities to create and analyze on their own.  During this time, the teacher’s role is a facilitator.  Allow students to work on their own or solicit the help of other students.  To check for understanding, it may be beneficial to have students report back their findings to the group (team check) or to the whole class. When team checking, remind students to incorporate speaking and listening strategies, to use mathematical language (SMP6) and to support their answer with a reasonable argument (SMP3)

After students have completed creating their tables, have them work on the final two questions in the power point.  This can be shared as whole group or in partners or use think-pair-share to get more thoughtful responses.

 

Question 1:  Students should be able to say that there cannot be an overlap of numbers when using intervals.  Intervals need to be equal too

Question 2: Students should see that Caleb did not read the plot correctly.  The numbers on the number line indicate the ages of campers and the x’s indicate how many campers.  Caleb read the line plot incorrectly.

Closure

15 minutes

Before starting on the TV worksheet, ask the students the following questions to assess understanding of the learning objective. Questions will be discussed  whole group.

  • What components need to be in a frequency table (category, tally, frequency, and title)
  • Could you find the mean, median, mode and range from a frequency table?
  • When using intervals, explain what that would look like?
  • What can’t you determine when using intervals?
  • What components are in a line plot? (number line, x’s or dots, title)
  • Can you find the mean, median, mode and range in a line plot?
  • Can you tell how many people were surveyed in a line plot or frequency table?
  • How are a line plot and frequency table alike?

Question #6:  There is a common misconception when working with line plots and finding the mean.  Students have difficulty making the connection that the amount of x’s indicates the frequency of the event happening.  Hit this question hard.  Get kids to tell you how to find the mean (add up all of the data and divide by how many) then tell them to think about a line plot (what do the x’s represent).  So, if we want to find the mean, how would that look when writing it out?  Also, ask the students if there is a large number of data values, can we simplify the amount of information going in to the calculator?  My students want to put every number in the calculator and they run out of space.  We talk about trying to simplify our calculations.  I ask them how to simplify repeated addition, looking to get them to say multiplication.  So some students will write the value amount of the data above the x’s and then put that in the calculator. 

(TV watching, Navigating though Data Analysis in Grades 6 – 9, NCTM)

Allow students time to work on the TV watching worksheet.  This is an application problem that involves components learned thus far.  If students do not finish, they may take it home to complete.

If they are done, have the students compare answers with a partner or discuss whole group.  This could also be done as the DO NOW for the next day.