Illuminations: How Do You Organize the Counties in Your State?

How Do You Organize the Counties in Your State?

Comparing Counties

Students use the data from previous lessons to find the range, median, and mode of the populations. They then compare their data with their partner's data.

As a culminating activity, this lesson combines the data and activities performed during this unit. Students are involved in class discussions and comparisons of the population data.

Learning Objectives
 
Students will:
  • compare numbers by ordering data from greatest to least
  • find the range, median, and mode of their U.S. Census data
  • organize and display data from the U.S. Census
  • represent data using tables and graphs
  • analyze data
  • describe important features of the set of data

Materials
 
Index cards from Lesson 2
Chart paper
Data collected in previous lessons

Instructional Plan

Students begin by reviewing the data from the previous 2 lessons. They can use their index cards made in Lesson 2 in this unit. They proceed as noted below.

As students complete each step, discuss with them the greatest populations and the least populations.

Students should be engaged in the following activities:

  1. Arranging the populations in order from least to greatest
  2. Underlining the greatest and least population
  3. Subtracting the least from the greatest to find the range
  4. Using the ordered data to find the median, or middle number
  5. Finding the number that occurs the most or the mode

Students should record their own ranges, median, and modes on a piece of paper.

Depending on students' prior experiences in finding range, median, and mode, you may need to provide direct instruction in these skills.

Once each student has found the range, median, and mode for his or her set of data, match each student with a partern. Each student should share his or her data and make comparisons between the two sets. How close was each statistic? Did any student notice anything unusual about their data?

 

Culminating Activity

Students begin the final activity by reviewing the data collected throughout this series of lessons. This lesson will be partly whole class and partly in groups. Students should brainstorm possible ways to figure out the most frequently chosen county. Using the spreadsheet might be the easiest way to compare the data, as students could work in groups to gather group statistics first and then report to the class. You should record the counties most frequently picked on a chart. For example, you may choose to use a tally chart. Decide what characteristics this county has that might have made it the most popular.

Have children discuss in groups the populations of the most frequently picked counties. List the populations on the chart of the most frequently picked counties. Discuss possible uses for the collection of this data. Discuss other information you could gather with this particular data.

Questions for Students
 

Would the range, median, and mode be the same if you arranged the populations in order from greatest to least rather than least to greatest?

[Yes, as long as the data is in order, the median doesn't change; ordering data does not affect the mode or range.]

How do you find the range of a set of data?

[Find the difference of the largest data and the smallest data.]

How do you find the median of a set of data?

[Order the data from least to greatest or greatest to least, and then find the middle number.]

What would happen to the median if you left out one of the populations?

[The median would be "shifted".]

If there were an even amount of numbers in your data, how would you find the median?

[Find the average of the two middle numbers after they have been ordered.]

What is the mode? Is it always the same as the median?

[The mode is the number that appears the most often. It may or may not be the same as the median.]

If all the numbers are different, is there a mode? Can there be more than one mode?

[In that case, there is no mode; Yes, there can be more than one mode.]

Which statistic is better: range, median, or mode?

[The answer depends upon what kind of information you need.]

What correlations do you see between the most frequently picked counties and their populations?

[Student responses may vary.]

How do these counties compare to your home county?

[Student responses may vary.]

What occupations would benefit from the data you collected during this set of lessons?

[Answers may include advertisers, shopping mall developers, Federal Government employees, etc.]

Assessment Options
 
  1. Have students record their data on separate sheet of paper to be turned in. This should be a good measure of their ability to compute the range, median, and mode.
  2. As you monitor students’ participation and involvement in paired work, you can assess their understanding of the statistical process. Continuing to monitor their analysis of the data can be a valuable tool in assessing their growth on these skills.

Extensions
 
  1. Using the index cards made in lesson 2, students can work in a different pair and combine each member's populations to find the range, median, and mode.
  2. Students could also pick 2 cards from their 10; then assign students to different pairs, and combine their cards. Ask them to continue by analyzing their populations finding the range, median, and mode.
  3. Students can use their spreadsheet files to find the range, median, and mode using the formulas (functions) provided by the software.

Teacher Reflection
 
  • What other ways can the students organize into groups to offer other options of practice of range, median, and mode?
  • Could this lesson be done after lesson 2 or does it help to have the students organize the data into a spreadsheet first?
  • Is there any other way you could use the population data?
  • What different methods of graphing did the students choose?
  • Did the students understand the importance of collecting this data?
  • Where students able to find the relationship between the population of each county and the most popular county picked in the class?

NCTM Standards and Expectations
 
Data Analysis & Probability 3-5
  1. Collect data using observations, surveys, and experiments.
  2. Recognize the differences in representing categorical and numerical data.
  3. Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
  4. Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set.
This lesson prepared by Grace M. Burton and Carol Midgett.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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