Math 103 - Classroom Activity #2

Math 103 - CooleyStatistics for Teachers OCC

Classroom Activity #2 – State Names

Using multiple representations, students analyze the frequency of letters that occur in the names of all 50 states.

Learning Objectives

Students will:

Determine the number of times that each letter of the alphabet is used when writing the names of all 50 states.
Understand how various representations, including steam-and-leaf plots, box-and-whisker plots, and bar graphs, can be used to organize the data.

Materials

Map of the United States (optional)
State Names Activity Sheet

Instructional Plan

Say to students, "Spell the names of all 50 states." Before they get too far in writing all the state names, ask the following questions as an introduction to this lesson:

Which letter will you use most? Which letter will you use least?
Will you use every letter of the alphabet? Are there any letters that you will not use at all?
Which state name has the most letters?

Allow students to speculate answers to each of these questions, and have them justify their guesses.

Display the names of all 50 states. (You can display the names as an alphabetical list, or you can simply display a map of the United States that shows the state names.) Ask, "Could you answer those questions just by looking at all of the names like this?" The point in asking this question is to make students realize that the data needs to be organized in a better way.

Then, have students use the State Names activity sheet to identify the frequency of each letter.

Circulate as students work, and observe their process. If students are not using a systematic approach, ask questions such as, "How will your method guarantee that each letter is counted exactly once?" To check student work, the following are the frequencies of each letter when all 50 state names are written:

Letter / Freq. / Letter / Freq. / Letter / Freq. / Letter / Freq. / Letter / Freq.
A / 61 / G / 8 / M / 14 / S / 32 / Y / 6
B / 2 / H / 15 / N / 43 / T / 19 / Z / 1
C / 12 / I / 44 / O / 36 / U / 8
D / 11 / J / 1 / P / 4 / V / 5
E / 28 / K / 10 / Q / 0 / W / 11
F / 2 / L / 15 / R / 22 / X / 2

As an alternative, students can use letter frequency tools that can be found on the internet to determine

how many times each letter appears. However, allowing students to determine the frequency by hand is valuable for two reasons. First, it gives students practice using a systematic process for organizing information. Second, and more importantly, the tick marks used to keep track of letter frequency will form a representation when the tally is complete; the number of tick marks indicates how often each letter occurs, and the amount of space required to record all of the tick marks gives a visual representation of the relative frequency.

Once the frequency analysis is completed, explain to students that the data can be represented in various ways.

Have students represent the data in three different ways: bar graph, stem-and-leaf plot, and box-and-whisker plot.

Questions For Students

Is it possible to determine which letter is used most in the names of all 50 states just by looking at a list of names? What is a better way to determine what letter is used most?

[Count the number of times each letter is used, and organize the data in a table or graph.]

What are some of the advantages of using bar graphs, stem-and-leaf plots, and box-and-whisker graphs?

[Bar graphs show the relative amounts of items in the data. Just by looking at the heights of the bars, you can easily determine which items are more common. A stem-and-leaf plot allows you to easily determine where most of the data occurs—at the upper end, the lower end, or in the middle. A box-and-whisker plot allows you to easily see how the data is divided.]

Assessment Options

1.Have students write a paragraph in their math journals about the advantage of organizing data in

bar graphs, stem-and-leaf plots, and box-and-whisker plots, as opposed to interpreting raw data. In addition, have them compare bar graphs, stem-and-leaf plots, and box-and-whisker plots, and indicate which representation is most useful.

2.Allow students to use the number of letters in the state names, state postal codes, or other sets of data to create various representations. (Using the data for the number of letters in each state name will allow students to answer the question, "What state requires the most letters to spell?", which was asked during the lesson but could not be answered using the letter frequency data.)

Extensions

Allow students to do a frequency analysis by including the Canadian provinces or the Mexican states when collecting data, or repeat the activity for these other countries in North America.

Students can use the State Data Map on the NCTM’s Illuminations Website to investigate other data about states. In addition to considering the number of letters in state names, students can also explore population, number of senators, gasoline usage, and other data sets.

NCTM Standards and Expectations

Data Analysis & Probability 3-5

Use measures of center, focusing on the median, and understand what each does and does

not indicate about the data set.

2. Compare different representations of the same data and evaluate how well each

representation shows important aspects of the data.

3.Describe the shape and important features of a set of data and compare related data sets,

with an emphasis on how the data are distributed.

4.Represent data using tables and graphs such as line plots, bar graphs, and line graphs.

5.Collect data using observations, surveys, and experiments.

Data Analysis & Probability 6-8

Select, create, and use appropriate graphical representations of data, including histograms,

box plots, and scatterplots.

References

This lesson was obtained from the NCTM Illuminations website. (

This lesson has been modified by TopCatMath.com. Originally created by Samuel E. Zordak.

State Names Activity SheetNAME ______

The names of all 50 states are listed below. Record the number of times that each letter of thealphabet is

used.

Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa KansasKentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire

New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota

Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming

LETTER / TALLY / FREQ. / LETTER / TALLY / FREQ.
A / N
B / O
C / P
D / Q
E / R
F / S
G / T
H / U
I / V
J / W
K / X
L / Y
M / Z

1.Which letter is used most often?

2. Are there any letters that are not used at all?

3. What state requires the most letters to spell?