Prior to the beginning of this lesson, you will want to find a website listing all of the presidents and their party affiliation. A simple search on the internet should provide viable options. You may also choose to bookmark this site such that students have easy access to the chosen resource.
Start the lesson by engaging students in a discussion about the
Presidents of the United States. You might ask: What factors influenced
our last presidential race? Are there typical characteristics of a
person running in any Presidential race? There are many answers to
these questions. If no students suggest party affiliation and age at
the time the person enters office, bring these characteristics into the
Discuss the data provided for each president with the class.
Use questions to structure the discussion. What is the difference
between raw data and summarized data? [Raw data is the individual
values while summarized data is presented in a way for analyzing the
data.] If I wanted to find the number of Presidents in each party, how
could I summarize the data? [Frequency table, bar chart, line chart,
and/or histogram.] What would be the title for the columns of the frequency
table? [Political Party, Frequency.]
While distributing the Charting the Difference Activity Sheet, divide students into pairs a computer for each pair to
share. If fewer computers are available, groups of 3 can be used with
assign roles, such as announcer, recorder, and checker. However, avoid
groups with more than 3, as there will be students with nothing to do.
Charting the Difference Activity Sheet
Remind students on how to record data in frequency tables. Have them record the frequencies in groups of five tally marks.
As students begin their bar graphs for the political party data,
check the graphs being created for correctness. Ask questions to help
struggling students. How is the frequency scaling determined? [by the
range of the frequency column] What should the frequency scaling be
based on the lowest and highest frequency? [0-20 with marks at 5, 10,
15, 20] Since the political parties are separate categories, makes sure
students' bars do not touch each other but are of the same width.
Circulate through the room as students work on the inauguration
ages frequency table, asking questions like the following examples to
- What is different about the data being collected in this frequency table?
[The data is numerical, not categorical like the previous table.]
- Are we going to list every age at inauguration to summarize the data?
[No, there would be too many rows.]
- What intervals of numbers might work better? How many intervals will there be?
[Decades might work, but there would only be 3 intervals,
which would not make the graph very informative. Intervals of 5 years
would be better because then there would be 6 categories.]
- Did the order of the political parties matter in the previous table? Does it matter in this table?
[The categories in the first table are not related so they
can be in any order. In this table, it makes sense for the categories
to be in ascending or descending order since the categories are
intervals of numbers.]
After all groups have finished, have the groups compare answers in a
class discussion. Call on students to give their answers to the
questions. As they do this, point out in ages at inauguration frequency
table that the categories are numeric intervals in an increasing order
with no gaps between the numbers. The graph also has no gaps between
the bars. This is because there is no gap between the numbers for the
ages. For example, one bar ends at 44 and then next starts at 45. This
is a difference between the two frequency tables and this affects the
graphs. To check for understanding, ask students: Why is it the bars in
bar graphs do not touch and the bars in histograms do touch? [Bar graph
bars do not touch because the data is categorical; histogram bars do
touch because the categories intervals of continuous numbers.]
While students share their generalizations from Question 5, use questions such as those in Questions for Students
to show that some answers cannot be determined by the graphs but may
have to be researched using the raw data or using other sources.
Summarize Question 6, draw a table on the board with a column
for characteristics of bar graphs and a second column for
characteristics of histograms. A representative from each group can
then add an observation to either or both columns, comparing and
contrasting the attributes of the different graphs. Allow students to
add statements one group at a time without repeat a prior statement.
This will become more difficult as more groups go, so try to choose
groups with longer answers to Question 6 after groups with shorter
answers. A partially complete table may look like this:
|graph title and labeled axes||graph title and labeled axes|
|Bars do not touch.||Bars do touch.|
|Vertical scale is frequency.||Vertical scale is frequency.|
|categorical data||numerical data|
Charting the Difference Answer Key
Questions for Students
1. Why are there more Democratic and Republican Presidents than Presidents from other parties?
[These have been the dominant parties in the United States
for most of the country's history. The other parties are older. For
example, the Whig party eventually became the current Republican party.]
2. When you are old enough to vote, do you think there will be the same 2 major parties?
[Answers will vary.]
3. Were there any other parties on the ballot during the last election?
[Yes. This changes with each election. Encourage students
interested in the political parties to continue their research after
4. What age range were most presidents’ ages on their Inauguration Day?
5. Who was the youngest president when inaugurated? Where did you find your answer?
[Theodore Roosevelt; the raw data.]
6. Who was the oldest president when he took the Oath of Office and where did you get this information?
[Ronald Reagan; the raw data.]
7. How many Presidents died in office?
[8: Garfield, Harding, Harrison, Kennedy, Lincoln, McKinley, F. Roosevelt, and Taylor.]
8. How many Presidents are still living?
[Answers will vary depending on when this lesson is used.]
- Did the students remember how to make proper Frequency Tables?
- Were the students comfortable using the internet to gather the data?
- Do the students remember to include titles, scales, etc. in their Bar Charts and Histograms?
- Did students use the data from the web site to make additional conclusions?
- Did all students participate in the group activity?
The students will:
- Summarize raw data in a frequency table.
- Determine the category of the data as categorical or numerical.
- Create the appropriate chart (histogram or bar chart).
- Analyze data using histograms and bar charts.
NCTM Standards and Expectations
- Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.
- Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
- Design investigations to address a question and consider how data-collection methods affect the nature of the data set.
- Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
- Recognize the differences in representing categorical and numerical data.
Common Core State Standards – Mathematics
Grade 3, Measurement & Data
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ''how many more'' and ''how many less'' problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
Grade 7, Stats & Probability
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Grade 8, Stats & Probability
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
Grade 6, Stats & Probability
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
Grade 7, Stats & Probability
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
Grade 7, Stats & Probability
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
Grade 8, Stats & Probability
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
Common Core State Standards – Practice
Make sense of problems and persevere in solving them.
Model with mathematics.
Use appropriate tools strategically.
Look for and make use of structure.