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,
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.
Have students access at least one of these web sites for data collection:
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|