Topic:
Math - Histogram graphs
Objectives:
Students will understand the concept of histograms and the importance of using and reading
histograms correctly.
Students will be able to display and interpret data in a histogram.
Materials needed:
Print off four graphs for each student. You may use this free PDF from TeacherVision.com:
http://www.teachervision.fen.com/tv/printables/bargraph.pdf
Have colored pencils or crayons available to each student (optional).
Have empty Kleenex boxes or shoe boxes for each group of 3 students.
Have scrap pieces of paper, each student needs a piece of paper for each group in the class.
Available internet
Strategies:
Introduction:
Before class starts, have the shoe boxes spread around the outside of the room. Each shoe box
needs writing utensils and enough scrap paper for each student.
Form the class into groups of three students. Have each group think of a numerical question
such as “How many hours of sleep did you get last night?” or “How many minutes are your
showers?” or “How many hours do you watch TV a day?” or “What is your favorite time of
day?” Once they confirm their question with you, have them write that question on a piece of
paper and place it next to a shoe box. If some groups finish before other groups, have them
discuss how they think that the class will answer their question. The answers do not have to be
within any numerical range.
Once all of the shoeboxes are ready, each student should go to each question and put their
individual answer on the scrap paper and place it in the shoebox. (Each student should
individually answer.) Once finished with this, the groups will gather their answers and work
through the lesson with teacher direction. (Teachers are encouraged to make their own
shoebox as well to help understanding.)
Lesson steps:




Begin by setting the shoebox activity to the side.
Explain the concept of a histogram
o Students should know some different types of graphs, such as circle graphs, bar
graphs, or line graphs. Review this concept if necessary.
o Histograms are another type of graph. It is a bar graph that is used to display and
organize data. This bar graph is displayed mostly in equal intervals. That is that
the x-axis is not a specific number, but equal groups of numbers. Show students
an example of a histogram and explain each part: the title, the y axis is the
frequency, and the x-axis is our intervals. You may use this link:
http://www.tutorvista.com/q/statistics-analyze-and-interprethistograms/88105/
Explain how to construct a Histogram. This will use the introduction to the lesson.
o Organize the answers from smallest to largest numerically. Explain how you
would find equal intervals for your question. Then have the groups decide on
where to set their intervals. Go around and monitor each group.
o Then make a chart. As you fill in your chart, have them fill in theirs as a group.
Interval
Tallies
Frequency
o Then construct the bar graph. Construct yours along with the students so that
students can follow along, either using a doc camera or smart board. Stop
between steps to check for understanding and clarifying.
o Use the graphs printed from earlier. Have each student make their own
graph of the shoebox activity.
o Label the x and y axis and the title
o Create the intervals along the x axis
o For each interval, draw the bar to the necessary height.
o (optional) Students may color these graphs for clarity.
Then return to the above link or use your own histogram and ask questions. From the
link above, you could ask “What is the difference in the number of directors that make
3-4 movies and 5-6 movies?” or “How many movies, based on this graph, is a director
most likely to direct in his/her career?” Answers would be 5 to the first and 3-4 or 11-12.
Other questions may be asked.
o Ask students to individually make a new histogram to the one in the link. Have
the intervals be 0-4, 5-8, 9-12. Students could brainstorm and write down
difference they find in the two graphs, the pros and cons of each graph, and


which graph would they use. Discuss what they wrote down. Talk about why a
graph is more accurate. If conflicting ideas, have them debate their case. Then
ask how many directors make 7 movies. The answer would be that there is no
way to tell using this graph.
Make one more histogram with the students (have them fill their sheets out as well)
using this data. Hours of rain in one week in different cities around the United States: 3,
0, 9, 1, 4, 2, 0, 3, 6, 14, 4, 2, 5, 3, 7, 3, 0, 8, 3, 10
o Organize the data: 0, 0, 0, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 6, 7, 8, 9, 10, 14
o Make a chart:
Interval
Tallies
Frequency
0-3
IIIIIIIIIII
11
4-6
IIII
4
7-9
III
3
10-12
I
1
13-15
I
1
o Construct a Histogram
Finally, ask students about the importance of histograms. Have them journal about how
histograms could be used in the world and which occupations make use of this type of
graph. Discuss the importance of reading them correctly. Discuss some potential flaws
of histograms.
o Histograms organize data that is easy to interpret. Many different occupations
use histograms to predict outcomes, find stats for athletes, find average salaries,
etc.
o Reading them correctly means interpreting data correctly. This makes labels
extremely important.
o Flaws could be in the data, in the labeling, or in the graphing. Just because data
is in a histogram does not make it true!!
Closure:
Explain the assignment to students. Remind them of their project and how this will help
their report. Ask for any additional questions, and have them start on their assignment.
Assignment:


Have students visit http://www.almanac.com/weather/history/states
This assignment should be done individually, but they will have their group working on the exact
same region if questions arise.






On this website, students should enter the location their project group was assigned.
They should choose the date of the day that it is today and look at the weather of the
past years on that date. Remind students that this is a good start to their project!
Students may either make a histogram about the temperature or precipitation.
Students should collect data from the past 20 years. If certain students are
overwhelmed by how much data 20 years produces, have them collect 10 years or less.
The x-axis would be intervals of temperature or precipitation. The y-axis will be the
number of years that it reached those intervals.
Students should turn in both their chart and graph.
Give them time at the end of class to get research done in case some of them do not
have internet access at home.
If the textbook has a section on histograms, you may assign questions from that chapter
to check for understanding and ability to interpret histograms. If the textbook does not
have quality questions, ask students questions about their graph that they turn in. These
could include:
o What is the highest temperature/most rainfall in that city?
o What range of temperature or amount of precipitation is most likely? What is
the least likely temperature to occur?
o What percent of years have a temperature/precipitation in this interval?
o In what year was the lowest temperature/precipitation? (Cannot be determined
by the graph alone.)
Rubric:
Category
Level 1: Minimal
Competency
Level 2: Basic
Competency
Data
Students do not
have enough
data, and their
data is incorrect.
Students do not
complete a
histogram.
Students have
minimal data.
Students are not
able to answer
questions
correctly.
Histogram
Questions
Level 3:
Advanced
Competency
Students have
most of the
necessary data.
Level 4:
Outstanding
Competency
Students have
necessary data.
Students create
a histogram
without labels or
intervals.
Students create
a correct
histogram.
Students answer
some answers
correctly.
Students answer
most questions
correctly and
show
understanding.
Students create
a correct
histogram that is
neat and well
organized.
Students answer
all questions
correctly and
show
understanding.
Evaluation:
Students will be evaluated through in-class work and observation to show understanding in the
importance of correctly using and reading histograms. Students will show ability in creating and
displaying a histogram through the assignment with the chart and corresponding graph.
Students will also show skills of interpreting graphs correctly through a book assignment or
answering questions about their work.