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Bar Graph Investigations

  • Lesson
Number and OperationsData Analysis and Probability
Grace M. Burton
Location: unknown

During this lesson, the students apply what they know about comparison subtraction by constructing bar graphs and using them to answer questions. They conduct a survey to gather data and then complete a bar graph. They also use the data to generate a bar graph using technology.

Ask the students to name their favorite kind of fruit. As they do so, write each one on the board. Then ask each student to place a tally mark next to his or her favorite fruit. When all have done so, ask what kind of fruit was named most often. Now display a large bar graph and call on volunteers to title the graph, label the rows with the fruits named, and fill in the number of squares in that row that is equal to the mentions that kind of fruit received. Now ask the students to compare the rows of the graph by posing a question such as, "How many more students liked apples than liked oranges?" Next, encourage the students to generate similar questions, and call on their peers to answer them.

Now assign the students to groups of four students each. Hold up a fan of index cards so that the students cannot see what is written on them and ask each group to take one card.

Note: Before the lesson, write on separate file cards survey questions and three or four answers. Such questions could include:

  • Which color do you like best: red, yellow, blue, or green?
  • What is your favorite pizza topping: pepperoni, mushroom, or plain cheese?
  • What ice cream flavor do you like best: vanilla, chocolate, or strawberry?
  • What is your favorite subject: math, reading, social studies, or science?

Next ask the group to make a tally chart on which they can record the answers to their question.

Tally Chart
Blue| | |
Red| | | |
Yellow| | |
Green| |

Encourage the students to think of a way that they can survey at least ten classmates. Allow plenty of time for the students to collect the data, and then ask them to make a bar graph.

Distribute Graph Paper to the students.

pdficonGraph Paper 

Students should create a bar graph on the graph paper.

When they have done so, ask them to think of four questions they can answer by looking at their bar graph.

Bar Graph


You may wish to circulate around the room to be sure that all students can enter their data on their bar graph. When they are ready, ask each group of students to tell the class what they know about their fellow students from looking at the bar graph that they have created. [Although the students may start with questions that can be answered by simply looking at the length of one bar, encourage them to ask questions that require the comparison of two or more bars as well.] Lead the students to notice which bar was the longest and which the shortest. [You may choose to tell them that the difference between these numbers is called the range.] Ask them to subtract to find the difference between the greatest number and the least number in their set of data.

Next display the Bar Grapher Tool.

appicon Bar Grapher Tool 

Now ask one group to enter their data into the recording section. Ask them to choose a name for the bar graph and the colors of bars that they would like for each bar. Then ask questions about the bar graph such as: How many more students liked red the best? Did more students like blue than liked green? Encourage the presenting group to pose other such questions and call on classmates to answer them. [The graphs are printable, so you may want to print a copy for a class display.] Then allow the other groups to enter their data and ask their questions.

End the lesson by encouraging the students to copy the bar graph and to write three things they learned from it for their portfolio.

Assessment Options 

  1. As students are generating bar graphs, you can record observations on the Class Notes Recording Sheet.
  2. Students may record some of the comparisons they made using the Fact Families Activity Sheet.
    pdficon  Fact Families Activity Sheet 

Questions for Students 

  1. What information did our first bar graph show? Which fruit was the favorite? Which was second? How many more students liked the favorite fruit than liked the second favorite?
  2. Which kind of fruit was the least favorite? How many fewer students liked that kind of fruit than liked (grapes) the best?
  3. Suppose two more students had chosen (oranges). How would the graph have been different?
  4. Look at this group's graph. (Choose one group's graph to display. As an example, assume it was a graph of favorite colors illustrated above.) How many students voted that red was their favorite? Is that more than the number that chose blue? How many more? What was the least favorite of the four colors? How many picked that one? How many students picked the favorite color of the class? (Repeat with each of the group's graphs.)

Teacher Reflection 

  • Which students were able to construct tally charts? Which were able to complete bar graphs with little or no help?
  • Did students remember to title their graphs and label the rows?
  • Which students were able to generate and answer questions based on data shown in a bar graph? Which could generate comparison questions?
  • Which group worked well together? What additional help is needed for students who worked less well together?
  • What will I do differently the next time that I teach this lesson?

Learning Objectives

Students will:

  • Conduct surveys to collect data.
  • Create bar graphs using the data from those surveys.
  • Use subtraction to analyze data from bar graphs.


NCTM Standards and Expectations

  • Understand the effects of adding and subtracting whole numbers.
  • Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  • Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  • Develop fluency with basic number combinations for addition and subtraction.
  • Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
  • Pose questions and gather data about themselves and their surroundings.
  • Represent data using concrete objects, pictures, and graphs.

Common Core State Standards – Mathematics

Grade 1, Measurement & Data

  • CCSS.Math.Content.1.MD.C.4
    Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Grade 2, Measurement & Data

  • CCSS.Math.Content.2.MD.D.10
    Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.