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Comparing Columns on a Bar Graph

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

During this lesson, students apply what they know about comparison subtraction by constructing bar graphs and using the graphs to answer questions.

Have the students indicate their favorite juice by choosing a like-colored connecting cube, for example, red for tomato juice, orange for orange juice, yellow for apple juice, and purple for grape juice. Record this data on the chalkboard.

334 Juice

Then ask four volunteers to each collect all the cubes of one color and snap them together. Place the connected cubes side by side to form a bar graph. Then ask such questions as “How many more children liked orange juice best than liked grape juice best?” Encourage children to pose related questions and call on classmates to answer them. Then model for the students how to translate the cube graph to a graph on paper. You may wish to model the bar graph on the overhead projector.

pdficonGraph Paper 

The example below shows the following results:

tomato juice (2), orange juice (8), apple juice (10), and grape juice (6).

Encourage students to draw the bar graph on their own graph paper.

334 Sample bar graph

Students should record, on paper, some questions that they answered from the bar graph.

appicon Bar Grapher Tool 

Next, open the Bar Grapher Tool and project for students to see. This tool allows you to enter your own data and graph it, or you may use pre-selected data and graph it. Create a bar graph for students to view. Once you have created the bar graph, pose questions which require students to use subtraction to compare. (Note: It would be best if you enter your own data for this class example, so the numbers are whole numbers and are relevant to the students' lives.)


Distribute additional graph paper to the students and have them write their first names, one letter to a square, in the first row. Then have them write their last names in the second row. Now ask them to generate subtraction equations about the comparison of the letters in their first and last names and to share these with their classmates. [Example: "Becky Burton" would suggest the subtraction equation 6 - 5 = 1.]

Questions for Students 

1. What information did our bar graph show?

[Our bar graph showed people's favorite types of juices.]

2. Which juice was the favorite? Which was second? How many more children liked the first juice than liked the second?

[Answers will depend upon the actual class data.]

3. Which of the juices was the least favorite? How many fewer students liked the least favorite than liked the second least favorite juice?

[Answers will depend upon the actual class data.]

4. Suppose two more children had chosen orange juice. What would have happened to the graph?

[The bar for orange juice would have increased by 2.]

5. How many children voted in this survey? How did you determine that? Is that number more than 20? How many more?

[Answers will depend upon the actual class data.]

Teacher Reflection 
  • Which children have demonstrated an understanding of subtraction? What extension activities are appropriate for those children?
  • What would you do differently the next time that you teach this lesson?

Learning Objectives

Students will:
  • Construct bar graphs.
  • Use subtraction to process data from a bar graph.

NCTM Standards and Expectations

  • 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.