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Data Analysis and Probability
Grace M. Burton
Location: unknown

Students make human bar graphs and circle graphs, then draw them on paper and use a Web site to generate them. Posing and answering questions using the graphs will give the students an opportunity to apply their problem-solving and communication skills. They will also find the mode for a set of data.

Bar Graphs

Invite the students to name the different ways potatoes can be prepared. The lesson begins with the collection and display of qualitative, that is, non-numeric data. Choose four of the ways to prepare potatoes (for example: French Fries, mashed, potato, or baked), and have the students write their favorite way from among those four on an index card. Draw a line on the floor (Various surfaces require different tools for denoting a line on the floor. Tape may be used on carpet. An erasable marker might be used on vinyl flooring.) Label four points, one for each way. Then ask the students to form lines behind the choice that they have written on the index card. Call on a volunteer from each line to count the students in that line. Now ask the students to step aside and make a column with their index cards, laying them flat on the floor. Ask the students to stand in a ring around the graph and notice how their cards take their places to form a graph. Instruct the students that they will now record their preferences in a bar graph by recording each card with their names on a set of axes you have drawn on the board.

1337 potato bar 

Now ask the students to title the bar graph and to notice which choice was most popular. Tell them that the most frequently selected item is called the mode. [In the example above, French Fries was the most frequently selected item.] Next, give them graph paper, and ask them to copy the bar graph from the board. Encourage the students to take turns asking questions that can be answered by looking at the bar graph and calling on classmates to answer the questions.

Circle Graphs

To prepare for this activity, cut four lengths of yarn that are five to six feet long. Now ask the students who picked salad to stand beside each other. (Give the last person in that line one end of a long piece of yarn. Place the other end of the string at a point that will become the center of a circle graph.) Have those who chose French Fries line up beside those who selected salad and give the last person a second piece of yarn. Repeat with the other two groups. Now ask the last student from the last group to walk around to make a circle by standing next to the first student who got in line. Stand in the middle of the circle and hold the other ends of the yarn lengths. Tell the students they have now made a circle graph or pie chart. (Students will form the circle with the last student in a particular category holding one end of the yarn and you will hold the other end of the yarn while standing in the center of the circle to complete the pie chart.) Next, invite the students to notice which part of the circle is the largest. Ask them how this compares with the bar graph. Then ask them how they could find the mode for this data set. [It will be the largest sector.]

1337 image3 

Next, log on to the National Library of Virtual Manipulative's Pie Chart. Call on a volunteer to enter the data from the bar graph of potato preferences. Then select a student to click on the "Draw Chart" command. Ask the students to share what they can learn from the chart about the potato preferences represented in the room. Now tell the students your preference and ask a volunteer to change the graph so that it now includes your preference. [Although students at this level may not be able to understand the percentages shown on the pie chart, they might enjoy seeing this popular graph. Pie charts, or circle graphs, are helpful in showing the relationship of a part to a whole or the relative relationships among parts.]

Now ask the students to sketch the pie chart and compare this forms of representation with the bar graph that they made earlier in the lesson. [A bar graph is a graph that uses bars to show data whereas a pie chart uses sections of a whole to show data.] Next, ask the students to visit the Create A Graph web site, choose "Bar" as the type of graph, and enter the data for the potato preferences. Print out the bar graph to pass around while you ask the students how the bar graph is similar to, and different from, the circle graph.

To provide a record of the lesson, ask the students to staple together their bar graph and circle graph of potato preferences and to write two questions that can be answered by looking at these representations. When they have done so, call on individual students to read their questions for the rest of the class to answer. Then collect these papers for the students' unit portfolios.

Assessment Option 

At this stage of the unit, it is important to know whether students can do the following:
  • Create bar graphs and circle graphs
  • Find the range, mode, median, and mean of a data set
You may wish to make entries on the Class Notes recording sheet concerning the progress of the students toward the learning goals in this lesson. Your observations about their strengths and needs can provide a basis for future enrichment and remediation planning. Such records will also be helpful to other teachers and volunteers who work with the students in your class.


Students may also wish to use one of the NCTM applets for creating bar graphs. They can use the Bar Grapher in place of the previously mentioned bar graphing tool, or they may use both tools and compare the graphs created.

appicon Bar Grapher 


Questions for Students 

1. What word did we use to describe the most popular preference for potatoes?


2. Suppose a new student came into the class, and we wanted to include her vote. How would that change our graph? The mode?

[One of the bars in the bar graph would be higher, and one sector of the circle graph would be larger. The mode would only change if the new student chose the most popular potato.]

3. Can we tell from the bar graph which type of potato each student liked best?

[Look at the height of the bar, and then look at the vertical axis.]

Teacher Reflection 

  • Which students could identify the mode in each representation?
  • Were all students able to form questions that could be answered by looking at the representations? Were they able to answer the questions posed by other students?
  • Could they compare the characteristics of the graphs?
  • Which of the students could write clear questions that could be answered by looking at the graph?
  • Would I make any adjustments the next time that I teach this lesson?
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Learning Objectives

Students will:

  • Create bar graphs and circle graphs.
  • Use the graphs they have created to answer questions about mode.

NCTM Standards and Expectations

  • Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
  • Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed.

Common Core State Standards – Mathematics

Grade 3, Measurement & Data

  • CCSS.Math.Content.3.MD.B.3
    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.