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Can You Picture It?

Data Analysis and Probability
Grace M. Burton
Location: unknown

This lesson builds on the experiences of the previous lesson. Students collect data about favorite vegetables and record the data in a pictograph and interpret this representation. They also create and use legends for the pictograph.

Review the data collected in the previous lesson and the process for recording food preferences. Explain to students that in this lesson they use another method for collecting data. Provide copies of the Pictograph Activity Sheet and explain to students that they will show the data another way, in a pictograph. [A pictograph uses pictures to show data.]

pdficon Pictograph Activity Sheet

Draw four lines on the board and label the rows with the four most popular vegetables, as shown below.

Corn ___________ 
Carrots ___________ 
Peas ___________ 
Green Beans ___________ 
___ = 1 student

Ask the students what the title of the pictograph should be. Enter their suggestion above the graph and tell the students they should come up one by one and draw a smiley face next to their favorite vegetable of the four listed. When the class is ready, invite them to discuss what they notice from the pictograph. Encourage them to make comparisons between the rows as well as telling the number of faces in each row. Now ask, "How many votes does each face represent?" [One] Model how to create a legend at the bottom of the chart. [See the legend above for an example.]

Now format a second chart near the first one, but use the legend "___ = 2." Ask the students what that might mean. [Each smiley face now stands for two votes.] Now ask partners to work together to make a pictograph with that legend. When the children are ready, call on groups to share the charts they made. [If there are odd numbers of votes in a row, guide the students to understand that half a face should be drawn.]

Corn ___________ 
Carrots ___________ 
Peas ___________ 
Green Beans ___________ 
___ = 2 students  

You may wish to collect the second pictograph made to serve as a first entry for students' unit portfolios. Ask the students to include a description of how to make a pictograph.

Use the Colors of Health website (perform a simple internet search) as a guide to talk about the five colors of fruits and vegetables (red, yellow/orange, white, green, blue/purple). Then, choose "Track" on the top menu.

Show the students the week-long diary using the "My Dashboard" button, and distribute to each student the Bar Graph Activity Sheet. Tell the students to copy the tracking form and use it for a week to record their food choices in the appropriate boxes onto the Bar Graph Format.

Note: This diary will be referenced in future lessons, and students will need a complete diary for the end-of-unit activity.

pdficon Bar Graph Activity Sheet

Encourage them to decorate the sheet and remind them to save their food diaries until the end of the unit. (If you prefer not to have students record their actual food choices, ask them to make up ideal choices for each day.)

Assessment Option

At this stage of the unit, it is important to know whether the students can do the following:
  • Collect and tally real-world data
  • Classify data according to a given attribute
  • Create pictographs
  • Pose questions about the data set that can be answered from the representations
To help you assess individual progress toward learning goals, guiding questions for formative assessment are suggested in each lesson. As you focus on individual accomplishments, you may wish to record these accomplishments on Class Notes recording sheet. You may find your records useful when discussing the students' progress toward learning targets with students, parents or caregivers, administrators, and colleagues. These notes can also provide documentation for mandated Individual Education Plans.
Move on to the next lesson, Healthy Eating.

Questions for Students 

1. Look at the first pictograph we made. Which row had the most pictures? What does that mean?

[Answers will depend upon data collected. The row with the most pictures means it was the most popular category.]

2. Which row had the fewest pictures? How many fewer was that than the number of pictures in the row that had the most?

[Answers will depend upon data collected. The row with the fewest pictures means it was the least popular category.]

3. Look at the second pictograph we made. Which row had the most pictures? The least? How was the legend different? What does that mean?

[Once again, answers will depend upon data collected. The legend was different in that the first pictograph, one smiley face stood for one person. In the second pictograph, one smiley face stood for two people.]

4. When a smiley face represents two votes, how do you show that ten people chose that vegetable? 11 people?

[You would use 5 smiley faces; 5 and a half smiley faces]

5. How is a tally chart like a pictograph? How is it different?

[They are similar in they both display data and can be used to show preferences or "favorites." They are different in that a tally chart uses slashes, or tallies, to stand for one person each. In a pictograph, the picture can represent any number of people, depending on the data collected.]

6. How would you describe making a pictograph to a friend?

[Student responses will vary.]

Teacher Reflection 

  • Were all students able to contribute to the creation of the pictograph?
  • Were all students able to answer questions from the pictograph?
  • Which students were able to complete a pictograph in which a symbol stood for more than one vote? What instructional experiences do they need next?
  • Which pairs worked well together? Which pairs should I change in the next lesson?
  • What adjustments will I make the next time that I teach this lesson?
Data Analysis and Probability

Tally Time

Students tally data about food preferences and learn the convention of displaying a set of five tallies. Students also answer pose and answer questions about the data.
Data Analysis and Probability

Healthy Eating

Students collect data about classmates' healthy food knowledge. They create bar graphs, pose and answer questions about the data by looking at the graphs, and find the range and mode.
Data Analysis and Probability

What Is Your Favorite?

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.
Data Analysis and Probability

Let's Compare

Students collect numerical data, generate graphs, and compare two data sets. They also find the mean, mode, median, and range of the data sets. Students communicate with each other and the teacher and practice their problem-solving skills.
Data Analysis and Probability

Alphabet Soup

In this lesson, students construct box-and-whisker plots. Students use the box-and-whisker plots to identify the mean, mode, median, and range of the data set. Representation is the major focus of this lesson.
Data Analysis and Probability

Glyphs for All Reasons

Students learn a powerful way to display data, the glyph. Representation, communication, and problem solving are important parts of this lesson.

Learning Objectives

Students will:

  • Collect real-world data.
  • Create a pictograph based upon the data collected.
  • Pose questions about the data that can be answered from the graphs.

NCTM Standards and Expectations

  • Design investigations to address a question and consider how data-collection methods affect the nature of the data set.
  • Collect data using observations, surveys, and experiments.
  • Represent data using tables and graphs such as line plots, bar graphs, and line graphs.

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.