Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on

Pin it!
Google Plus

Freckle Face

Look at Me
Data Analysis and Probability
Edie Skipper
Location: unknown

This lesson initiates the development of skills in collecting and recording data. Students collect data about a partner's face and tally the data from the whole class. They learn the convention for displaying a set of five using tally marks. Then students create a pictograph and pose and answer questions about the data set.

To assess prior knowledge, ask the students wearing sneakers to stand and form a column in a free space within the room. Ask the students not wearing sneakers to stand and form a column alongside the column of students wearing sneakers. (If all students are wearing sneakers, choose another classification system, such as glasses/no glasses.) Explain to the students that they have just collected and displayed data. Record the data on a line plot on the board. Have the students return to their seats. Ask questions to focus the students' attention on the information displayed on the line plot. This exercise will help you determine the students' experiences and knowledge with regard to collecting and recording data.

If it is possible, read the book Freckle Juice by Judy Blume on the day of the lesson. If this book is not available, read or tell another story about a child with freckles. Call the students together and tell them that they are to select a partner and look at their partner to determine if he or she has freckles. Ask the students to describe where on the face freckles usually are found.

Draw on the board or chart paper a copy of the tally chart below.

545 Freckles board

Introduce the convention for grouping five tally marks for easier counting.

545 Cross hatch

Invite the students, one at a time, to place a tally mark in the correct row to describe their partner's face. When all the students have recorded the data, call on a volunteer to count the number of tallies in each row and record the number at the end of the row.

Give each student a self-stick note. Ask the students to draw pictures of their faces, with freckles if they have them and without freckles if they do not have them. Now explain that they will show the data another way--using a pictograph rather than tally marks. (A pictograph is a graph that uses pictures to show data.)

Draw two lines on the board and tell the students that the top line will show how many students in the room have freckles; label the far-left column "Have Freckles." Then ask the students what the second line should be labeled, and enter their suggestion in the far-left column in the second line of the grid.

Have Freckles
Do Not Have Freckles

When the students are ready, invite them to place their drawings on the pictograph, being careful that each drawing abuts the one before it. Now ask a student to count the number of faces in each row and to write the total amount at the end of the line. Encourage the students to formulate questions that can be answered by looking at the pictograph.

Collecting and keeping student work samples will allow you to review the students' growth over time, assess their understanding of mathematical concepts, and address any areas of misconception or lack of knowledge. Ask the students to attach their self-stick note to an index card and to write on the card two sentences that describe this lesson. This card might be a suitable first entry for a portfolio of work completed and assessed during this unit of study. If it is appropriate for their level, ask the students to include a subtraction sentence that describes the comparison of the two categories, "Freckles" and "No Freckles."

  • Paper  
  • Chart paper  
  • Crayons and markers  
  • Self-stick notes  
  • Index cards  
  • Book: Freckle Juice by Judy Blume 

Assessment Options 

  1. To facilitate a rich class discussion, use the Questions for Students. You may wish to take anecdotal records on students' responses to these questions as you plan your instruction for the rest of this unit.
  2. As you focus on individual accomplishments, you may wish to record these accomplishments on the Class Notes recording sheet. You may find this information useful when discussing the students' progress toward learning targets with parents, administrators, colleagues, and the students themselves.
Move on to the next lesson, The Eyes Have It.

Questions for Students 

1. Can you name the two categories we collected data about? How did we show what we found out? How else did we show it?

[Freckles, no freckles; Using tally marks; We also used a pictograph.]

2. How did we make it easier to count the tally marks in the tally chart? Why did that step make it easier?

[We used a diagonal line to show 5; we can count by 5s.]

3. What questions can you answer from looking at the tally chart?

[Questions may include: How many more students had no freckles than freckles? What is the difference between the two groups?]

4. Look at the pictograph that we made. Which row contained more pictures? What information does that provide for you about students in our class and freckles?

[Answers will depend upon the class data set.]

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

[Both show categorical data; tally charts use tally marks, and pictographs use pictures to represent numbers.]

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

[Student responses may vary, but they should be able to explain the basic process of creating a pictograph.]

Teacher Reflection 

  • Which students were able to make single tallies? Which students understood how and why tallies are collected in groups of five?
  • Were all the students able to contribute to the creation of the tally chart? The pictograph?
  • Were all the students able to answer questions from the tally chart? From the pictograph?
  • Which students did not meet the objectives of this lesson? What instructional experiences do they need next?
  • Would I make any adjustments the next time that I teach this lesson?
Data Analysis and Probability

The Eyes Have It

Students collect data about the eye color of class members. They create bar graphs with several classifications of data. They pose and answer questions about the data by looking at the graph, and they find the range and mode.
Data Analysis and Probability

Up on Top

In this lesson students generate bar graphs. Posing and answering questions using the graphs gives them an opportunity to apply their reasoning and communication skills. They also consider whether a given category is likely, certain, or impossible.
Data Analysis and Probability

Making Glyphs

In this lesson, students learn a powerful way to display data—using a glyph. They collect data and create pictures using the data. Students also interpret glyphs made by other students.

Learning Objectives

Students will:
  • 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.

NCTM Standards and Expectations

  • Sort and classify objects according to their attributes and organize data about the objects.
  • Represent data using concrete objects, pictures, and graphs.
  • Describe parts of the data and the set of data as a whole to determine what the data show.

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.