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Alike and Different

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

This lesson focuses on the observation of properties and the classification of objects to build ideas about variables. Students compare objects to identify similarities and differences. In addition, students are introduced to Venn Diagrams.

Provide a class button box. Using a transparent container enables students to readily observe some properties and begin to consider classification strategies. Pass the container and have each student select two buttons. (Asking students to close their eyes when choosing might expedite the process of selecting buttons.) Ask each student to consider how his or her two buttons are alike and how they are different. Invite students to exchange one button and repeat the activity. In the prekindergarten and kindergarten classes, the teacher will record similarities on a chart such as the one shown below.



First- and second-grade students may do this as a class activity or individually on the Alike and Different activity sheet.

pdficon Alike and Different Activity Sheet 

Post the list of likenesses and differences in the classroom and amend or extend it as needed. This discussion helps students identify multiple variables and helps them become more flexible in their thinking.

The following activity is based on the story The Elves and the Shoemaker and allows students to sort shoes. In it students have the opportunity to experience another method of displaying data using a Venn Diagram, which causes them to relate data in a different way.

The teacher reads the story as students sit around in a circle. Students take off their shoes and discuss ways to group the shoes. Two non-overlapping hula-hoops are placed where all can see them. One file card is placed in each hoop. The identified properties are recorded on a chart for future reference. These labels should be chosen so they do not overlap such as brown and large or brown and not brown. The shoes are organized within the hula-hoops according to their properties listed on the file cards. Labels for the sorts are determined by a discussion among the students and teacher. Have students tell how the shows in each hoop are alike. Count the number of shoes in each group.

Some questions that would help promote an understanding of the mathematics would be the following:

What kinds of shoes do our class members wear?
How are they alike?
How are they different?
How did we decide to place shoes within the groups?
Is there another way that we could sort our shoes?

Students can next discuss attributes (such as color, style, or material) that could be used to classify the shoes worn by members of the class, sort the shoes, and then represent the results in a Venn diagram, in a table, and in a graph. A blank floor graph made from butcher paper or a shower curtain makes it easy for young children to place their shoes in a column, see the number in each, and discuss the information that can be derived from the graph. The columns should be labeled and a title should be chosen. In addition, the students should predict the types of shoes worn by the students in other classes in the school.

Use the Elves and Shoemaker Activity Sheet to record the results of the class discussion.

pdficon Elves and Shoemaker Activity Sheet 


  1. Refer to previous documentation about the status of the class regarding students’ understanding of properties and their ability to sort and classify objects. Identify students who are ready for the next activity and challenge them with steps beyond this lesson. (For example, “My button has….(properties from the chart).” “My button does not have…(Properties from the chart).” Students can record their responses on the My Button Has and Hasn't Activity Sheet.
  2. Organize those students that need additional practice into small groups and provide similar activities with different objects such as keys, shells, or beads. The questions as in the previous lesson are appropriate.


Further extensions include asking students to create another story about elves making other kinds of clothing. A preliminary discussion could focus on the properties of the clothing and the types of clothing that the elves could make. Or, have students draw a picture of the main idea of the story or compose a class letter thanking the elves for making the shoes.

Questions for Students 

1. Which properties on the chart could you use to sort your buttons?
2. Which pairs of properties could you use to sort your buttons?
3. What properties are not on the list that could fit your buttons?
4. Could you find someone with buttons like yours?

Teacher Reflection 

  • Which similarities did students notice when creating their Venn Diagrams?
  • Which differences did students notice?
  • What other learning experiences would enable students to compare properties of concrete objects and would also be important to the students?
  • What additional learning experiences do students need?
  • Are students able to accurately name the properties of the buttons?
  • Which properties do most of the students attend to?
  • Are students able to use more than one property to sort the buttons?
Data Analysis and Probability

Properties Everywhere

This lesson captures students’ interest, provides a review of the primary unit objectives and assesses students’ prior knowledge. This experience focuses students’ attention on the attributes of objects and rules for sorting them while building vocabulary for describing attributes and for classifying objects.
Data Analysis and Probability

Alike and Different

This lesson focuses on the observation of properties and the classification of objects to build ideas about variables. Students compare objects to identify similarities and differences. In addition, students are introduced to Venn Diagrams.
Data Analysis and Probability

Naming Rows and Columns

In this lesson, the teacher models how to organize data and use the vocabulary associated with collecting, organizing, and displaying data. Students learn the difference between rows and columns, how to label and select a title for graphs, and what comparative terms to use to describe relationships between and among the various sets of buttons.
Data Analysis and Probability

Show and Tell

This lesson allows students to describe their graphs using appropriate vocabulary and to develop skills in posing and responding to questions about their graphs. Students also demonstrate an understanding of how to organize and interpret data. In addition, this lesson helps students move from the concrete through pictorial to abstract representations of displays of data, namely a graph.

Learning Objectives

Students will:

  • Use the terms "alike" and "different" to make comparisons
  • Identify multiple variables when sorting
  • Use Venn Diagrams to compare properties

NCTM Standards and Expectations

  • Pose questions and gather data about themselves and their surroundings.
  • Sort and classify objects according to their attributes and organize data about the objects.

Common Core State Standards – Mathematics

-Kindergarten, Measurement & Data

  • CCSS.Math.Content.K.MD.B.3
    Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

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.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP1
    Make sense of problems and persevere in solving them.
  • CCSS.Math.Practice.MP4
    Model with mathematics.
  • CCSS.Math.Practice.MP5
    Use appropriate tools strategically.
  • CCSS.Math.Practice.MP7
    Look for and make use of structure.