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Show and Tell

Data Analysis and Probability
Grace M. Burton
Location: unknown

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.

Distribute blank Blank Graphing Grid Paper and the button collections from the previous lesson.

pdficon Graphing Grid Activity Sheet

Have students re-sort their buttons and place them on the grid. Have students share with a partner their sorting rule. Ask students draw pictures of what their grids look like and explain what the graphs tell about the buttons. You might also choose to adapt the Paper Buttons Activity Sheet for students to create a pictorial graph of the button data.
Remind first- and second-grade students to add labels and a title. Reconvene the class as a whole group. Ask students to show and explain their graphs. If appropriate, students can write descriptions and explanations. These graphs and written descriptions may be used to create a classroom bulletin board or display for the hall.

Encourage students to use appropriate vocabulary such as row, column, titles, labels, sets, sort, and properties. Encourage students to ask questions about each other’s graphs, allowing the student who organized the graph to respond to the questions.

Next, give students another piece of grid paper, and have them use the recording of the graph they created in the first half of this lesson. Model for students how to color a grid to match the pictorial representation of the “real button” graph. Have students color their grid paper to match the concrete graph from the previous lesson. Remind students who are capable to provide a title for the graph and labels for the columns. For young students at this grade band, the teacher might prepare class titles and labels.

Sharing recordings and discussing the graphs allows students to formulate their thoughts, use appropriate vocabulary, and clarify and extend their understanding. It enables you to observe what students know and can apply, what they are in the process of learning, and what they still need to learn.

Assessment Options

  1. Use the Class Notes to document which students grasp the concepts and which need extra work with these ideas.
    pdficon Class Notes 
  2. Sharing recordings and discussing the graphs allows students to formulate their thoughts, use appropriate vocabulary, and clarify and extend their understanding. It enables you to assess what they know and can apply, what they are in the process of learning, and what they still need to learn.
  3. Students could stand on a floor grid (made from butcher paper or a shower curtain) representing the number of people who live in their household, the number of siblings, the number and kinds of pets, and so forth. Next students could color squares on a grid to match their pictorial representations. Always have students develop questions about graphs and respond to questions about graphs.
  4. Venn Diagrams are also excellent tools for displaying data about pets. Some categories might be: dogs, cats, both dogs and cats, neither dogs nor cats. Students could then use class pictures, self-portraits, and pictures of objects to complete pictorial graphs. This offers students experiences with overlapping categories.


  1. To help students make the transition from concrete to abstract representations, use commercial “stampers” or stickers to create a pictorial graph from data. Repeat this activity using other objects. These representations would allow students to understand the relationship between the objects and the pictures that represent them.
  2. Give students small objects to sort, organize, and display on a bar graph. Ask students to sort the objects and name their sorting rule, then record this information by drawing a picture or writing the rule. Next have students place the objects on the graph grid (provided at the end of this lesson) to create a concrete graph. Finally ask them to generate an abstract grid by coloring a separate graph grid to represent the sorted objects.

    Students at the upper end of this grade band should include a title and labels. Some younger students may be able to copy a title and label and others might dictate them. These two samples should be reviewed to determine the level of understanding of each student.


Questions for Students 

  1. How many columns of buttons are there?
  2. How many different sets of buttons were a part of this group?
  3. Which column has more buttons?
  4. Which column has the fewest buttons?
  5. Are there any columns that are equal in length? Do they represent the same number of items? How do you know?
  6. What other questions could you ask about or answer from your graph?

Teacher Reflection

  • What knowledge and skills do students need to better describe graphs?
  • In which other mathematics experiences do we or could we use a grid?
  • How can I help students focus on important ideas to record about this and other mathematics lessons?
  • What learning experiences that we routinely use would help students develop and respond to questions? How can these be changed to better facilitate question posing?
  • What new assessment tools would enable me to gather data on my students’ performance and progress toward learning targets?
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

Grandma's Button Box

In this lesson, students have opportunities to identify properties and to sort, classify, organize, and display data. They solve problems and make, explain, and defend conjectures. They extend their knowledge by making generalizations and consolidating their thinking.
AlikeAndDifferent ICON
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.
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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.

Learning Objectives

Students will:

  • Sort buttons.
  • Create pictorial graphs of their button data.

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.
  • 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

-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.

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.

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.