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Naming Rows and Columns

Data Analysis and Probability
Grace M. Burton
Location: unknown

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.

Select one set of buttons saved from previous lessons in this unit.

Unit Icon Unit: Amazing Attributes

Organize buttons so that each row and each column has a unique property. Using an overhead projector and a grid allows all students the opportunity to see the display of the button data. To ensure one-to-one correspondence between and among columns, be certain that no more than one button is in each space. Discuss with students what name would be appropriate for each column.

When all the buttons are placed, ask students to identify and describe observations about relationships between and among the buttons, such as which set has the most buttons, which has fewest, how many more are in the various columns, and what is the total number of buttons. Model the use of an appropriate title for the graph and labels for the columns. Record and post the demonstration models for students to reference.

Have students record on plain paper the demonstration graph you created. Make certain to reiterate the need to align the columns in rows to ensure one-to-one correspondence as you would when using a grid. Discuss how the student’s graphs compare with the demonstration graph. Probe those areas that are not clear to the students. Keep the recordings made by students to monitor their growth in understanding and application of sorting, classifying, organizing, and displaying data.

Store each student’s buttons in a labeled, zip-top plastic bag so that students can use the same set of buttons for the next (and last) lesson, Show and Tell

LPgeneric Show and Tell

See fig. 4.23, on page 112 of Principles and Standards for School Mathematics for an example of such a data display.

Older students at this grade band may relate the number of buttons in each column with the number of buttons in each set they sorted. They should also be able to organize the buttons with little or no assistance. Younger students may need help in recognizing this relationship.

Assessment Options

1. The assessment tool, Key Ideas and Words, offers a checklist of skills required for sorting, organizing, and displaying data and will help you track students’ grasp of important ideas related to graphing.

pdficon Key Ideas and Words 

2. Use the Student Checklist to keep track of those students who are moving towards mastery.

pdficon Class Notes 


1. Give groups of students a handful on buttons and have them duplicate the lesson (they are free to discard any buttons or exchange them for ones so that they can make a good table). Make sure students label their table, rows, and columns.

2. Have students write a journal entry of what they have learned so far in the unit, what they are still struggling with, and any questions they make have.

Questions for Students 

[Answers will vary.]

  1. How many columns of buttons are there?
  2. How many different sets of buttons were parts 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? If columns are of equal length are they also equal in number? How do you know?
  6. What other questions could you ask about or answer from this graph?

Teacher Reflection 

  • What other data could I model for students that would have meaning for them?
  • What learning experiences will help students develop and answer questions about graphs?
  • How might I connect the essential ideas with lessons about data with lessons about other mathematics content?
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.
ShowAndTell ICON
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:

  • Identify the difference between rows and columns.
  • Label and select a title for graphs.
  • Use comparative terms to describe relationships between and among the various sets of buttons.

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.

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.