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Properties Everywhere

Data Analysis and Probability
Grace M. Burton
Location: unknown

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.

While students remain in their seats, ask them to identify things within the classroom that can be sorted and to name specific attributes to guide the sorting. Some examples students might suggest are the following:

  • Things to sort by color: crayons, markers, papers, hair color, eye color, backpacks, and clothes
  • Things to sort by shape: tables, books, blocks
  • Things to sort by size: books, students, pencils, and shoes.

Record and post this information on a chart for future reference. The format provided on the Objects to Sort Recording Sheet will familiarize students with the recording format.

Give small groups of students bowls of crayons or pencils. Have students sort the crayons however they wish (be vague on purpose, so that the groups' results will vary). While students are doing this, circulate the room and make note of all the different ways groups are sorting.



After students have finished sorting, display one group's sorting results. Ask the class if they can guess how this group sorted their objects. Have students defend their answers.

pdficonObjects to Sort Recording Sheet 

Distribute the Objects to Sort Recording Sheet (one copy per group). Invite students to complete the sheet by using more specific sorting rules. Students will have to sort the crayons by such the following categories:

  • Color (they can mark the crayon onto the paper)
  • Size (students may use length, width, or both)
  • Type (ex: crayons with and without wrapping)
  • Shape (ex: crayons with tips vs. those that resemble cylindrical cylinders)

Note that students may interpret the categories differently, which is acceptable. This will be a good opportunity to engage students in math talk.

Depending on the time available for class, use the Questions for Students to wrap up the lesson, or move onto the next lesson, Alike and Different.



  1. The guiding questions help students focus on the mathematics and aid you in understanding the students’ level of knowledge and skill with the mathematical concepts of this lesson.
  2. One of the assessment tools provided is a recording sheet entitled Class Notes. It is helpful to record students’ current level of understanding as a way to plan instruction and to monitor and measure their growth toward meeting the learning objectives. Documenting information about students’ understanding throughout the lesson can help you focus on each student’s needs and strengths and thus increase students’ learning opportunities.
    pdficonClass Notes 


  1. Many students in the early grades will need multiple sorting experiences. You may wish to ask students to use these procedures as they sort other objects such as small toys, models of vegetables or fruits, jewelry, keys, tops for containers, bread clips, and coins.
  2. Have students think about other categories that they can sort by. For example, people can be sorted by gender, eye color, hair color, etc.
Questions for Students 
[All answers will vary.]
  1. What kinds of shoes do you have at your house? (Encourage students to look at their own shoes and think about shoes they have at home such as dress shoes, mom’s high-heeled shoes, basketball shoes, slippers, and sandals.)
  2. What was your rule for sorting? Why did you choose it?
  3. Could you use one other rule that is different from the one you used?
  4. Could you use more than one property or attribute for sorting?
  5. What things could you sort at home? (Students might name toys, clothes, groceries, shoes, etc.)
  6. Do you sort objects at home by where they belong? If so, where? Answers might include the pantry, drawers, toy chest, and so forth.
Teacher Reflection
  1. Which management strategies were most effective?
  2. Which management strategies were least effective?
  3. Which students met all the objectives of this lesson? What extension activities are appropriate for those students?
  4. Which students did not meet the objectives of this lesson? What instructional experiences do they need next? What mathematical ideas need clarification?
  5. What adjustments would you make the next time you teach this lesson?
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.
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 how items are sorted by color, size, type and shape.
  • Defend their reasoning for sorting.

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.

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 1, Geometry

  • CCSS.Math.Content.1.G.A.1
    Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP7
    Look for and make use of structure.
  • CCSS.Math.Practice.MP8
    Look for and express regularity in repeated reasoning.