# Prekindergarten: Unit PK.MD.B.3-4, Sort objects into given categories and compare quantities

**Unit Overview**

**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan B3: Sorting Objects

Lesson Seed B3: Sorting Blocks

**Download Seeds, Plans, and Resources (zip)**

**Content Emphasis By Clusters in Grade PK**

**Progressions from Common Core State Standards in Mathematics**

Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery..

### Unit Overview

In this unit, students sort objects into either self-selected categories or given categories. They compare the categories either visually or by aligning the objects one-to-one. By doing this, they determine which has more or less, or if they are equal. At this level, students are not expected to give a ‘numeric’ comparison of the categories.

**Teacher Notes:**

- Review the Progressions for K, Counting and Cardinality; K–5, Operations and Algebraic Thinking at:
to see the development of the understanding of measurement and data as stated by the Common Core Standards Writing Team, which is also the guiding information for the PARCC Assessment development.*http://commoncoretools.files.wordpress.com/2012/07/ccss_progression_gm_k5_2012_07_21.pdf* - When implementing this unit, be sure to incorporate the Enduring Understandings and Essential Questions as the foundation for your instruction, as appropriate.
- Students should engage in well-chosen, purposeful, problem-based tasks. A good mathematics problem can be defined as any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific correct solution method (Hiebert et al., 1997). A good mathematics problem will have multiple entry points and require students to make sense of the mathematics. It should also foster the development of efficient computations strategies as well as require justifications or explanations for answers and methods.
- Students would benefit from the use of real-world situations in which to visualize the different relationships and relate it to their prior knowledge. Classroom time can be spent on discussing strategies, models, and reasoning.
- This unit focuses on students organizing objects into categories which are either self-selected or given and then comparing those categories either visually or by aligning the objects one-to-one to determine which has more or if the categories are equal. It should be understood that a student at this level is not expected to compare the categories numerically.

**Enduring Understandings:**

- The way that data is collected, organized and displayed influences interpretation.
- Grouping is a way to count, measure, and estimate.
- Objects can be sorted based on common attributes.

**Focus Standards (Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework documents for Grades 3-8):
**

**PK.CC.B.5**Representing a number (0-5, then to 10) by producing a set of objects with concrete materials, pictures, and/or numerals (with 0 representing a count of no objects),**PK.CC.B.6**Recognize the number of objects in a set without counting (Subitizing). (Use 1-5 objects.)**PK.CC.B.7**Explore relationships by comparing groups of objects up to 5 and then 10. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (includes group with up to 5 objects).

**Possible Student Outcomes:**

The student will:

- Sort objects by a common attribute into different groups.
- Organize the sorted categories of objects by lining them up to tell which has more, less, or if they have the same number of objects in each category.
- Compare the groups of objects to tell which has more, less, or if they are equal.
- Explain why they know that one category has more, less, or the same number of objects as another.

**Evidence of Student Learning: **

**Fluency Expectations and Examples of Culminating Standards:**

**Common Misconceptions:**

- Miscounting the objects in different categories when comparing.
- Misaligning the objects in different categories when comparing.
- Incorrectly sorting objects into categories.
- Incorrectly using the vocabulary related to comparing.

**Interdisciplinary Connections:**

*Literacy standards within the Maryland Common Core State Curriculum*

*Science, Technology, Engineering, and Mathematics standards*

*Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education, and fine arts, among others.*

**Sample Assessment Items: ***The items included in this component will be aligned to the standards in the unit and will include:*

*Items purchased from vendors*

*PARCC prototype items*

*PARCC public released items*

*Maryland Public release items*

*Formative Assessment*

### Interventions/Enrichments:

*(Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)*

### Vocabulary/Terminology/Concepts:

*This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.*

*Part I – Focus Cluster:*

(There is no specific vocabulary highlighted in this Cluster.)
*Part II – Instructional Connections outside the Focus Cluster*

** subitize: ** the ability to recognize the total number of objects or shapes in a set without counting.

Example: Recognizing that this face of a cube has five dots without counting them.

**: counting while aligning each number said to an object, picture, etc. in order to solve a problem.**

*verbal counting:***is the understanding that when counting a set, the last number represents the total number of objects in the set.**

*cardinality understanding:*Example:

**This is a set of 3 stars.**

**Resources**

__http://wps.ablongman.com/ab_vandewalle_math_6/0,12312,3547876-,00.html Reproducible blackline__Reproducible blackline masters__http://lrt.ednet.ns.ca/PD/BLM_Ess11/table_of_contents.htm__mathematics blackline masters__http://yourtherapysource.com/freestuff.html__Simple activities to encourage physical activity in the classroom__http://www.mathsolutions.com/index.cfm?page=wp9&crid=56__Free lesson plan ideas for different grade levels__http://www.nctm.org/__National Council of Teachers of Mathematics__www.k-5mathteachingresources.com__Extensive collection of free resources, math games, and hands-on math activities aligned with the Common Core State Standards for Mathematics__http://elementarymath.cmswiki.wikispaces.net/Standards+for+Mathematical+Practice__Common Core Mathematical Practices in Spanish__http://mathwire.com/__Mathematics games, activities, and resources for different grade levels__https://www.pbslearningmedia.org/__interactive online and offline lesson plans to engage students. Database is searchable by grade level and content__http://www.cast.org/udl/index.html__Universal Design for Learning__https://www.havefunteaching.com/__Various resources, including tools such as sets of Common Core Standards posters.

### Math Related Literature

- Reid, Margarette S.
*The Button Box* - Dotlich, Rebecca Kai
*What Is Square?*

### References:

- ------. 2000.
*Principles and Standards for School Mathematics*. Reston, VA: National Council of Teachers of Mathematics. - Arizona Department of Education. “Arizona Academic content Standards.” Web. 28 June 2010

__http://www.azed.gov/standards-practices/common-standards/__ - Bamberger, H.J., Oberdorf, C., Schultz-Ferrell, K. (2010).
*Math Misconceptions: From Misunderstanding to Deep Understanding*. - Burns, M. (2007 )
*About Teaching Mathematics: A K-8 Resource.*Sausalito, CA: Math Solutions Publications. - Clements, D.H., and McMillen, S. (1996). Rethinking “concrete” manipulatives.
*Teaching Children Mathematics*, 2(5): 270–279. - Copley, J. (2010).
*The Young Child and Mathematics*. Reston, VA: National Council of Teachers of Mathematics. - North Carolina Department of Public Instruction. Web. February 2012.
- Van de Walle, J. A., Lovin, J. H. (2006).
*Teaching Student-Centered mathematics, Grades K-3*. Boston, MASS: Pearson Education, Inc.