# Gr. PK Unit: Add & Subtract

**Unit Overview**

**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan A1: In the construction zone

Lesson Seed A2: Building with Five blocks

Lesson Seed A 3: Fill the Dump Truck

**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

This unit introduces addition and subtraction to students through the use of objects, fingers, mental images, drawings, sounds, acting out situations, and verbal explanations. Students will explore composing and decomposing numbers to 5. They will **decompose** quantities less than or equal to 5 in pairs in more than one way. For any given quantity from 0 to 5, students will use objects or drawings as well as their number sense to find that quantity needed to make 5.

**Teacher Notes:**

- Review the Progressions for Grades K-5 Counting and Cardinality; K-5 Operations and Algebraic Thinking at
to see the development of the understanding of counting and number 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/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf* - When implementing this unit, be sure to incorporate the Enduring Understandings and Essential Questions as the foundation for your instruction.
- All of the Standards in this Domain are essential precursors to building number sense and computational fluency. Building a strong foundation with concrete activities is crucial for long-term understanding.
- A student-centered, problem-solving approach which helps promote the Standards for Mathematical Practice is recommended. This is best developed through carefully planned instruction that includes purposeful number talks in the classroom.
- The focus of this Cluster is NOT the written number sentence (equation) but rather many hands-on experiences putting numbers together and taking them apart through the use of concrete manipulatives and real world experiences. This incorporates the tactile, visual, and abstract experiences and assists in developing conceptual understanding.
- Continue to develop number sense by reinforcing early number relationships. These early number relationships include but are not limited to anchors to 5, part-part-total, one more/two more/one less/two less, and spatial relationships. Students should see 5 as 4 and 1, 2 and 3, five ones, and so on.
- A student's understanding of quantity is determined by his or her ability to construct relationships based on varying quantities. Constructing relationships is dependent upon a child's ability to make comparisons between sets of objects. For prekindergarten students, this includes the conceptual understanding of more and less. These concepts initially create some confusion for students. For example, a set of five objects is more than a set of one object. Conversely, a set of five objects is less than a set of eight objects. Experiences for these concepts should include using a multitude of contexts and manipulatives.
- The term, less, is a more difficult concept than more when children compare quantities. The first reason is because the term, more, is used quite frequently in children's conversations. Examples of this are:
*"Would you like more juice?" "May I have more paper?"*Rarely do young children ask for*"less"*of something. - Also, thinking about the meaning of less is difficult. Something that is not there is more abstract than thinking about something that can be seen as having more. The concept of less needs to be modeled. When students line up two quantities being compared in two rows and use a matching strategy and one-to-one correspondence, it helps them to understand what is less and what is more.

**Enduring Understandings:**

- Operations create relationships between numbers.
- The relationships among the operations and their properties promote computational fluency.
- Real world situations can be represented concretely, symbolically, and graphically
- There can be different strategies to solve a problem, but some are more effective and efficient than others.
- The context of a problem determines the reasonableness of a solution.
- The ability to solve problems is the heart of mathematics.
- Numbers can be composed or decomposed in a variety of ways.

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

**PK.OA.A.1**Explore addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, or verbal explanations (up to 5).**PK.OA.A.2**Decompose quantity (less than or equal to 5) into pairs in more than one way (e.g., by using objects or drawings).**PK.OA.A.3**For any given quantity from 0 to 5, use objects or drawings to find the quantity that must be added to make 5.

**Possible Student Outcomes:**

The student will:

- Use concrete materials, pictures, words, and actions to represent addition and subtraction and continue to build their number sense about computation.
- Represent composition of numbers to 5 using concrete materials, drawings, acting it out, and/or verbal statements.
- Represent decomposition of numbers to 5 using concrete materials, drawings, acting it out, and/or verbal statements.
- Determine the number needed to make 5, when given any number from 0 to 5.
- Become engaged in problem solving that is about thinking and reasoning.
- Learn to collaborate with peers in an environment that encourages student interaction and conversation that will lead to mathematical discourse about what it means to add and what it means to ‘put together’ (composing) and what it means to ‘take apart’ or ‘take from’ (decomposing).

**Evidence of Student Learning: **

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

**Common Misconceptions:**

- Lack of one-to-one correspondence.
- Thinking that addition always means “put together” or “join” and subtraction always means “take away” or “separate,” makes it difficult for students to solve a variety of addition and subtraction problem types that don’t fit these descriptors.
- Students misunderstand what is asked for in the problem. Example: Problem: “Sara has 4 pencils and Tiara has 1 pencil. How many more pencils does Sara have than Tiara?” The student responds “4” because Sara has 4 which is more than 1. The student misses the fact that they were asked to determine how many more Sara has, or the difference between the numbers each girl has.
- Adding when subtraction is needed or subtracting when addition is needed.
- Always finding the total regardless of the question asked.
- Does not relate the combining of groups of objects to addition and/or does not interpret the counting of all of the objects as an answer to the question ‘How many are there altogether?’

**Interdisciplinary Connections:**

Interdisciplinary connections fall into a number of related categories:

*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*

*Online Assessment/Tasks:*

### Interventions/Enrichments/PD:

*(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:*

** processes of addition:** the strategies or approaches used to solve addition problems, including ‘putting together’ and ‘adding to’. Examples:

** processes of subtraction: **: the strategies or approaches used to solve subtraction problems, including ‘taking apart’, ‘taking from’, and ‘comparing’. Examples:

** visualization**: ability to picture a problem in your head or use concrete materials to determine the solution.

** decomposition**: breaking a number into two or more parts to make it easier with which to work.
Example: When combining a set of 5 and a set of 8, a student might decompose 8 into a set of 3 and a set of 5, making it easier to see that the two sets of 5 make 10 and then there are 3 more for a total of 13.

Decompose the number 4; 4 = 1+3; 4 = 3+1; 4 = 2+2

Beginning in Grade 3: Decompose the number ⅗ ;⅗ = ⅕ + ⅕ +⅕

*Part II – Instructional Connections outside the Focus Cluster*

** rote counting: **: reciting numbers in order from memory without aligning them to objects, pictures, etc.

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

*verbal counting:***: rote counting or learning the number names in standard sequence.**

*Stable Order Count:*

**one-to-one correspondence:**: rote counting or learning the number names in standard sequence.**: 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.**

*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.

*regular configurations/structured sets:* using well-known arrangements, such as ten frames or tally marks to organize number quantities.

*varied configurations or representations* displaying number quantities in varied arrangements. Example: Displaying a set of five as:

**or**

__http://wps.ablongman.com/ab_vandewalle_math_6/0,12312,3547876-,00.html__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__https://www.digiblock.com/__Lesson plans for mathematics__http://sci.tamucc.edu/~eyoung/literature.html__links to mathematics-related children’s literature__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.k8accesscenter.org/training_resources/MathWebResources.asp__valuable resource including a large annotated list of free web-based math tools and activities.__http://www.cast.org/udl/index.html__Universal Design for Learning__http://engageny.org/wp-content/uploads/2012/05/Shifts-for-Students-and-Parents.pdf__Information for parents and students about the Shifts associated with the CCSS.__https://www.havefunteaching.com/__Various resources, including tools such as sets of Common Core Standards posters.__http://michellef.essdack.org/links__Numerous mathematics links.__https://www.illustrativemathematics.org/__Tasks that align with the MD CCSS.__http://www.insidemathematics.org/index.php/home__Mathematics resources for teachers.__https://www.nctm.org/standards/mathcommoncore/__Math Common Core Coalition__https://mathstory.com/mathstory.com/multimediapage/multimediapage.html__Songs for learners of all ages.__http://udltechtoolkit.wikispaces.com/__UDL Wiki with virtual manipulatives and other math tools.__http://www.coloring.ws/construction3.htm__Construction templates.__http://commoncore.fcoe.org/sites/commoncore.fcoe.org/files/resources/8%20practices%20matrix.pdf__Standards of Student Practice in Mathematics Proficiency Rating.__http://www.nctm.org/standards/mathcommoncore/__Math Common Core Coalition

### Math Related Literature

- Dahl, Michael.
__One Big Building__.

Notes: This fun counting book that follows the construction of a building, from one plan to twelve stories. Students will enjoy finding hidden numbers on an illustrated activity page. - Enderle, Judith Ross.
__Six Creepy Sheep__.

Notes: The sheep’s numbers dwindle as they run into fairies and pirates in this fun counting book. - Gackenbach, Dick.
__A Bag Full of Pups__.

Notes: Explore the concept of subtraction as taking away by reading about a boy who wants one of Mr. Mullins’ twelve pups. - Hughes, Shirley.
__When We Went to the Park__.

Notes: A counting book about a walk to the city park. - Lewis, Kevin.
__My Truck is Stuck__.

Notes: This book explores how many engines it takes to get a pothole-ambushed dump truck unstuck and other problems. - Olson, K.C.
__Construction Countdown__.

Notes: Count down from ten to one while learning that every kind of truck has an important job.

### 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*. - Bamberger, H.J., Oberdorf, C. (2010).
*Activities to Undo Math Misconceptions, Grades PreK-Grade 2*. Portsmouth, NH: Heinemann. - 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.

http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/3rd.pdf - Parrish, S. (2010).
*Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5*. Sausalito, CA: Math Solutions. - Seely, Cathy.(2009)
*Faster Isn't Smarter: Messages About Math, Teaching, and Learning in the 21st Century*. Sausalito, CA: Math Solutions. - Van de Walle, J. A., Lovin, J. H. (2006).
*Teaching Student-Centered mathematics, Grades K-3*. Boston, MASS: Pearson Education, Inc.