## Unit Overview

**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan A.3: Building Bridges

Lesson Seed A.1: Developing Counting Routines

**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 rote counting and verbal counting to the Prekindergarten student. It provides for them to practice rote counting (repeating the memorized counting sequence) and apply verbal counting (meaningful counting of objects, people, etc.,) to solve problems, such as finding out how many objects are in a set. Students develop an understanding of the relationship between numbers and quantities and connect counting to cardinality while working with numbers first to 5 and then to 10. Students use concrete materials to build sets for a number up to 10. Students explore the concept of just after and just before a given number in the counting sequence to 10. Although students at this level are not expected to write numerals, they are expected to recognize written numerals 0 through 10, and match those numbers with sets of the same value. They will model that, when counting, they pair each object with one and only one number name. They will be able to demonstrate that when counting, the number names are said sequentially. Students will solidify the understanding that the last number name said tells the number of objects counted. They will also explore the fact that each successive number name refers to a quantity that is one larger.

**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, 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.

**Enduring Understandings:**

- Numbers and counting are a part of our everyday life.
- Numbers can represent quantity, position, location, & relationships.
- Counting finds out the answer to “how many” in objects/sets.

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

**PK.CC.B.4**Understand the relationship between numbers and quantities to 5, then to 10; connect counting to cardinality

**Possible Student Outcomes:**

The student will:

- Use concrete materials to model one-to-one correspondence when counting.
- Count sequentially.
- Tell “how many” are in a set of objects after counting them.
- Explain that, when you count, each successive number name is one more than the number name before it.
- Demonstrate an understanding that the number of objects is the same regardless of their arrangement or the order in which they were count (conservation of number)
- When given a number up to 10, count out that many objects.

**Evidence of Student Learning:**

*The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.*

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

**Common Misconceptions:**

- Skipping numbers while rote counting.
- Lack of one-to-one correspondence.
- You ALWAYS have to start at 1.
- Zero is not a number.
- Skipping objects or recounting objects when counting a set of objects.

**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*

**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.*

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

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

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

This is a set of 3 stars.

** Subitizing** 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: **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.

** varied configurations or representations**displaying number quantities in varied arrangements. Example:

Displaying a set of five as:

or |

**Relevant Kindergarten Vocabulary:**

** conservation of number**the ability to understand that the quantity of a set does not change, no matter how the objects of the set are displayed or moved around.

**Free Resources:**

- The Common Core Standards Writing Team (01 May, 2011). Progressions for Grades K-5 Counting and Cardinality; K-5 Operations and Algebraic Thinking accessed at
__http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf__ - Okta's Rescue, a counting game at the illuminations website link:
__http://illuminations.nctm.org/ActivityDetail.aspx?ID=219__ - Concentration, a number matching game at the illuminations website link:
__http://illuminations.nctm.org/ActivityDetail.aspx?ID=73__ - Number games, including building sets to 5 at the illuminations website link:
__http://illuminations.nctm.org/ActivityDetail.aspx?ID=74__ - Number games, including building sets to 10 at the illuminations website link:
__http://illuminations.nctm.org/ActivityDetail.aspx?ID=75__ __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.__http://digiblock.com/__Lesson plans for using Digi-Blocks__http://sci.tamucc.edu/~eyoung/literature.html__links to mathematics-related children's literature.__http://www.nctm.org/__National Council of Teachers of Mathematics.__http://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.__http://www.pbs.org/teachers/math/__interactive online and offline lesson plans to engage students. Database is searchable by grade level and content.__http://www/k8accesscenter.org/training_resources/MathWebbResources.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.