**Essential Questions: **

**Unit Overview**

**Lesson Plans and Seeds**

- Lesson Plan A1: Eating shapes
- Lesson Seed A2: Exploration of Shapes
- Lesson Seed A 3: Geoboard Shapes
- Lesson Seed A4: Grab and Sort Shapes
- Lesson Seed A5: Hot Potato Shapes
- Lesson Seed A6: Making Shapes
- Lesson Seed A7: Painting Dot Shapes
- Lesson Seed A8: Roll and Match
- Lesson Seed A9: My Shape Book
- Lesson Seed A10: Spinner Shapes
- Lesson Seed A11: Shape Match
- Lesson Seed A12: Shape Hunt
- Lesson Seed A13: A Tin Full of Shapes

**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, Prekindergarten students identify and describe two-dimensional shapes (circles, triangle, rectangles; including a square which is a special rectangle) by observing, touching, cutting, combining, folding, drawing, and/or copying them. Students can also create shapes with their bodies. Since their environment is made up of shapes, students should learn to identify shapes by both sight and touch. It is important for students to participate in active experiences which expose them to a great variety of shapes, engaging in motivating tasks that include both examples and non-examples of shapes. Sorting shapes by applying real-life experiences is also a critical skill in this unit. This includes students grouping squares and rectangles together and understanding that a square is a special kind of rectangle, as well as the ability to explain their groupings. It is not necessary for students to name the shapes or even identify attributes at this time. However, it is important to expose students to the correct geometric terms for shapes. They should be given opportunities to identify shapes by both name and appearance.

**Teacher Notes:**

- Review the Progressions for K-6 at:
__http://commoncoretools .files.wordpress.com /2012/06/ccss_progression _g_k6_2012_06_27.pdf__to see the development of the understanding of Geometry as stated by the Common Core Standards Writing Team, which is also the guiding information for the PARCC Assessment development. - 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.
- Learning about Geometry does not progress in the same way as learning about number, where the size of the number gradually increases and new kinds of numbers are considered later. Instead, students’ reasoning about Geometry develops through five sequential levels in relation to understanding spatial ideas. In order to progress through the levels, instruction must be sequential and intentional. These levels were hypothesized by Pierre van Hiele and Dina van Hiele-Geldof. For more information about the van Hiele Levels of Geometric Thought listed below, please go to:
__http://gogeometry .com/mindmap/ van_hiele_ geometry_level.html__- Level 0: Visualization
- Level 1: Analysis
- Level 2: Informal Deduction
- Level 3: Deduction
- Level 4: Rigor

- Use many real-world
**examples and non-examples**of two-dimensional shapes in order to provide greater depth of understanding as well as to begin noticing them based on similar characteristics. Using the word ‘not’ when introducing**non-examples**and allow students opportunities to work with shapes that are**non-examples**. - When experiencing the properties of two-dimensional shapes kinesthetically, children can be encouraged to participate in free play as well as more directed exploration, such as sorting by attributes and characteristics. Allow time for students to test and share their ideas through play and working in collaborative groups or in pairs in order to emphasize the properties and characteristics of a concept. Encourage students to use descriptive language when discussing two-dimensional shapes and the characteristics of these shapes. For example, children may notice that triangles have three “corners”.
- Students develop geometric concepts and spatial reasoning from experience with two perspectives on space: the shapes of objects and the relative positions of objects. Combining the teaching of Geometry with number concepts reinforces the fact that mathematical content is related.
- Through your discussions and interactions with students, emphasize reasoning with attributes and properties of two-dimensional figures as emphasized in the Maryland Common Core Standards, as opposed to simply identifying figures, which is typically only a vocabulary exercise.
- As prekindergarten students group shapes by attributes, it is important to be aware that initially, their sorting rules may be inconsistent. It can be challenging for 4- and 5-year-olds to classify a set of objects in more than one way (Copley, 2003). Students may make use sorting rules such as, “I like this color” or, “these are all big or all rectangles” before considering other attributes, such as sound, texture, or function.

**Enduring Understandings:**

- Geometry and spatial sense offer ways to interpret and reflect on our physical environment.
- Analyzing geometric relationships develops reasoning and justification skills.
- If I join shapes, I can create new shapes.

**Focus Standards **

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

**PK.G.A.1**Match like (**congruent**and**similar)**shapes.**PK.G.A.2**Group the shapes by attributes.

**Possible Student Outcomes:**

The student will:

- Identify and describe two-dimensional shapes (circles, triangles, rectangles; including a square which is a special rectangle).
- Match similar shapes when given various two-dimensional shapes (students do not need to name the shapes or even identify attributes at this time).
- Sort shapes by applying real-life experiences of sorting.
- Gain knowledge that rectangles and squares may be grouped together as 4-sided figures.
- Explain the groupings made when sorting.
- Distinguish
**examples and non-examples**of various shapes. - Become engaged in problem solving that is about thinking and reasoning.
- Collaborate with peers in an environment that encourages student interaction and conversation that will lead to mathematical discourse about geometry.

**Evidence of Student Learning: **

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

**Common Misconceptions:**

- Thinking that if the position of the shape changes, the name of the shape changes.
- Confusing the attributes of shapes with their properties. This is common for students in Prekindergarten, and they are not required to know the attributes of a shape.
- Thinking that the way a shape is oriented is part of what defines it.

**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.*

*Part I – Focus Cluster:*

** congruent:** having the same size and shape, but not necessarily the same orientation. All corresponding parts of congruent figures have the same measure. Examples: length, height, and weight

Example:

** similar: ** having the same shape but not necessarily the same size, and not necessarily the same orientation.

Example:

** examples and non-examples of shapes: ** Examples are polygons that are all the same shape but may be different sizes and orientations, while non-examples are shapes that are different from the type named

Example:

** positional relationships: **comparing objects or shapes by their placement to each other. Descriptive words would include above, below, next to, in front of, behind, near, far, beside, etc

Example:

*Part II – Instructional Connections outside the Focus Cluster*

*(There are no additional vocabulary words outside of the Focus Cluster related to this unit in the Prekindergarten Framework.)*

**Resources:**

**Free Resources:**

__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://yourther apysource.com/ freestuff.html__Simple activities to encourage physical activity in the classroom__http://www.mathsol utions.com/index .cfm?page=wp9&crid=56__Free lesson plan ideas for different grade levels__https://www.digiblock.com/__Lesson plans for mathematics__http://www.nctm.org/__National Council of Teachers of Mathematics__www.k-5mathteac hingresources.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.havefun teaching.com/__Various resources, including tools such as sets of Common Core Standards posters.__https://www.illustrat ivemathematics.org/__Tasks that align with the MD CCSS.__http://blog.mathatplay. org/page/4/__Blog which centers on mathematics for young children.__http://www.readwritethink .org/classroom-resources /lesson-plans/book- sorting-using-observation -145.html__Sorting lesson ideas.

### Math Related Literature

- Hoban, Tana.
__Shapes, Shapes, Shapes and So Many Circles, So Many Squares__.

Notes: These books include photographs of objects found in the real world. - Walsh, Ellen Stoll.
__Mouse Shapes__.

In this story with three mice as the main characters, the text is simple and the author uses both color and shapes to capture children’s attention.

### References:

- ------. 2000.
*Activities for Three-, Four-, and Five-Year-Olds: Showcasing Mathematics for the Young Child*. Reston, VA: National Council of Teachers of Mathematics. - ------. 2000.
*Principles and Standards for School Mathematics*. Reston, VA: National Council of Teachers of Mathematics. - Baroody, A.J. & Benson, A. (2001). Early number instruction.
*Teaching Children Mathematics, 8(3), 154-158.* - Copley, J. (2010).
*The Young Child and Mathematics*. Reston, VA: National Council of Teachers of Mathematics. - Copley, J., Jones, C., & Dighe, J. (2007).
*Mathematics: The Creative Curriculum Approach.*. Washington, D.C.: Teaching Strategies, Inc. - The Common Core Standards Writing Team (23 June 2012).
*Progressions for the Common Core State Standards in Mathematics (draft), accessed at:*.

__http://commoncoretools. files.wordpress.com /2012/06/ccss_progression _g_k6_2012_06_27.pdf__ - 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. - National Association for the Education of Young Children and National Council of Teachers of Mathematics (2002).
*Early childhood mathematics: Promoting good beginnings. A joint position statement of the National Association for the Education of Young Children (NAEYC) and National Council of Teachers of Mathematics(NCTM).*Retrieved 06/14/2009 from the web at: - 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.