Prekindergarten: Unit PK.G.A.1-2, Identify and Describe Two-Dimensional Shapes (circles, triangles, rectangles; including a square which is a special rectangle)

Progressions from Common Core State Standards in Mathematics

For an in-depth discussion of the overarching, “big picture” perspective on student learning of content related to this unit, see:

The Progressions for Geometry at: http://commoncoretools.files.wordpress.com/2012/06/ccss_progression_g_k6_2012_06_27.pdf stated by the Common Core Standards Writing Team, which is also the guiding information for the PARCC Assessment development.

Vertical Alignment: Vertical curriculum alignment provides two pieces of information: (1) a description of prior learning that should support the learning of the concepts in this unit, and (2) a description of how the concepts studied in this unit will support the learning of additional mathematics.

1. Possible Key Advances from Previous Grades:

   Prior to Prekindergarten, students:

   1. Use shapes in their environment (plates are round, napkins are squares, etc.).

2. Additional Mathematics
   In Kindergarten, students:

   1. Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as above, below, beside, in front of, behind, and next to.
   2. Correctly name shapes regardless of their orientations or overall size.
   3. Identify shapes as two-dimensional or three-dimensional.
   4. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and properties (such as sides of equal length).
   5. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
   6. Compose simple shapes to form larger shapes.

Students in Grade 1:

1. Distinguish between defining attributes and non-defining attributes.
2. Build and draw shapes to possess defining attributes.
3. Compose two-dimensional shapes or three-dimensional shapes to create a composite shape.
4. Compose new shapes from composite shapes.
5. Partition circles and rectangles into two and four equal shares.
6. Describe partitioned shares using the words halves, fourths, and quarters.
7. Use the phrases half of, fourth of, and quarter of.
8. Describe the whole as two of, or four of the shares.

Students in Grade 2:

1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.
2. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
3. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
4. Partition circles and rectangles into two, three, or four equal shares.
5. Describe shares using the words halves, thirds, half of, a third of, etc. and describe the whole as two halves, three thirds, four fourths.
6. Recognize that equal shares of identical wholes need not have the same shape.

Students in Grade 3:

1. Understand concepts of area and relate area to multiplication and to addition.
2. Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
3. Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category.
4. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
5. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

In Grades 4 and beyond, students:

1. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
2. Graph points on the coordinate plane to solve real-world and mathematical problems.
3. Classify two-dimensional figures into categories based on their properties.
4. Solve real-world and mathematical problems involving area, surface area, and volume.
5. Draw, construct, and describe geometrical figures and describe the relationships between them.
6. Solve real-life and mathematical problems involving angle measure, are, surface area, and volume.
7. Understand congruence and similarity using physical models, transparencies, or geometry software

Possible Organization of Unit Standards: This table identifies additional grade-level standards within a given cluster that support the over-arching unit standards from within the same cluster. The table also provides instructional connections to grade-level standards from outside the cluster.

Over-Arching Standards	Supporting Standards within the Cluster	Instructional Connections outside the Cluster
PK.G.A.1 Match like (congruent and similar) shapes.		PK.G.B.3 Match and sort three-dimensional shapes. PK.MD.A.2 Directly compare two objects with a measureable attribute in common, using words such as longer/shorter; heavier/lighter, or taller/shorter.
PK.G.A.2 Group the shapes by attributes.		PK.G.B.4 Describe three-dimensional objects using attributes. PK.G.B.5 Compose and describe structures using three-dimensional shapes. Descriptions may include shape attributes, relative position, etc. PK.MD.B.3 Sort objects into self-selected and given categories.

Connections to the standards for Mathematical Practice: This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. These proficiencies correspond to those developed through the Literacy Standards. The statements provided offer a few examples of connections between the Standards for Mathematical Pratice and the Content Standards of this unit. The list is not exhaustive and will hopefully prompt further reflection and discussion.

In this unit, educators should consider implementing learning experiences which provide opportunities for students to:

1. Make sense of problems and persevere in solving them.
   1. Determine what the problem is asking for:
   2. Determine whether concrete or virtual models, pictures, mental images, or words are the best tools for solving the problem.
   3. Check the solution with the problem to verify that it does answer the question asked.
2. Reason abstractly and quantitatively
   1. Compare the sorting of shapes with that done by other students.
   2. Use descriptive language to support your sorting of shapes.
3. Construct Viable Arguments and critique the reasoning of others.
   1. Compare shapes used by others with yours.
   2. Examine the steps taken that produce an incorrect response and provide a viable argument as to why the process produced an incorrect response.
4. Model with Mathematics
   1. Construct visual models using concrete or virtual manipulative, or pictures to justify thinking and display the solution.
5. Use appropriate tools strategically
   1. Use shapes and models, as appropriate.
   2. Use the straws, sticks, and other building materials to construct shapes.
6. Attend to precision
   1. Use mathematics vocabulary such as shape, circle, square, corners, sides, etc. properly when discussing problems.
   2. Demonstrate understanding of the mathematical processes required to solve a problem by carefully showing all of the steps in the solving process.
   3. Correctly write and read equations that describe the groups of shapes that were sorted.
7. Look for and make use of structure.
   1. Use the similar characteristics of shapes.
   2. Use the relationships between shapes to sort them into groups.
8. Look for and express regularity in reasoning
   1. Use the patterns illustrated in your sorting to explain why you grouped the shapes the way that you did.
   2. Use the relationships between similar shapes to explain your reasoning.

Content Standards with Essential Skills and Knowledge Statements and Clarifications:

The Content Standards and Essential Skills and Knowledge statements shown in this section come directly from the Maryland State Common Core Curriculum Frameworks. Clarifications were added as needed. Educators should be cautioned against perceiving this as a checklist. All information added is intended to help the reader gain a better understanding of the standards.