## Geometry

**Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).**

This entire cluster asks students to understand that certain attributes define what a shape is called (number of sides, number of angles, etc.) and other attributes do not (color, size, orientation). Using geometric attributes, the student identifies and describes squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres. Throughout the year, Kindergarten students move from informal language to describe what shapes look like (e.g., “That looks like an ice cream cone!”) to more formal mathematical language (e.g., “That is a triangle. All of its sides are the same length”).

In Kindergarten, students need ample experiences exploring various forms of the shapes (e.g., size: big and small; types: triangles, equilateral, isosceles, scalene; orientation: rotated slightly to the left, ‘upside down’) using geometric vocabulary to describe the different shapes. Students in Kindergarten typically recognize figures by appearance alone, often by comparing them to a known example of a shape, such as the triangle on the left (see below). For example, students in Kindergarten typically recognize that the figure on the left as a triangle, but claim that the figure on the right is not a triangle, since it does not have a flat bottom. Thus, the properties of a figure are not recognized or known.

Students typically make decisions on identifying and describing shapes based on perception, not reasoning.

Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are:

Students locate and identify shapes in their environment. For example, a student may look at the tile pattern arrangement on the hall floor and say, “Look! I see squares! They are next to the triangle.” At first students may use informal names e.g., “balls,” “boxes,” “cans”. Eventually students refine their informal language by learning mathematical concepts and vocabulary and identify, compare, and sort shapes based on geometric attributes.*

Students also use positional words (such as those italicized in the standard) to describe objects in the environment, developing their spatial reasoning competencies. Kindergarten students need numerous experiences identifying the location and position of actual two-and-three-dimensional objects in their classroom/school prior to describing location and position of two-and-three-dimension representations on paper.

Kindergarten students typically do not yet recognize triangles that are turned upside down as triangles, since they don’t “look like” triangles. Students need ample experiences manipulating shapes and looking at shapes with various typical and atypical orientations. Through these experiences, students will begin to move beyond what a shape “looks like” to identifying particular geometric attributes that define a shape.

Students identify objects as flat (2-dimensional) or solid (3-dimensional). As the teacher embeds the vocabulary into students’ exploration of various shapes, students use the terms two-dimensional and three-dimensional as they discuss the properties of various shapes.

2-dimensional shapes:

Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are:

**squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, spheres, flat, solid, side, corner, angle, edge, face,**positional vocabulary (e.g.,**above, below, beside, in front of, behind, next to, same, different**, etc.).**K.G.1**

K.G.1Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such asK.G.1

**above, below, beside, in front of, behind,**and**next to**.Students locate and identify shapes in their environment. For example, a student may look at the tile pattern arrangement on the hall floor and say, “Look! I see squares! They are next to the triangle.” At first students may use informal names e.g., “balls,” “boxes,” “cans”. Eventually students refine their informal language by learning mathematical concepts and vocabulary and identify, compare, and sort shapes based on geometric attributes.*

Students also use positional words (such as those italicized in the standard) to describe objects in the environment, developing their spatial reasoning competencies. Kindergarten students need numerous experiences identifying the location and position of actual two-and-three-dimensional objects in their classroom/school prior to describing location and position of two-and-three-dimension representations on paper.

**K.G.2**

K.G.2Correctly name shapes regardless of their orientations Through numerous experiences exploring and discussing shapes, students begin to understand that certain attributes define what a shape is called (number of sides, number of angles, etc.) and that other attributes do not (color, size, orientation). As the teacher facilitates discussions about shapes (“Is it still a triangle if I turn it like this?”), children question what they “see” and begin to focus on the geometric attributes.K.G.2

Kindergarten students typically do not yet recognize triangles that are turned upside down as triangles, since they don’t “look like” triangles. Students need ample experiences manipulating shapes and looking at shapes with various typical and atypical orientations. Through these experiences, students will begin to move beyond what a shape “looks like” to identifying particular geometric attributes that define a shape.

**K.G.3**

K.G.3Identify shapes as two-dimensional (lying in a plane, “flat”) or three dimensional (“solid”).K.G.3

Students identify objects as flat (2-dimensional) or solid (3-dimensional). As the teacher embeds the vocabulary into students’ exploration of various shapes, students use the terms two-dimensional and three-dimensional as they discuss the properties of various shapes.

2-dimensional shapes:

3-dimensional shapes:

**K.G.4**

**Analyze, compare, create, and compose shapes.**

K.G.4Analyze 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 other attributes (e.g., having sides of equal length).

K.G.4

Students relate one shape to another as they note similarities and differences between and among 2-D and 3-D shapes using informal language. For example, when comparing a triangle and a square, they note that they both are closed figures, have straight sides, but the triangle has 3 sides while the square has 4. Or, when building in the Block Center, they notice that the faces on the cube are all square shapes. Kindergarteners also distinguish between the most typical examples of a shape from obvious non-examples. For example: When identifying the triangles from a collection of shapes, a student circles all of the triangle examples from the non-examples pictures of triangles.

**K.G.5**

Analyze, compare, create, and compose shapes.

Analyze, compare, create, and compose shapes.

**K.G.5**Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Students apply their understanding of geometric attributes of shapes in order to create given shapes. For example, students may roll a clump of play-doh into a sphere or use their finger to draw a triangle in the sand table, recalling various attributes in order to create that particular shape.

**K.G.6**

Analyze, compare, create, and compose shapes.

K.G.6Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

Analyze, compare, create, and compose shapes.

K.G.6

This standard moves beyond identifying and classifying simple shapes to manipulating two or more shapes to create a new shape. This concept begins to develop as students move, rotate, flip, and arrange puzzle pieces to complete a puzzle. Kindergartners use their experiences with puzzles to use simple shapes to create different shapes. For example, when using basic shapes to create a picture, a student flips and turns triangles to make a rectangular house. Students also combine shapes to build pictures. They first use trial and error (part a) and gradually consider components (part b)*.