Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Lower Primary
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [K.GM]

OREGON MATH STANDARDS (2021): [K.GM]

Overview

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. 

Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

2021 Oregon Math Guidance: K.GM.A.1

ODE and Oregon Math Project Logo

Cluster: K.GM.A - Identify and describe shapes.

STANDARD: K.GM.A.1

 Standards Statement (2021):

Describe objects in the environment using names of shapes and describe the relative positions of these objects in their environment.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

 N/A

K.GM.B.4, K.GM.B.5, K.GM.B.6

 N/A

K.G.A.1

K.GM.A Crosswalk

 Standards Guidance:

Clarifications

  • Students use appropriate directional language to indicate where things are in their environment (for example: positions, distances, order).
  • Kindergarten students should be able to explain the location of an object in relation to another object using positional language, such as “above,” “below,” “beside,” “in front of,” “behind,” or “next to.”

Teaching Strategies

  • Use positional terms such as above, below, beside, in front of, behind, and next to when describing position of an object. For example, the box is under the chair or the bear is next to the table.

Boundaries

  • Students can identify the following two-dimensional shapes based on attributes:
    • Square, circle, triangle, rectangle, hexagon, oval, rhombus
  • Students can identify the following three-dimensional shapes based on attributes:
    • Cubes, cones, cylinders, spheres

Progressions

  • Students refine their informal language by learning mathematical concepts and vocabulary so as to increasingly describe their physical world from geometric perspectives, e.g., shape, orientation, spatial relations (MP4).
  • Students increase their knowledge of a variety of shapes, including circles, triangles, squares, rectangles, and special cases of other shapes such as regular hexagons, and trapezoids with unequal bases and non-parallel sides of equal length.
  • Students also begin to name and describe three-dimensional shapes with mathematical vocabulary, such as “sphere,” “cube,” “cylinder,”and “cone.” Finally, in the domain of spatial reasoning, students discuss not only shape and orientation, but also the relative positions of objects, using terms such as “above,” “below,” “next to,” “behind,” “in front of,” and “beside.”  (Please reference page 6 in the Progression document).

Examples

  • “The cup is beside the pencil."
  • “The boy is behind the girl in line.”
  • In a sequence of pictures, the student would describe the position of a particular object.

2021 Oregon Math Guidance: K.GM.A.2

 ODE and Oregon Math Project Logo

Cluster: K.GM.A - Identify and describe shapes.

STANDARD: K.GM.A.2

 Standards Statement (2021):

Correctly name common two-dimensional and three-dimensional geometric shapes regardless of their orientations or overall size.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

 N/A

K.GM.B.4, K.GM.B.5, K.GM.B.6

 N/A

K.G.A.2

K.GM.A Crosswalk

 Standards Guidance:

 

Clarifications 

  • Students should distinguish between defining attributes of two-dimensional shapes and three-dimensional figures versus non-defining attributes (e.g., triangles are closed and three-sided, a defining attribute versus triangles are red, non-defining attribute).
  • Students should be able to build and draw shapes based on defining attributes. Two-dimensional shapes should be limited to triangles, squares, and rectangles.
  • Students should be able to identify a shape’s attributes, regardless of its orientation (i.e., flipped) or position (i.e., turned).

Boundaries

  • Students can identify the following two-dimensional shapes based on attributes:
    • Square, circle, triangle, rectangle, hexagon, oval (ellipse), rhombus
  • Students can identify the following three-dimensional shapes based on attributes:
    • Cubes, cones, cylinders, spheres

Terminology

  • The terms below are used to clarify expectations for the teaching professional. Students are not required to use this terminology when engaging with the learning objective.
    • Attributes – characteristics of two-dimensional shapes and three-dimensional figures, including geometric properties.
    • Defining attributes – include number of sides, faces, vertices (corners), and angles.
    • Non-defining attributes – include size, orientation, texture, and color.

Progressions

  • Students learn to name shapes such as circles, triangles, and squares, whose names occur in everyday language, and distinguish them from nonexamples of these categories, often based initially on visual prototypes. (Please reference page 6 in the Progression document).

Examples

2021 Oregon Math Guidance: K.GM.A.3

 ODE and Oregon Math Project Logo

Cluster: K.GM.A - Identify and describe shapes.

STANDARD: K.GM.A.3

 Standards Statement (2021):

Identify shapes as two-dimensional or three-dimensional.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

 N/A

K.GM.B.4, K.GM.B.5, K.GM.B.6

 N/A

K.G.A.3

K.GM.A Crosswalk

 Standards Guidance:

 

Clarifications 

  • Students will name flat shapes as two-dimensional or solid shapes as three-dimensional. Example would be a square is flat but a cube is solid.
  • In the domain of shape, students learn to match two-dimensional shapes even when the shapes have different orientations.

Teaching Strategies

  • Have students explain their decisions about shape names or classifications prompts students to attend to and describe certain features of the shapes. That is, concept images and names they have learned for the shapes are the raw material from which they can abstract common features.

Progressions

  • In the domain of shape, students learn to match two-dimensional shapes even when the shapes have different orientations.
  • Students need to explain their decisions about shape names or classifications prompts students to attend to and describe certain features of the shapes. That is, concept images and names they have learned for the shapes are the raw material from which they can abstract common features.
  • Students identify faces of three-dimensional shapes as two-dimensional geometric figures and explicitly identify shapes as two-dimensional (“flat” or lying in a plane) or three-dimensional ("solid"). (Please reference page 6 in the Progression document).

Examples

  • Have students identify faces of three-dimensional shapes as two-dimensional geometric figures and explicitly identify shapes as two-dimensional (“flat” or lying in a plane) or three-dimensional ("solid").
  • Illustrative Mathematics:

2021 Oregon Math Guidance: K.GM.B.4

 ODE and Oregon Math Project Logo

Cluster: K.GM.B - Analyze, compare, create, and compose shapes.

STANDARD: K.GM.B.4

 Standards Statement (2021):

Analyze and compare two and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts and attributes.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

K.GM.A.1, K.GM.A.2, K.GM.A.3

1.GM.A.1

 N/A

K.G.B.4

K.GM.B Crosswalk

 Standards Guidance:

Clarifications

  • Students recognize and name common two-dimensional and three-dimensional shapes, their parts and attributes.
  • Students should be able to identify basic shapes, including squares, circles, triangles, rectangles, hexagons, octagons, cubes, cones, cylinders, and spheres.
  • Students begin to understand how three-dimensional figures are composed of two-dimensional shapes.

Teaching Strategies

  • Develop spatial sense by connecting geometric shapes to students’ everyday lives.
  • Initiate natural conversations about shapes in the environment. Have students identify and name two and three-dimensional shapes in and outside of the classroom and describe their relative position.
  • Ask students to find rectangles in the classroom and describe the relative positions of the rectangles they see, e.g. This rectangle (a poster) is over the sphere (globe).
  • Teachers can use a digital camera to record these relationships.

Terminology

  • The terms below are used to clarify expectations for the teaching professional.  Students are not required to use this terminology when engaging with the learning objective.
    • Attributes – characteristics (i.e., two- dimensional shapes (lying in a plane, “flat”) and three-dimensional figures (“solid”), including geometric properties.). An example of an attribute is having sides of equal length.
    • Vertices – corners of a geometric figure

Examples

  • Example a square has 4 equal sides and 4 corners/vertices and a cube has 8 equal sides with 8 corners/vertices and 6 faces. The intent is not for students to yet have the formal language, but teachers can start to guide the transition from informal to formal mathematical language.
  • The base and top of a cylinder is a circle.
  • Illustrative Mathematics:

2021 Oregon Math Guidance: K.GM.B.5

 ODE and Oregon Math Project Logo

Cluster: K.GM.B - Analyze, compare, create, and compose shapes.

STANDARD: K.GM.B.5

 Standards Statement (2021):

Represent shapes in the world by building shapes from components and drawing shapes.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

K.GM.A.1, K.GM.A.2, K.GM.A.3

1.GM.A.1

 N/A

K.G.B.5

K.GM.B Crosswalk

 Standards Guidance:

 

Clarification

  • Standard includes student explaninations about their decisions for shape names or classifications. That is, concept images and names they have learned for the shapes are the raw material from which they can abstract common features.

Teaching Strategies

  • Prompt students to attend to and describe certain features of the shapes.
  • Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
  • Crate simple composite shapes using pattern blocks, such as a square and rectagle could represent a house. 

Progressions

  • Students need to explain their decisions about shape names or classifications prompts students to attend to and describe certain features of the shapes. That is, concept images and names they have learned for the shapes are the raw material from which they can abstract common features.
  • Students represent shapes informally with drawings and by building them from components (e.g., manipulatives such as sticks). With repeated experiences such as these, students become more precise (MP6). (Please reference page 6 in the Progression document).

Examples

  • Build 2-dimensional shapes or 3-dimensional shapes using manipulatives and other components. Example building a house using marshmallows and toothpicks or Legos.
  • Models – sticks with clay balls, toothpicks with marshmallows, popsicle sticks, technology, etc.

 

2021 Oregon Math Guidance: K.GM.B.6

  ODE and Oregon Math Project Logo

Cluster: K.GM.B - Analyze, compare, create, and compose shapes.

STANDARD: K.GM.B.6

 Standards Statement (2021):

Compose common shapes to form larger shapes.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

K.GM.A.1, K.GM.A.2, K.GM.A.3

1.GM.A.2

 

K.G.B.6

K.GM.B Crosswalk

 Standards Guidance:

 

Clarifications

  • Students manipulate objects and describe the process for fitting objects together.
  • Students combine simple shapes to form new shapes. 

Teaching Strategies

  • Students should be able to form (compose) larger shapes by putting together smaller shapes through exploration and play.
  • Have students not only build shapes from components, but also compose shapes to build pictures and designs.
Progressions
  • An important area for kindergartners is the composition of geometric figures. Students not only build shapes from components, but also compose shapes to build pictures and designs. Initially lacking competence in composing geometric shapes, they gain abilities to combine shapes–first by trial and error and gradually by considering components–into pictures. At first, side length is the only component considered. Later experience brings an intuitive appreciation of angle size. (Please reference page 7 in the Progression document).

Examples

  • Exploring Tessellations
  • What shapes can you create with these two triangles?"
  • Use more than one shape to build a larger shape. Example two triangles make a rhombus or two trapezoids to make a hexagon.
  • Students combine two-dimensional shapes and solve problems such as deciding which piece will fit into a space in a puzzle, intuitively using geometric motions (slides, flips, and turns, the informal names for translations, reflections, and rotations, respectively).  Students can construct their own outline puzzles and exchange them, solving each other’s.

​​​​​

2021 Oregon Math Guidance: K.GM.C.7

  ODE and Oregon Math Project Logo

Cluster: K.GM.C - Describe and compare measurable attributes.

STANDARD: K.GM.C.7

 Standards Statement (2021):

Describe several measurable attributes of a single object using measurable terms, such as length or weight.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

K.NCC.C.6

K.GM.C.8

 N/A

K.MD.A.1

K.GM.C Crosswalk

 Standards Guidance:

Clarifications

  • Students use a variety of techniques and standard and non-standard tools to measure and compare length, volume (capacity) and weight
  • Students independently orders objects using one characteristic and describes the criteria used.
  • In Kindergarten, students should use language such as heavier, lighter, longer, taller, shorter, wider, larger, and smaller.
  • In Kindergarten, students may use a variety of techniques and tools to compare, describe, and order objects. Students may use a referent object being compared as a tool to describe the other object(s).

Terminology

  • Measurable attributes can be vocabulary that describe the length, weight or shape of an object.
  • The terms below are used to clarify expectations for the teaching professional.  Students are not required to use this terminology when engaging with the learning objective.
    • Attributes – characteristics (i.e., length, height, width, or weight)
    • Referent object – an object used as the standard of comparison

Progressions

  • Students often initially hold undifferentiated views of measurable attributes, saying that one object is “bigger” than another whether it is longer, or greater in area, or greater in volume, and so forth. For example, two students might both claim their block building is “the biggest.”
  • Conversations about how they are comparing—one building may be taller (greater in length) and another may have a larger base (greater in area)—help students learn to discriminate and name these measureable attributes. As they discuss these situations and compare objects using different attributes, they learn to distinguish, label, and describe several measureable attributes of a single object. (Please reference page 6 in the Progression document)

Examples

  • Directly compare the heights of two objects and describe one object as taller/shorter.
  • A student may describe a shoe as, “The red shoe is heavier than the blue shoe (the blue shoe is the referent in this case)!  The red shoe is also longer!”
  • Illustrative Mathematics:

2021 Oregon Math Guidance: K.GM.C.8

  ODE and Oregon Math Project Logo

Cluster: K.GM.C - Describe and compare measurable attributes.

STANDARD: K.GM.C.8

 Standards Statement (2021):

Directly compare two objects with a measurable attribute in common, and describe which object has “more” or “less” of the attribute.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

K.GM.C.7

1.GM.B.4

K.DR.B.2, 1.DR.B.2

K.MD.A.2

K.GM.C Crosswalk

 Standards Guidance:

 

Clarifications

  • Students describe sets as having more, less, same as/equal.
  • Students can tell numbers that come before and after a given number up to 10. 
  • Students should be able to understand that each successive number name refers to a quantity that is one larger and the previous number name is one less.

Teaching Strategies

  • Use comparative vocabulary to directly compare two objects.
  • Have students directly compare lengths in simple situations, such as comparing people’s heights, because standing next to each other automatically aligns one endpoint.

Progressions

  • Kindergartners easily directly compare lengths in simple situations, such as comparing people’s heights, because standing next to each other automatically aligns one endpoint. However, in other situations they may initially compare only one endpoint of objects to say which is longer. Discussing such situations (e.g., when a child claims that he is “tallest” because he is standing on a chair) can help students resolve and coordinate perceptual and conceptual information when it conflicts. (Please reference page 6 in the Progression document).

Examples