All categories Categories All categories Not categorized (CC) Counting and Cardinality (G) Geometry (MD) Measurement and Data (NBT) Number and Operation in Base Ten (OA) Operations and Algebraic Thinking Prioritized Standards

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# Counting and Cardinality

## Narrative for the (CC) Counting and Cardinality

Counting and Cardinality and Operations and Algebraic Thinking are about understanding and using numbers. Counting and Cardinality underlies Operations and Algebraic Thinking as well as Number and Operations in Base Ten. It begins with early counting and telling how many in one group of objects. Addition, subtraction, multiplication, and division grow from these early roots.

Students usually know or can learn to say the counting words up to a given number before they can use these numbers to count objects or to tell the number of objects. In Kindergarten, students develop understanding of the relationship between numbers and quantities and connect counting to cardinality - to count a group of objects, they pair each word said with one object.  Students also develop fluency with counting to 100 by ones and tens, count to answer "how many" questions, use counting strategies to compare groups of objects, and apply counting strategies when solving addition and subtraction problems.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-00.CC.01

Kindergarten (MAT) Targeted Standard
(CC) Counting Cardinality
Cluster: Know number names and the count sequence.

#### MAT-00.CC.02

Under Development

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Know number names and the count sequence. MAT-00.CC.02 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). Count backward from a given number within 10.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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#### MAT-00.CC.03

Kindergarten (MAT) Targeted Standard
(CC) Counting Cardinality
Cluster: Know number names and the count sequence.

#### MAT-00.CC.04

Under Development

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Count to tell the number of objects.. MAT-00.CC.04 Understand the relationship between numbers and quantities; connect counting to cardinality.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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#### MAT-00.CC.04.a

Under Development

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Count to tell the number of objects. MAT-00.CC.04.a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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#### MAT-00.CC.04.b

Under Development

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Count to tell the number of objects. MAT-00.CC.04.b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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#### MAT-00.CC.04.c

Under Development

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Count to tell the number of objects. MAT-00.CC.04.c Understand that each successive number name refers to a quantity that is one larger.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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#### MAT-00.CC.05

Kindergarten (MAT) Targeted Standard
(CC) Counting Cardinality
Cluster: Know number names and the count sequence.

##### MAT-00.CC.05 Count to answer how many questions.
a. Tell how many objects up to 20 are in an arranged pattern (e.g., a line or an array) or up to 10 objects in a scattered configuration.
b. Represent a number of objects up to 20 with a written numeral.
c. Given a number from 1-20, count out that many objects.

#### MAT-00.CC.06

Kindergarten (MAT) Targeted Standard
(CC) Counting Cardinality
Cluster: Compare numbers.

#### MAT-00.CC.07

Under Development

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Compare numbers. MAT-00.CC.07 Compare two numbers between 1 and 10 presented as written numerals.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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# Geometry

## Narrative for the (G) Geometry

Understanding and describing shapes and space is one of the two critical areas of Kindergarten mathematics. Students develop geometric concepts and spatial reasoning from experience with two perspectives on space: the shapes of objects and the relative positions of objects.

In the domain of shape, students learn to match two-dimensional shapes even when the shapes have different orientations. They learn to name shapes such as circles, triangles, and squares, whose names occur in everyday language, and distinguish them from non-examples of these categories, often based initially on visual models. Students also begin to name and describe three-dimensional shapes with mathematical vocabulary, such as “sphere,” “cube,” “cylinder,” and “cone.” They 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.

A second 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.

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.”  They use these spatial reasoning competencies, along with their growing knowledge of three-dimensional shapes and their ability to compose them, to model objects in their environment.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-00.G.01

Under Development

 MAT-00 Targeted Standards(G) Domain: Geometry Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). MAT-00.G.01 Describe objects in the environment using names of shapes and solids (squares, circles, triangles, rectangles, cubes, and spheres).

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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#### MAT-00.G.02

Kindergarten (MAT) Targeted Standard
(G) Geometry
Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

#### MAT-00.G.03

Under Development

 MAT-00 Targeted Standards(G) Domain: Geometry Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). MAT-00.G.03 Identify shapes and solids (squares, circles, triangles, rectangles, cubes, and spheres) as two-dimensional or three-dimensional.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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