# MAT-00 "I can ... statements"

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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

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Know number names and the count sequence. MAT-00.CC.01 Count to 100 by ones and by tens. Counts backward from 20 by ones.

## Student Learning Targets:

### Knowledge Targets

• I can count to 100 by ones.

• I can count to 100 by tens.

### Skills (Performance) Targets

• I can count to 100 by ones.
• I can count to 100 by tens.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Student is able to count without error to 120 starting at any number. I can count (out loud and written) to 120 starting from any number. 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 Student is able to count to 100 by ones without error. and Student is able to count to 100 by tens without error. I can count out loud to 100 by ones starting from one. I can count out loud to 100 by tens starting from ten. - 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 rote count to at least 50 by ones without error. and Student is able to rote count to at least 50 by tens without error. I can count out loud to 50 by ones starting from one. I can count out loud to 50 by tens starting from 10. - 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 rote count up to 20 by ones, but may have errors among the teen numbers. I can count out loud to 10 starting from one with no mistakes. I can count out loud higher than 10 but I make some mistakes. - 0.5 Limited or no understanding of the skill is demonstrated. Student is unable to rote count to 10 without error.

## Resources

### Vocabulary

• Count
• Number Words (zero - one hundred)

#### 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.

## Resources

### Vocabulary

• List

#### MAT-00.CC.03

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Know number names and the count sequence. MAT-00.CC.03 Write numbers sequentially from 0 to 20. Write a given number from 0 to 20.   (Note: The second part of this standard is assessed within 00.CC.05 - Count to answer "How many.")

## Student Learning Targets:

### Skills (Performance) Targets

• I can write numbers from 0 to 20 in order.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Student is able to write numbers to 100 with no errors. I can write numbers 0-100 in order with no mistakes. - 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 Student is able to write numbers 0-20 in order with no errors. I can write numbers 0-20 in order with no mistakes. - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. Student is able to write numbers 0-20 with no more than two errors. 2.0 Student is able to write numbers above 10, with no errors existing for writing numbers 0-10 in order. I can write numbers 0-10 in order with no mistakes. - 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 write numbers 1-10, with no errors existing for writing numbers 1-5. I can write numbers 1-5 in order with no mistakes. - 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• number words (zero - twenty)

#### 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.

## Resources

### Vocabulary

• List

#### 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.

## Resources

### Vocabulary

• List

#### 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.

## Resources

### Vocabulary

• List

#### 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.

## Resources

### Vocabulary

• List

#### MAT-00.CC.05

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Count to tell the number of objects. MAT-00.CC.05 Count to answer how many questions.

## Student Learning Targets:

### Reasoning Targets

• I can match a number to show how many objects I count.

### Skills (Performance) Targets

• I can count to tell you how many.
• I can write a number to show how many.
• I can count the number of things asked for.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Advanced criteria under development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content. - 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 Student is able to write a number to show "how many" up to 20 objects without error. I can write a number to show how many objects I count with no mistakes. - 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 match a numeral to a quantity up to 20 objects without error. I can match numbers to show how many objects I count with no mistakes. - 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 count/show quantities up to 20 objects when asked with no errors for the quantities 1 to 5. I can count/show up to 5 objects when asked for with no mistakes. - 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• number words (zero - twenty)
• count

#### MAT-00.CC.06

 MAT-00 Targeted Standards(CC) Domain: Counting and Cardinality Cluster: Compare numbers. MAT-00.CC.06 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group up to 10 objects, e.g., by using matching and counting strategies.

## Student Learning Targets:

### Reasoning Targets

• I can compare groups to decide which is greater than, less than, or equal to another group. (up to 10 objects)

### Skills (Performance) Targets

• I can show/create a group that has an equal amount to another group.
• I can show/create a group that is less than the amount in another group.
• I can show/create a group that is greater than the amount in another group.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Advanced criteria under development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content. - 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 Student is able to identify/create groups greater than, less than, and equal to another group without error. I can show/create a group that has an equal amount to another group. I can show/create a group that is less than the amount in another group. I can show/create a group that is greater than the amount in another group. - 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 demonstrate understanding of at least 2 of the 3 concepts: greater than, less than, and equal to another group without error. I can show/create a group that has an equal amount to another group. I can show/create a group that is less than the amount in another group. I can show/create a group that is greater than the amount in another group. - 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 identify or create groups using the terms "more, less, bigger, smaller, and/or same. I can show which group has more or less, is bigger or smaller. I can show a group that has the same amount as another group. 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

• greater than
• less than
• equal to
• more / bigger
• less / smaller
• same

#### 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.

## Resources

### Vocabulary

• List

#### MAT-00.G.02

 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.02 Correctly name shapes and solids (squares, circles, triangles, rectangles, cubes,and spheres) regardless of their orientations or overall size.

## Student Learning Targets:

### Knowledge Targets

• I can name 2-D and 3-D shapes.

### Reasoning Targets

• I can understand the size of a shape does not change its name.
• I can understand the direction of a shape does not change its name.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Advanced criteria under development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content. - 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 Student is able to correctly name all 2-D and 3-D shapes - circle, square, triangle, rectangle, hexagon, and rhombus, cube, cone, cylinder, and sphere. I can name the 2-D shapes asked for - circle, square, triangle, rectangle, hexagon, and rhombus. I can name the 3-D shapes asked for - cube, cone, cylinder, and sphere. 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 correctly name all 2-D shapes correctly - circle, square, triangle, rectangle, hexagon, and rhombus. I can name the 2-D shapes asked for - circle, square, triangle, rectangle, hexagon, and rhombus. - 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 name basic 2-D shapes - circle, square, and triangle. I can name circles, squares, and triangles. - 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• square
• circle
• triangle
• rectangle
• hexagons
• cube
• cone
• cylinder
• sphere
• flat
• solid
• side
• corner
• angle
• edge
• face
• 2-D
• 3-D

#### 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.

## Resources

### Vocabulary

• List

#### MAT-00.G.04

Under Development

 MAT-00 Targeted Standards(G) Domain: Geometry Cluster: Analyze, compare, create, and compose shapes. MAT-00.G.04 Compare and classify two-dimensional shapes (squares, circles, triangles,rectangles) of different sizes and orientations, using informal language to describe their similarities, differences, and attributes.

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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.

## Resources

### Vocabulary

• List

#### MAT-00.G.05

Under Development

 MAT-00 Targeted Standards(G) Domain: Geometry Cluster: Analyze, compare, create, and compose shapes. MAT-00.G.05 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

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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.

## Resources

### Vocabulary

• List

#### MAT-00.G.06

Under Development

 MAT-00 Targeted Standards(G) Domain: Geometry Cluster: Analyze, compare, create, and compose shapes. MAT-00.G.06 Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle?

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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.

• List

# Measurement and Data

## Narrative for the (MD) Measurement and Data

Measurement is the process of assigning a number to a magnitude of some attribute shared by some class of objects, such as length, relative to a unit. 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

As students work with data in Grades K–5, they build foundations for their study of statistics and probability in Grades 6 and beyond, and they strengthen and apply what they are learning in arithmetic. Kindergarten work with data uses counting and order relations. First- and second-graders solve addition and subtraction problems in a data context.

Students in Kindergarten classify objects into categories, initially specified by the teacher and perhaps eventually elicited from students. For example, in a science context, the teacher might ask students in the class to sort pictures of various organisms into two piles: organisms with wings and those without wings. Students can then count the number of specimens in each pile. Students can use these category counts and their understanding of cardinality to say whether there are more specimens with wings or without wings.

## 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.MD.01

Under Development

 MAT-00 Targeted Standards(MD) Domain: Measurement and Data Cluster: Describe and compare measurable attributes. MAT-00.MD.01 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single 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.

## Resources

### Vocabulary

• List

#### MAT-00.MD.02

Under Development

 MAT-00 Targeted Standards(MD) Domain: Measurement and Data Cluster: Describe and compare measurable attributes. MAT-00.MD.02 Directly compare two objects with a measurable attribute in common, to see which object has more of/less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

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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.

## Resources

### Vocabulary

• List

#### MAT-00.MD.03

Under Development

 MAT-00 Targeted Standards(MD) Domain: Measurement and Data Cluster: Classify objects and count the number of objects in each category. MAT-00.MD.03 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

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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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# Number and Operation in Base Ten

## Narrative for the (NBT) Number and Operation in Base Ten

Students’ work in the base-ten system is intertwined with their work on counting and cardinality, and with the meanings and properties of addition, subtraction, multiplication, and division. Work in the base-ten system relies on these meanings and properties, but also contributes to deepening students’ understanding of them.

In Kindergarten, teachers help children lay the foundation for understanding the base-ten system by drawing special attention to 10. Children learn to view the whole numbers 11 through 19 as ten ones and some more ones. They decompose 10 into pairs such as 1 9, 2 8, 3 7 and find the number that makes 10 when added to a given number such as 3. Students use objects, math drawings, and equations to describe, explore, and explain how the “teen numbers,” the counting numbers from 11 through 19, are ten ones and some more ones.

## 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.NBT.01

 MAT-00 Targeted Standards(NBT) Domain: Number and Operation in Base Ten Cluster: Work with numbers 11­-19 to gain foundations for place value. MAT-00.NBT.01 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8);.

## Student Learning Targets:

### Reasoning Targets

• I can understand numbers 11-19 are made of a group of ten ones plus some more ones.

### Skills (Performance) Targets

• I can show how many tens and how many ones make a written number.
• I can show you how many ones make a ten.
• I can break a number apart to show tens and ones.
• I can write the number a base ten picture shows.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Student is able to compose and decompose numbers, identify the number of tens and ones, and identify the value of digits in a number within 100. (1st grade) - 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 Student is able to correctly decompose numbers 11-19 into a group of ten and ones. I can show how many tens and how many ones make a written number. I can break a number apart to show a ten and ones. - 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 correctly write numbers 11-19 given a base ten model (objects or drawings) of the number. I can write the number a base ten picture or model shows. - 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 identify objects or drawings that represent a ten and some more ones, but may have a simple counting error. I can show the picture or objects that tell how many tens and how many ones are asked for. I can show how many ones make a ten. - 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• number words (one - nineteen)
• left overs
• 10 = ten ones
• tens
• ones

# Operations and Algebraic Thinking

## Narrative for the (OA) Operations and Algebraic Thinking

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.

In Kindergarten, students develop meanings for addition and subtraction as they encounter problem situations, and they extend these meanings as they encounter increasingly difficult problem situations in Grade 1. They represent these problems in increasingly sophisticated ways. And they learn and use increasingly sophisticated computation methods to find answers. Students learn and use mathematical and non-mathematical language, especially when they make up problems and explain their representation and solution.

Students in Kindergarten work with the following types of addition and subtraction situations: Add To with Result Unknown; Take From with Result Unknown; and Put Together/Take Apart with Total Unknown and Both Addends Unknown.

## 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.OA.01

Under Development

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.01 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

• I can

• I can

• I can

• I can

## 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.

## Resources

### Vocabulary

• List

#### MAT-00.OA.02

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.02 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

## Student Learning Targets:

### Reasoning Targets

• I can decide when I need to add or subtract in a problem.

### Skills (Performance) Targets

• I can solve addition word problems.
• I can solve subtraction word problems.
• I can use drawings or objects to show the problem.

## Resources

### Vocabulary

• join
• put together
• separate
• take away
• take apart
• take from
• subtract
• plus
• minus
• equal to
• same as
• less
• total
• sum
• difference

#### MAT-00.OA.03

Under Development

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.03 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

• I can

• I can

• I can

• I can

## 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.

## Resources

### Vocabulary

• List

#### MAT-00.OA.04

Under Development

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.04 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

• I can

• I can

• I can

• I can

## 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.

## Resources

### Vocabulary

• List

#### MAT-00.OA.05

Under Development

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.05 Fluently add and subtract within 5.

• I can

• I can

• I can

• I can

## 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.

## Resources

### Vocabulary

• List

#### MAT-00.OA.05.a

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.05.a Fluently add basic facts within 5

## Student Learning Targets:

### Knowledge Targets

• I can say the answer for addition facts to 5 quickly (within 5 seconds).

## Resources

### Vocabulary

• sum

#### MAT-00.OA.05.b

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.05.b Fluently subtract basic facts within 5

## Student Learning Targets:

### Knowledge Targets

• I can say the answers to subtraction facts within 5 quickly (within 5 seconds).

## Resources

### Vocabulary

• subtract
• subtraction facts
• difference
• minus

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