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# Geometry

## Narrative for the (G) Geometry

In Grade 1, students reason about shapes. They describe and classify shapes, including drawings, manipulatives, and physical-world objects, in terms of their geometric attributes. That is, based on early work recognizing, naming, sorting, and building shapes from components, they describe in their own words why a shape belongs to a given category, such as squares, triangles, circles, rectangles, rhombuses, (regular) hexagons, and trapezoids (with bases of different lengths and nonparallel sides of the same length). In doing so, they differentiate between geometrically defining attributes (e.g., “hexagons have six straight sides”) and non-defining attributes (e.g., color, overall size, or orientation).

Students compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) using other shapes. Students also decompose shapes by partitioning circles and rectangles into two and four equal shares, describe the shares using the words such as halves, fourths, and quarters.

## 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-01.G.01

Under Development

 MAT-01 Targeted Standards(G) Domain: GeometryCluster: Reason with shapes and their attributes. MAT-01.G.01 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining 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-01.G.02

Under Development

 MAT-01 Targeted Standards(G) Domain: GeometryCluster: Reason with shapes and their attributes. MAT-01.G.02 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

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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-01.G.03

(G) Geometry
Cluster: Represent and interpret data.

# Measurement and Data

## Narrative for the (MD) Measurement and Data

First graders continue working on using direct comparison to measure—carefully, considering all endpoints—when that is appropriate. In situations where direct comparison is not possible or convenient, they should be able to use indirect comparison and explanations that draw on transitivity. Once they can compare lengths of objects by direct comparison, they could compare several items to a single item, such as finding all the objects in the classroom the same length as (or longer than, or shorter than) their forearm. Another important set of skills and understandings is ordering a set of objects by length.

Directly comparing objects, indirectly comparing objects, and ordering objects by length are important practically and mathematically, but they are not length measurement, which involves assigning a number to a length. Students learn to lay physical units such as centimeter or inch manipulatives end-to-end and count them to measure a length.

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 Grade 1 begin to organize and represent categorical data. For example, if a collection of specimens is sorted into two piles based on which specimens have wings and which do not, students might represent the two piles of specimens on a piece of paper, by making a group of marks for each pile, as shown below (the marks could also be circles, for example). The groups of marks should be clearly labeled to reflect the attribute in question. Students in Grade 1 can ask and answer questions about categorical data based on a representation of the data.

## 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-01.MD.01

Under Development

 MAT-01 Targeted Standards(MD) Domain: Measurement and DataCluster: Measure lengths indirectly and by iterating length units. MAT-01.MD.01 Order three objects by length; compare the lengths of two objects indirectly by using a third 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-01.MD.02

Under Development

 MAT-01 Targeted Standards(MD) Domain: Measurement and DataCluster: Measure lengths indirectly and by iterating length units. MAT-01.MD.02 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

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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-01.MD.03

(MD) Measurement and Data
Cluster: Tell and write time.

#### MAT-01.MD.04

(MD) Measurement and Data
Cluster: Represent and interpret data.

# 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 first grade, students learn to view ten ones as a unit called a ten. The ability to compose and decompose this unit flexibly and to view the numbers 11 to 19 as composed of one ten and some ones allows development of efficient, general base-ten methods for addition and subtraction. Students see a two-digit numeral as representing some tens and they add and subtract using this understanding.

First graders use their base-ten work to compute sums within 100 with understanding.  Concrete objects or drawings afford connections with written numerical work and discussions and explanations in terms of tens and ones.  First graders also engage in mental calculation, such as mentally finding 10 more or 10 less than a given two-digit number without having to count by 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-01.NBT.01

(NBT) Number and Operations in Base Ten
Cluster: Extend the counting sequence.

#### MAT-01.NBT.02

(NBT) Number and Operations in Base Ten
Cluster: Understand place value.

##### MAT-01.NBT.01 Demonstrate understanding that the two digits of a two-digit number represent amounts of tens and ones, including:
a. 10 can be thought of as a bundle of ten ones — called a “ten.”.
b. The numbers from 11 to 19 are composed of a ten and additional ones.
c. Multiples of 10 up to 90 represent a number of tens and 0 ones.

#### MAT-01.NBT.02.a

Under Development

 MAT-01 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Understand place value. MAT-01.NBT.02.a Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones — called a “ten.”

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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-01.NBT.02.b

Under Development

 MAT-01 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Understand place value. MAT-01.NBT.02.b Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

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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-01.NBT.02.c

Under Development

 MAT-01 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Understand place value. MAT-01.NBT.02.c Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

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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-01.NBT.03

Under Development

 MAT-01 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Understand place value. MAT-01.NBT.03 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

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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-01.NBT.04

Under Development

 MAT-01 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to add and subtract. MAT-01.NBT.04 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

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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-01.NBT.05

Under Development

 MAT-01 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to add and subtract. MAT-01.NBT.05 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

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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-01.NBT.06

Under Development

 MAT-01 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to add and subtract. MAT-01.NBT.06 Use place value understanding and properties of operations to add and subtract

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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

# Operations and Algebraic Thinking

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

Algebraic thinking is about generalizing arithmetic operations and operating on unknown quantities.  It involves recognizing and analyzing patterns and developing generalizations about these patterns.  In algebra, symbols can be used to represent generalizations. Operations and Algebraic Thinking deals with the basic operations - addition, subtraction, multiplication, and division - the relationships they model, the kinds of problems they can be used to solve, as well as, their mathematical properties and relationships.

First grade students extend their Kindergarten work in three major and interrelated ways. These include representing and solving a new type of problem situation – comparison; representing and solving problems in which the result is unknown, the change is unknown, and the start is unknown. (10 + 2 = ___; 9 + ___ = 15; ___ + 14=20); and develop more sophisticated strategies to extend addition and subtraction problem solving beyond 10, to problems within 20.

Students in 1st grade begin developing an algebraic perspective many years before they will use formal algebraic symbols and methods. They read to understand the problem situation, represent the situation and its quantitative relationships with expressions and equations, and then manipulate that representation if necessary, using properties of operations and/or relationships between operations. Linking equations to concrete materials, drawings, and other representations of problem situations affords deep and flexible understandings of these building blocks of algebra. Learning where the total is in addition equations (alone on one side of the equal sign) and in subtraction equations (to the left of the minus sign) helps students move from a situation equation to a related solution equation.

## 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-01.OA.01

(OA) Operations and Algebraic Thinking
Cluster: Represent and solve problems involving addition and subtraction.

#### MAT-01.OA.02

Under Development

 MAT-01 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Represent and solve problems involving addition and subtraction. MAT-01.OA.02 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

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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-01.OA.03

Under Development

 MAT-01 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Understand and apply properties of operations and the relationship between addition and subtraction. MAT-01.OA.03 Apply properties of operations as strategies to add and subtract.

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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-01.OA.04

Under Development

 MAT-01 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Understand and apply properties of operations and the relationship between addition and subtraction. MAT-01.OA.04 Understand subtraction as an unknown-addend problem.

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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-01.OA.05

Under Development

 MAT-01 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Add and subtract within 20. MAT-01.OA.05 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

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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-01.OA.06

(OA) Operations and Algebraic Thinking
Cluster: Add and subtract within 20.

#### MAT-01.OA.06.a

 MAT-01 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Add and subtract within 20. MAT-01.OA.06.a Add within 20, fluently to 10.

## Student Learning Targets:

### Knowledge Targets

• I can say the answer for addition facts to 10 quickly (within 5 seconds).

## Resources

### Vocabulary

• sum
• plus

#### MAT-01.OA.06.b

 MAT-01 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Add and subtract within 20. MAT-01.OA.06.b Subtract within 20, fluently to 10.

## Student Learning Targets:

### Knowledge Targets

• I can say the answer for subtraction facts to10 fluently (within 5 seconds).

## Rubric/Proficiency Scale

 Score Description Sample Activity 4.0 Student is able to answer subtraction facts to 20 with at least 90% accuracy given 5 seconds per fact. I can answer almost all subtraction facts to 20 quickly. - 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 demonstrate understanding of subtraction facts to 10 with at least 90% accuracy given 5 seconds per fact. I can say the answer for almost all subtraction facts to 10 quickly. - 2.5 Student answers subtraction facts to 10 with 80% accuracy given 5 seconds per fact. 2.0 Student is able to demonstrate understanding of subtraction facts to 10 with at least 70% accuracy given 5 seconds per fact. I can say the answer for many subtraction facts to 10 quickly. - 1.5 Student answers subtraction facts to 10 with 50% accuracy given 5 seconds per fact. 1.0 Student is able to demonstrate understanding of subtraction facts to 10 with less than 50% accuracy given 5 seconds per fact. I can say the answer for some subtraction facts to 10 quickly.                     ____________ and ___________________ Student is able to demonstrate understanding of subtraction facts to 5 with 85% accuracy given 5 seconds per fact. I can say the answer for subtraction facts to 5 quickly. - 0.5 Limited or no understanding of the skill is demonstrated. Student is unable to demonstrate understanding of subtraction facts to 5 with least 85% accuracy given 5 seconds per fact. (Kindergarten Target)

## Resources

### Vocabulary

• subtraction facts
• difference
• subtract
• minus

#### MAT-01.OA.07

Under Development

 MAT-01 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Work with addition and subtraction equations. MAT-01.OA.07 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

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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-01.OA.08

Under Development

 MAT-01 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Work with addition and subtraction equations. MAT-01.OA.08 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers.

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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.