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#### MAT-05.NF.07.c

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.07.c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.

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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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# 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.

As preparation for the Expressions and Equations domain in the middle grades, students in Grade 5 begin working more formally with expressions. They write expressions to express a calculation, e.g., writing 2 x (8+7) to express the calculation “add 8 and 7, then multiply by 2.” They also evaluate and interpret expressions, e.g., using their conceptual understanding of multiplication to interpret 3 x (18932+921) as being three times as large as 18932+921, without having to calculate the indicated sum or product. Students in Grade 5 begin to think about numerical expressions in ways that prepare their later work with variable expressions (e.g., three times an unknown length is 3 x L).

Students extend their Grade 4 pattern work by working briefly with two numerical patterns that can be related and examining these relationships within sequences of ordered pairs and in graphs. This work prepares students for studying proportional relationships and functions in middle school.

## 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-05.OA.01

Under Development

 MAT-05 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Write and interpret numerical expressions. MAT-05.OA.01 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

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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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### Vocabulary

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#### MAT-05.OA.02

Under Development

 MAT-05 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Write and interpret numerical expressions. MAT-05.OA.02 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

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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

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#### MAT-05.OA.03

(OA) Operations and Algebraic Thinking
Cluster: Analyze patterns and relationships.