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(OA) Operations and Algebraic Thinking

MAT-05.OA

BPSS-MAT logoDomain (OA)

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.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can

Product Targets

  • 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

Websites

  • Add resources with links, youtube or PDF

Vocabulary

  • List

 

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.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can

Product Targets

  • 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

Websites

  • Add resources with links, youtube or PDF

Vocabulary

  • List

 

MAT-05.OA.03

BPSS-MAT logo 5th Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Analyze patterns and relationships.

MAT-05.OA.03 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns. Graph the ordered pairs on a coordinate plane. Use the graph to verify relationships. 

proficiency scale iconProficiency Scale

MAT-05.OA.04

BPSS-MAT logo 5th Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Gain familiarity with factors and multiples.

MAT-05.OA.04 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. 

proficiency scale iconProficiency Scale