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(OA) Operations and Algebraic Thinking

MAT-01.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.

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

BPSS-MAT logo 1st Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Represent and solve problems involving addition and subtraction.

MAT-01.OA.01 Use strategies to add and subtract within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. 

proficiency scale iconProficiency Scale

MAT-01.OA.02

 Under Development

MAT-01 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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.

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-01.OA.03

 Under Development

MAT-01 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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.

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-01.OA.04

 Under Development

MAT-01 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Understand and apply properties of operations and the relationship between addition and subtraction.

MAT-01.OA.04 Understand subtraction as an unknown-addend problem.

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-01.OA.05

 Under Development

MAT-01 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Add and subtract within 20.

MAT-01.OA.05 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

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-01.OA.06

BPSS-MAT logo 1st Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Add and subtract within 20.

MAT-01.OA.06 Use strategies to add and subtract within 20. Fluently add and subtract within 10. 

proficiency scale iconProficiency Scale

MAT-01.OA.06.a

 

MAT-01 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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).

Reasoning Targets

Skills (Performance) Targets

Product Targets

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0

Student is able to answer addition facts to 20 with at least 90% accuracy given 5 seconds per fact.

I can answer almost all addition 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 addition facts for sums to 10 with at least 90% accuracy given 5 seconds per fact.

I can say the answer for almost all facts to 10 quickly.

 -
  2.5

Student answers facts to 10 with 80% accuracy given 5 seconds per fact.
2.0

Student is able to demonstrate understanding of addition facts for sums to 10 with at least 70% accuracy given 5 seconds per fact.

I can say the answer for many facts to 10 quickly.

 -
  1.5

Student answers facts to 10 with 50% accuracy given 5 seconds per fact.

1.0

Student is able to demonstrate understanding of addition facts for sums to 10 with less than 50% accuracy given 5 seconds per fact

I can say the answer for some addition facts to 10 quickly.

                    ____________ and ___________________

Student is able to demonstrate understanding of addition facts for sums to 5 with 85% accuracy given 5 seconds per fact.

I can say the answer for addition facts to 5 quickly.

 -
  0.5

Limited or no understanding of the skill is demonstrated.

Student is unable to demonstrate understanding of addition facts for sums to 5 with least 85% accuracy given 5 seconds per fact. (Kindergarten Target)

Resources

Websites

Vocabulary

  • addition facts
  • sum
  • add
  • plus

 

MAT-01.OA.06.b

 

MAT-01 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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).

Reasoning Targets

Skills (Performance) Targets

Product Targets

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

Websites

Vocabulary

  • subtraction facts
  • difference
  • subtract
  • minus

 

 

MAT-01.OA.07

 Under Development

MAT-01 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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.

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-01.OA.08

 Under Development

MAT-01 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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.

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