Second Grade Math


(OA) Operations and Algebraic Thinking

MAT-02.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 analysing 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.

Grade 2 students build upon their work in Grade 1 with operations and algebraic thinking in two major ways. They represent and solve situational problems which involve addition and subtraction within 100 rather than within 20, and they represent and solve two-step situational problems in which the result is unknown, the change is unknown, and the start is unknown. (20 + 15 = ___; 20 + ___ = 46; ___ + 14=26)

The experiences students have with addition and subtraction in Kindergarten and Grade 1 culminate in Grade 2 with students becoming fluent in single-digit addition facts and the related subtraction facts using the mental strategies as needed.  Fluency in each grade involves a mixture of just knowing some answers, knowing some answers from patterns (e.g., “adding 0 yields the same number”), and knowing some answers from the use of strategies. As an outcome of a multi-year process that heavily involves the interplay of practice and reasoning, students have sufficient experience with addition and subtraction to know single-digit sums from memory by the end of the K–2 grade span.

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-02.OA.01

 

MAT-02 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Represent and solve problems involving addition and subtraction.

MAT-02.OA.01 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

  • I can decide if I need to add or subtract to solve a word problem.

Skills (Performance) Targets

  • I can use addition and subtraction to solve one-step word problems
  • I can use addition and subtraction to solve two-step word problems.
  • I can represent what is happening in a problem using drawings, models, and numbers.
  • I can write an equation with a symbol for the unknown to represent a word problem.

Product Targets

 

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0

Student is able to solve two-step word problems using the four operations; represent these problems using equations with a letter for the unknown quantity; and assess the reasonableness of answers using mental computation and estimation strategies including rounding.

I can use addition, subtraction, multiplication, and division to solve two-step word problems.

I can write an equation to represent the problem using a letter for the unknown quantity.

I can use mental math and estimation strategies to decide if my answer is reasonable.

-
  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 use addition and subtraction within 100 to solve one and two-step problems with unknowns in all positions by using drawings and equations with a symbol for the unknown number to represent the problem (eg. 23 + 45 = ___ ; 23+ __ = 68; ___ +  45 = 68).

I can use addition and subtraction to solve one-step and two-step problems.

I can write an equation with a symbol for the unknown in all positions.

I can represent what is happening in a problem using drawings, models, or numbers.

-
  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 solve one-step problems and represent the problems with an equation using a symbol for the unknown.

I can use addition and subtraction to solve one-step problems using numbers under 100 with no mistakes.

I can show what is happening in a problem using drawings, models, or numbers.

I can write an equation with a symbol for the unknown 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 solve one-step word problems within 100, but may have minor counting errors within the solution.

and

Student attempts to represent the problems with an equations using a symbol for the unknown, but may have errors.

I can use addition and subtraction to solve one-step problems using numbers under 100, but I may have a mistake.

I can show what is happening in a problem using drawings, models, or numbers.

I can sometimes write an equation with a symbol for the unknown.

-
  0.5 Limited or no understanding of the skill is demonstrated.

Resources

Websites

Vocabulary

  • add
  • subtract
  • more
  • less
  • equal
  • equation
  • unknown
  • putting together
  • taking apart
  • taking from
  • addend
  • sum
  • difference

 


MAT-02.OA.02

 Under Development

MAT-02 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Add and subtract within 20.

MAT-02.OA.02 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit 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

 


MAT-02.OA.02.a

 

MAT-02 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Add and subtract within 20.

MAT-02.OA.02.a Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Know from memory: The ability to compute math facts with automaticity (3-5 seconds) and confidence (ND).

Student Learning Targets:

Knowledge Targets

  • I can answer addition facts to 20 quickly (3-5 seconds).

Reasoning Targets

Skills (Performance) Targets

Product Targets

 

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0 There are no advanced criteria for this task as recall of basic facts is foundational.  Application of this skill will occur within tasks requiring addition within 100 and word problems.
-
  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 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.

-
  2.5

No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.

Student is able to answer addition facts to 20 with 80% accuracy given 5 seconds per fact..

2.0

Student is able to answer addition facts to 20 with at least 75% accuracy given 5 seconds per fact.

I can answer many addition facts to 20 quickly.

-
  1.5

In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.

Student is able to answer addition facts to 20 with  50% accuracy given 5 seconds per fact.

1.0

Student is able to answer addition facts to 20 with less than 50% accuracy given 5 seconds per fact.

and

Student is able to answer addition facts to 10 with 90% accuracy given 5 seconds per fact.

I can answer almost all addition facts to 10 quickly.

I can answer some addition facts to 20 quickly.

-
  0.5

Limited or no understanding of the skill is demonstrated.

Student is unable to answer addition facts to 10 with at least 90% accuracy given 5 seconds per fact (1st grade target)

Resources

Websites

Vocabulary

  • addition facts
  • add
  • sum
  • know from memory
  • plus
  • equals

 


MAT-02.OA.02.b

 

MAT-02 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Add and subtract within 20.

MAT-02.OA.02.b Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Know from memory: The ability to compute math facts with automaticity (3-5 seconds) and confidence (ND).

Student Learning Targets:

Knowledge Targets

  • I can answer subtraction facts to 20 quickly (3-5 seconds).

Reasoning Targets

Skills (Performance) Targets

Product Targets

 

Rubric / Proficiency Scale

Score   Description Sample Activity
4.0 There are no advanced criteria for this task as recall of basic facts is foundational.  Application of this skill will occur within tasks requiring subtraction within 100 and word problems -
  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 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.

-
  2.5

No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.

Student is able to answer subtraction facts to 20 with 80% accuracy given 5 seconds per fact.

2.0

Student is able to answer subtraction facts to 20 with at least 75% accuracy given 5 seconds per fact.

I can answer many subtraction facts to 20 quickly.

-
  1.5

In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content.

Student is able to answer subtraction facts to 20 with 50% accuracy given 5 seconds per fact.

1.0

Student is able to answer subtraction facts to 20 with less than 50% accuracy given 5 seconds per fact.

and

Student is able to answer subtraction facts to 10 with at least 90% accuracy given 5 seconds per fact

I can answer almost all subtraction facts to 10 quickly.

I can answer some subtraction facts to 20 quickly.

-
  0.5

Limited or no understanding of the skill is demonstrated.

Student is able to answer subtraction facts to 10 with at least 90% accuracy given 5 seconds per fact (1st grade target)

Resources

Websites

Vocabulary

  • subtraction facts
  • difference
  • know from memory
  • minus
  • subtract
  • equals

 


MAT-02.OA.03

 Under Development

MAT-02 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Work with equal groups of objects to gain foundations for multiplication.

MAT-02.OA.03 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

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-02.OA.04

 Under Development

MAT-02 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Work with equal groups of objects to gain foundations for multiplication.

MAT-02.OA.04 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

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