(OA) Operations and Algebraic Thinking Categories All categories Not categorized Prioritized (G) Geometry (MD) Measurement and Data (NBT) Number and Operations in Base Ten (NF) Number and Operations - Fractions (OA) Operations and Algebraic Thinking

# 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.

Students in Grade 3 begin the step to formal algebraic language by using a letter for the unknown quantity in expressions or equations for one and two-step problems. As with two-step problems at Grade 2, which involve only addition and subtraction, the Grade 3 two-step word problems vary greatly in difficulty and ease of representation. More difficult problems may require two steps of representation and solution rather than one

Students focus on understanding the meaning and properties of multiplication and division and on finding products of single-digit multiplying and related quotients.  These skills and understandings are crucial; students will rely on them for years to come as they learn to multiply and divide with multi-digit whole number and to add, subtract, multiply and divide with fractions and with decimals.

All of the understandings of multiplication and division situations, of the levels of representation and solving, and of patterns culminate by the end of Grade 3 in fluent multiplying and dividing all single-digit numbers and 10. This is the outcome of a carefully designed learning process that heavily involves the interplay of practice and reasoning about the relationship between multiplication and division facts.

## 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 proficiency scales for individual standards within the Domain.

#### MAT-03.OA.01

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Represent and solve problems involving multiplication and division. MAT-03.OA.01 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.

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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-03.OA.02

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Represent and solve problems involving multiplication and division. MAT-03.OA.02 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

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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-03.OA.03

(OA) Operations and Algebraic Thinking
Cluster: Represent and solve problems involving multiplication and division.

#### MAT-03.OA.04

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Represent and solve problems involving multiplication and division. MAT-03.OA.04 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = [ ] ÷ 3, 6 x 6 = ?.

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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-03.OA.05

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Understand properties of multiplication and the relationship between multiplication and division. MAT-03.OA.05 Apply properties of operations as strategies to multiply and divide

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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-03.OA.06

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Understand properties of multiplication and the relationship between multiplication and division. MAT-03.OA.06 Understand division as an unknown-factor 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-03.OA.07

(OA) Operations and Algebraic Thinking
Cluster: Represent and solve problems involving multiplication and division.

##### MAT-03.OA.07 Using mental strategies, fluently multiply and divide within 100.
Use multiple strategies such as count-by/skip counting, doubles, double/doubles, double/double/doubles, derived facts, benchmark numbers, decomposition.

#### MAT-03.OA.07.a

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Multiply and divide within 100. MAT-03.OA.07.a Fluently multiply within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40/5 = 8) or properties of operations. By end of Grade 3, know from memory all products of two one-digit numbers. (Fluently multiply basic facts within 100)

## Student Learning Targets:

### Knowledge Targets

• I can recall from memory the products of multiplication facts up to 10 x 10.

### Reasoning Targets

• I can think about the facts I know to help me find the answers to the facts I need to learn

## Resources

### Vocabulary

• factor
• product
• unknown
• strategies
• mental computation
• know from memory
• multiplication facts
• properties of operations - how numbers work

#### MAT-03.OA.07.b

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Multiply and divide within 100. MAT-03.OA.07.b Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40/5 = 8) or properties of operations. By end of Grade 3, know from memory all products of two one-digit numbers. (Fluently divide basic facts within 100)

## Student Learning Targets:

### Knowledge Targets

• I can recall from memory the quotients of division facts to 100.

### Reasoning Targets

• I can think about the facts I know to help me find the answers to the facts I need to learn.

## Resources

### Vocabulary

• divide
• quotient
• unknown
• strategies
• mental computation
• know from memory
• division facts
• properties of operations - how numbers work

#### MAT-03.OA.08

(OA) Operations and Algebraic Thinking
Cluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic. Multiply and divide within 100.

#### MAT-03.OA.09

Under Development

 MAT-03 Targeted Standards (OA) Domain: Operations and Algebraic ThinkingCluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic. Multiply and divide within 100. MAT-03.OA.09 Standard Text

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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.