(OA) Operations and Algebraic Thinking

MAT-03.OA

Domain (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.

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 Thinking
Cluster: 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.

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-03.OA.02

Under Development

MAT-03 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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.

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-03.OA.03

3^rd Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Represent and solve problems involving multiplication and division.

MAT-03.OA.03 Using drawings and equations with a symbol for an unknown number, solve multiplication and division word problems within 100 in situations involving equal groups, arrays, and measurement quantities.

Proficiency Scale

MAT-03.OA.04

Under Development

MAT-03 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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 = ?.

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-03.OA.05

Under Development

MAT-03 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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

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-03.OA.06

Under Development

MAT-03 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: Understand properties of multiplication and the relationship between multiplication and division.

MAT-03.OA.06 Understand division as an unknown-factor 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-03.OA.07

3^rd Grade (MAT) Targeted Standard
(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.

Proficiency Scale

MAT-03.OA.07.a

MAT-03 Targeted Standards
(OA) Domain: Operations and Algebraic Thinking
Cluster: 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

Rubric / Proficiency Scale

Score		Description	Sample Activity
4.0	There are no advanced criteria for this task as this skill is foundational. Application of this standard will occur in solving 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 multiplication and division facts with at least 90% accuracy given 5 seconds per fact. I can answer almost all / all multiplication facts 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 multiplication with at least 85% accuracy given 5 seconds per fact.
2.0	Student is able to answer multiplication facts with at least 75% accuracy given 5 seconds per fact. I can answer many multiplication facts 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 multiplication facts with at least 50% accuracy given 5 seconds per fact.
1.0	Student is able to answer multiplication facts with at least 25% accuracy given 5 seconds per fact. I can answer some multiplication facts quickly.		-
	0.5	Limited or no understanding of the skill is demonstrated.

Resources

Websites

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 Thinking
Cluster: 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.

Rubric / Proficiency Scale

Score		Description	Sample Activity
4.0	There are no advanced criteria for this task as this skill is foundational. Application of this standard will occur in solving 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 division facts with at least 90% accuracy given 5 seconds per fact. I can answer almost all / all division facts 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 division facts with at least 85% accuracy given 5 seconds per fact.
2.0	Student is able to answer division facts with at least 75% accuracy given 5 seconds per fact. I can answer many division facts 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 division facts with at least 50% accuracy given 5 seconds per fact.
1.0	Student is able to answer division facts with at least 25% accuracy given 5 seconds per fact. I can answer some division facts quickly.		-
	0.5	Limited or no understanding of the skill is demonstrated.

Resources

Websites

Vocabulary

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

MAT-03.OA.08

3^rd Grade (MAT) Targeted Standard
(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.08 .Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies.

Proficiency Scale

MAT-03.OA.09

Under Development

MAT-03 Targeted Standards
(OA) Domain: 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 Standard Text

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.

Standards Book	MAT-03 "I can ... statements"
	(OA)	(NBT)	(NF)	(MD)	(G)
	Operations Algebraic Thinking	Number Operations Base Ten	Number Operations Fraction	Measurement Data	Geometry
Prioritized Standards
Kindergarten Math \| First Grade Math \| Second Grade Math Third Grade Math \| Fourth Grade Math \| Fifth Grade Math

MAT-03 "I can ... statements"

MAT-03.OA

Domain (OA)

Operations and Algebraic Thinking

Narrative for the (OA) Operations and Algebraic Thinking

Calculation Method for Domains

MAT-03.OA.01

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Skills (Performance) Targets

Product Targets

Proficiency (Rubric) Scale

Resources

Websites

Vocabulary

MAT-03.OA.02

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Skills (Performance) Targets

Product Targets

Proficiency (Rubric) Scale

Resources

Websites

Vocabulary

MAT-03.OA.03

MAT-03.OA.03 Using drawings and equations with a symbol for an unknown number, solve multiplication and division word problems within 100 in situations involving equal groups, arrays, and measurement quantities.

MAT-03.OA.04

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Skills (Performance) Targets

Product Targets

Proficiency (Rubric) Scale

Resources

Websites

Vocabulary

MAT-03.OA.05

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Skills (Performance) Targets

Product Targets

Proficiency (Rubric) Scale

Resources

Websites

Vocabulary

MAT-03.OA.06

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Skills (Performance) Targets

Product Targets

Proficiency (Rubric) Scale

Resources

Websites

Vocabulary

MAT-03.OA.07

MAT-03.OA.07 Using mental strategies, fluently multiply and divide within 100.

MAT-03.OA.07.a

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Rubric / Proficiency Scale

Resources

Websites

Vocabulary

MAT-03.OA.07.b

Student Learning Targets:

Knowledge Targets

Reasoning Targets

Rubric / Proficiency Scale

Resources

Websites

Vocabulary

MAT-03.OA.08

MAT-03.OA.08 .Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies.

MAT-03.OA.09

Student Learning Targets: