Grade 3 Mathematics Module 1, Topic A, Overview
Multiplication and the Meaning of the Factors
Lessons in Topic A move students toward understanding familiar repeated addition from Grade 2 in the form of array models, which become a cornerstone of the module. Students use the language of multiplication as they understand what factors are and differentiate between the size of groups and the number of groups within a given context. In this module the factors 2, 3, 4, 5, and 10 provide an entry point for moving into more difficult factors in later modules.
Grade 3 Mathematics Module 1, Topic B, Overview
Division as an Unknown Factor Problem
Study of factors links Topics A and B; Topic B extends the study to division. Students understand division as an unknown factor problem, and relate the meaning of unknown factors to either the number or the size of groups (3.OA.2, 3.OA.6). By the end of Topic B students are aware of a fundamental connection between multiplication and division that sets the foundation for the rest of the module.
Grade 3 Mathematics Module 1, Topic C, Overview
Analyzing Arrays to Multiply Using Units of 2 and 3
In Topic C, students use the array model and familiar skip-counting strategies to solidify their understanding of multiplication and practice related facts of 2 and 3. They become fluent enough with arithmetic patterns to “add” or “subtract” groups from known products to solve more complex multiplication problems (3.OA.1, 3.OA.9). They apply their skills to word problems using drawings and equations with a symbol to find the unknown factor (3.OA.3). This culminates in students using arrays to model the distributive property as they decompose units to multiply (3.OA.5).
Grade 3 Mathematics Module 1, Topic D, Overview
In Topic D students model, write and solve partitive and measurement division problems with 2 and 3 (3.OA.2). Consistent skip-counting strategies and the continued use of array models are pathways for students to naturally relate multiplication and division. Modeling advances as students use tape diagrams to represent multiplication and division. A final lesson in this topic solidifies a growing understanding of the relationship between operations (3.OA.7).
Grade 3 Mathematics Module 1, Topic E, Overview
Multiplication and Division Using Units of 4
Topic E shifts students from simple understanding to analyzing the relationship between multiplication and division. Practice of both operations is combined—this time using units of 4—and a lesson is explicitly dedicated to modeling the connection between them (3.OA.7). Skip-counting, the distributive property, arrays, number bonds and tape diagrams are tools for both operations (3.OA.1, 3.OA.2, 3.OA.9). A final lesson invites students to explore their work with arrays and related facts through the lens of the commutative property as it relates to multiplication (3.OA.5).
Grade 3 Mathematics Module 1, Topic F, Overview
Distributive Property and Problem Solving Using Units of 2–5 and 10
Topic F introduces the factors 5 and 10, familiar from skip-counting in Grade 2. Students apply the multiplication and division strategies they have used to mixed practice with all of the factors included in Module 1 (3.OA.1, 3.OA.2, 3.OA.3). Students model relationships between factors, analyzing the arithmetic patterns that emerge to compose and decompose numbers as they further explore the relationship between multiplication and division (3.OA.3, 3.OA.5, 3.OA.7, 3.OA.9).
In the final lesson of the module, students apply the tools, representations, and concepts they have learned to problem-solving with multi-step word problems using all four operations (3.OA.3, 3.OA.8). They demonstrate the flexibility of their thinking as they assess the reasonableness of their answers for a variety of problem types.
Multiplication and the Meaning of the Factors
Lessons in Topic A move students toward understanding familiar repeated addition from Grade 2 in the form of array models, which become a cornerstone of the module. Students use the language of multiplication as they understand what factors are and differentiate between the size of groups and the number of groups within a given context. In this module the factors 2, 3, 4, 5, and 10 provide an entry point for moving into more difficult factors in later modules.
Grade 3 Mathematics Module 1, Topic B, Overview
Division as an Unknown Factor Problem
Study of factors links Topics A and B; Topic B extends the study to division. Students understand division as an unknown factor problem, and relate the meaning of unknown factors to either the number or the size of groups (3.OA.2, 3.OA.6). By the end of Topic B students are aware of a fundamental connection between multiplication and division that sets the foundation for the rest of the module.
Grade 3 Mathematics Module 1, Topic C, Overview
Analyzing Arrays to Multiply Using Units of 2 and 3
In Topic C, students use the array model and familiar skip-counting strategies to solidify their understanding of multiplication and practice related facts of 2 and 3. They become fluent enough with arithmetic patterns to “add” or “subtract” groups from known products to solve more complex multiplication problems (3.OA.1, 3.OA.9). They apply their skills to word problems using drawings and equations with a symbol to find the unknown factor (3.OA.3). This culminates in students using arrays to model the distributive property as they decompose units to multiply (3.OA.5).
Grade 3 Mathematics Module 1, Topic D, Overview
In Topic D students model, write and solve partitive and measurement division problems with 2 and 3 (3.OA.2). Consistent skip-counting strategies and the continued use of array models are pathways for students to naturally relate multiplication and division. Modeling advances as students use tape diagrams to represent multiplication and division. A final lesson in this topic solidifies a growing understanding of the relationship between operations (3.OA.7).
Grade 3 Mathematics Module 1, Topic E, Overview
Multiplication and Division Using Units of 4
Topic E shifts students from simple understanding to analyzing the relationship between multiplication and division. Practice of both operations is combined—this time using units of 4—and a lesson is explicitly dedicated to modeling the connection between them (3.OA.7). Skip-counting, the distributive property, arrays, number bonds and tape diagrams are tools for both operations (3.OA.1, 3.OA.2, 3.OA.9). A final lesson invites students to explore their work with arrays and related facts through the lens of the commutative property as it relates to multiplication (3.OA.5).
Grade 3 Mathematics Module 1, Topic F, Overview
Distributive Property and Problem Solving Using Units of 2–5 and 10
Topic F introduces the factors 5 and 10, familiar from skip-counting in Grade 2. Students apply the multiplication and division strategies they have used to mixed practice with all of the factors included in Module 1 (3.OA.1, 3.OA.2, 3.OA.3). Students model relationships between factors, analyzing the arithmetic patterns that emerge to compose and decompose numbers as they further explore the relationship between multiplication and division (3.OA.3, 3.OA.5, 3.OA.7, 3.OA.9).
In the final lesson of the module, students apply the tools, representations, and concepts they have learned to problem-solving with multi-step word problems using all four operations (3.OA.3, 3.OA.8). They demonstrate the flexibility of their thinking as they assess the reasonableness of their answers for a variety of problem types.