## EngageNY - Module 1

## Module 1: Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10

## This module begins the year by building on students’ fluency with addition and knowledge of arrays.

**Topic A:**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.

**Lesson 1: Understand**

*equal groups*of as multiplication.****

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Lesson 2: Relate Multiplication to the array model**

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Additional Video**:

**LearnZillion**Enter the

**Quick Code: LZ3083**

**Lesson 3: Interpret the meaning of factors ─ the size of the group or the number of groups.**

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Topic B:**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.

**Lesson 4: Understand the meaning of the unknown as the size of the group in division.**

__.__

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Additional Video**:

**LearnZillion**Enter the

**Quick Code: LZ965**

**Lesson 5: Understand the meaning of the unknown as the number of groups in division.**

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Lesson 6: Interpret the unknown in division using the array model.**

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Topic C:**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**).

**Lesson 7: Demonstrate the commutativity of multiplication and practice related facts by skip-counting objects in array models.**

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Additional Video**:

**LearnZillion**Enter the

**Quick Code: LZ963**

**Lesson 8: Demonstrate the commutativity of multiplication and practice related facts by skip-counting objects in array models.**

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Lesson 9: Find related multiplication facts by adding and subtracting equal groups in array models.**

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Additional Video:**

**Math Rocks "Repeated Addition"**by Mr. Woller

**Lesson 10: Model the distributive property with arrays to decompose units as a strategy to multiply.**

__Instruction Guide:__**This is the link to see what the teachers use for classroom instruction.**

**Additional Video**:

**LearnZillion**Enter the

**Quick Code: LZ966**

**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**).

**Lesson 11: Model division as the unknown factor in multiplication using arrays and tape diagrams.**

**This is the link to see what the teachers use for classroom instruction.**

__Instruction Guide:__

Lesson 12: Interpret the quotient as the number of groups or the number of objects in each group using units of 2.

Lesson 12: Interpret the quotient as the number of groups or the number of objects in each group using units of 2.

**This is the link to see what the teachers use for classroom instruction.**

__Instruction Guide:__**Lesson 13:**Interpret the quotient as the number of groups or the number of objects in each group using units of 3.

**This is the link to see what the teachers use for classroom instruction.**

__Instruction Guide:__**Topic E:**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**).

**Lesson 14: Skip-Count objects in models to build fluency with multiplication facts using units of 4.**

**Lesson 15: Relate arrays to tape diagrams to model the commutative property of multiplication.**

**Lesson 16: Use the distributive property as a strategy to find related multiplication facts.**

**Lesson 17: Model the relationship between multiplication and division.**

**Topic F:**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**).

**Lesson 18: Apply the distributive property to decompose units.**

Lesson 19: Apply the distributive property to decompose units.

Lesson 20: Solve two-step word problems involving multiplication and division and assess the reasonableness of answers.

Lesson 21: Solve two-step word problems involving all four operations and assess the reasonableness of answers.

Lesson 19: Apply the distributive property to decompose units.

Lesson 20: Solve two-step word problems involving multiplication and division and assess the reasonableness of answers.

Lesson 21: Solve two-step word problems involving all four operations and assess the reasonableness of answers.