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Module 1

Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10

This 25-day module begins the year by building on students’ fluency with addition and knowledge of arrays.  Topic A initially uses repeated addition to find the total from a number of equal groups (2.OA.4).   As students notice patterns, they let go of longer addition sentences in favor of more efficient multiplication facts (3.OA.1, 3.OA.9).  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.

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.

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).

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). 

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).

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.

The mid-module assessment follows Topic C.  The end-of-module assessment follows Topic F

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Distribution of Minutes

  • Fluency Practice
  • Application Problem
  • Concept Development
  • Student Debrief
1
10 10 30 10
2
15 5 30 10
3
15 5 30 10
4
15 5 30 10
5
8 7 35 10
6
9 6 35 10
7
13 5 32 10
8
6 10 34 10
9
15 35 10
10
12 5 33 10
11
11 5 34 10
12
15 5 30 10
13
15 5 30 10
14
13 5 32 10
15
11 5 34 10
16
15 5 30 10
17
12 5 33 10
18
15 5 30 10
19
15 5 30 10
20
12 8 30 10
21
15 5 30 10

Mid-Module Assessment

End-of-Module Assessment