Students begin to explore the concepts of multiplication and division, beginning in the context of equal group and array problems, moving to skip-counting and repeated addition, and ending with more complex and/or abstract problems.
Unit 2 opens students’ eyes to some of the most important content students will learn in Grade 3—multiplication and division. In this unit, “students begin developing these concepts by working with numbers with which they are more familiar, such as 2s, 5s, and 10s, in addition to numbers that are easily skip counted, such as 3s and 4s,” allowing the cognitive demand to be on the concepts of multiplication and division themselves rather than the numbers (CCSS Toolbox, Sequenced Units for the Common Core State Standards in Mathematics Grade 3). Then in Unit 3, students will work on the more challenging units of 0, 1, 6–9, and multiples of 10.
In Grade 2, students learned to count objects in arrays using repeated addition (2.OA.4) to gain a foundation to multiplication. They’ve also done extensive work on one- and two-step word problems involving addition and subtraction, having mastered all of the problem types that involve those operations (2.OA.1). Thus, students have developed a strong problem-solving disposition and have the foundational content necessary to launch right into multiplication and division in this unit.
At the start of this unit, students gain an understanding of multiplication and division in the context of equal group and array problems in Topic A. To keep the focus on the conceptual understanding of multiplication and division (3.OA.1, 3.OA.2), Topic A does not discuss specific strategies to solve, and thus students may count all objects (a Level 1 strategy) or remember their skip-counting and repeated addition (Level 2 strategies) from Grade 2 to find the product. In Topics B and C, however, the focus turns to developing more efficient strategies for solving multiplication and division, including skip-counting and repeated addition (Level 2 strategies) as well as “just knowing” the facts, which works toward the goal that “by the end of grade 3, [students] know from memory all products of two single-digit numbers and related division facts” (3.OA.7). As the Operations and Algebraic Thinking Progression states, “mastering this material and reaching fluency in single-digit multiplications and related division may be quite time consuming because there are no general strategies for multiplying or dividing all single-digit numbers as there are for addition or subtraction” (OA Progression, p. 22). Thus, because “there are many patterns and strategies dependent upon specific numbers,” they first work with factors of 2, 5, and 10 in Topic B, since they learned these skip-counting sequences in Grade 2. Then in Topic C, they work with the new factors of 3 and 4. Only then, when students have developed more familiarity with these factors, will students solve more complex and/or abstract problems with them, including determining the unknown whole number in a multiplication or division equation relating three whole numbers (3.OA.4) and solving two-step word problems using all four operations (3.OA.3, 3.OA.8), assessing the reasonableness of their answers for a variety of problem types in Topic D.
Throughout the unit, students engage in a variety of mathematical practices. The unit pays particular attention to reasoning abstractly and quantitatively, as students come to understand the meaning of multiplication and division and the abstract symbols used to represent them (MP.2). Further, students model with mathematics with these new operations, solving one- and two-step equations using them (MP.4).
This introduction to multiplication and division is further deepened in Unit 3, when students will explore the more difficult factors of 0, 1, 6–9, and multiples of 10. Then, in Unit 4, students will explore area as an application of multiplication. In Grade 4, their understanding of multiplication and division will be even more nuanced, when they will come to understand multiplicative comparison and solve word problems involving it (4.OA.1, 4.OA.2). Further, they’ll solve multi-step word problems involving all four operations, at times needing to interpret a remainder in the context of the problem (4.OA.3). Lastly, students will become more fluent with multiplication and division, multiplying a whole number of up to four digits by a one-digit whole number and two two-digit numbers, as well as dividing up to four-digit dividends by a one-digit divisor (4.NBT.5, 4.NBT.6). Multiplication and division provide a foundation for myriad algebraic and geometric topics from linear functions to trigonometry, and thus, this content is critical for all future mathematical learning.
Pacing: 19 instructional days (16 lessons, 2 flex days, 1 assessment day)
This assessment accompanies Unit 2 and should be given on the suggested assessment day or after completing the unit.
Additional assessment tools to help you monitor student learning
and identify any skill or knowledge gaps.
Learn how to use these tools with our
Guide to Assessments
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array | multiplication/multiply |
commutative property/commutative | product |
equal group | quotient |
divide/division | row/column |
dividend | $$\times$$ |
divisor | $$\div$$ |
factor |
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Intellectual Prep for All Units
Unit-Specific Intellectual Prep
3.OA.A.1
Identify and create situations involving equal groups and describe these situations using the language and notation of multiplication.
3.OA.A.1
Identify and create situations involving arrays and describe these situations using the language and notation of multiplication.
3.OA.A.1
3.OA.A.2
3.OA.A.3
Identify and create situations involving unknown group size and find group size in situations.
3.OA.A.1
3.OA.A.2
3.OA.A.3
Identify and create situations involving an unknown number of groups and find the number of groups in situations.
3.OA.A.1
3.OA.A.2
3.OA.A.3
3.OA.B.6
Relate multiplication and division and understand that division can represent situations of unknown group size or an unknown number of groups.
3.OA.A.1
3.OA.C.7
Build fluency with multiplication facts using units of 2, 5, and 10.
3.OA.B.5
Demonstrate the commutativity of multiplication.
3.OA.A.2
3.OA.B.6
3.OA.C.7
Build fluency with division facts using units of 2, 5, and 10.
3.OA.A.1
3.OA.A.2
3.OA.A.3
Solve one-step word problems involving multiplication and division using units of 2, 5, and 10.
3.OA.A.1
3.OA.A.2
3.OA.B.5
3.OA.B.6
3.OA.C.7
Build fluency with multiplication and division facts using units of 3.
3.OA.A.1
3.OA.A.2
3.OA.B.5
3.OA.C.7
Build fluency with multiplication and division facts using units of 4.
3.OA.A.1
3.OA.A.2
3.OA.A.3
Solve one-step word problems involving multiplication and division using units of 3 and 4.
3.OA.A.4
3.OA.C.7
3.OA.D.8
Determine the unknown whole number in a multiplication or division equation relating three whole numbers, including equations with a letter standing for the unknown quantity.
3.OA.A.1
3.OA.A.2
3.OA.A.3
Solve one-step word problems involving multiplication and division and write problem contexts to match expressions and equations.
3.OA.D.8
Solve two-step word problems involving multiplication and division and assess the reasonableness of answers.
3.OA.D.8
Solve two-step word problems involving all four operations and assess the reasonableness of answers.
Key: Major Cluster Supporting Cluster Additional Cluster
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