Students deepen their understanding of multiplication and division, including their properties and extending their study of factors to include all units from 0 to 10, as well as multiples of 10 within 100.
Math
Unit 3
3rd Grade
Unit 3 extends the study of factors from 2, 3, 4, 5, and 10, which students explored in Unit 2, to include all units from 0 to 10, as well as multiples of 10 within 100. To work with these more challenging factors, students will rely on skipcounting (a Level 2 strategy) and converting to an easier problem (a Level 3 strategy dependent on the properties of operations). They then will apply their understanding of all four operations to twostep word problems as well as arithmetic patterns at the end of the unit.
Topic A begins by reminding students of the commutative property they learned in Unit 2, as well as introducing them to the distributive and associative properties, which they will rely upon for many of the strategies they learn for the larger factors. In order to be able to use these properties, they need to understand how to compute with a factor of 1, which they explore along with 0, as well as understand how to use parentheses. They’ll then explore the factors of 6, 7, 8, and 9 in Topics B and C. In Unit 2, when students were first introduced to multiplication and division with the easier factors of 25 and 10, students could count all of the objects to find the product, a Level 1 strategy, and used skipcounting as their fluency developed. But, because of the increased difficulty of 6–9 facts, students will not only rely on skipcounting (a Level 2 strategy), but also convert to an easier problem (a Level 3 strategy). Converting to an easier problem is dependent on the properties of operations (e.g., to find $$6\times7$$, think of $$5\times7$$ and add a group of 7 is dependent on the distributive property). Thus, students will work with the properties extensively throughout the unit, with their understanding of them and notation related to them growing more complex and abstract throughout the unit. In Topic D, students will multiply onedigit numbers by multiples of 10 and by twodigit numbers using the associative property. Finally, students solve twostep word problems involving all four operations, assessing the reasonableness of their answer, and identify arithmetic patterns and explain them using the properties of operations.
In Unit 3, students deepen their understanding of multiplication and division, including their properties. "Mathematically proficient students at the elementary grades use structures such as…the properties of operations…to solve problems" (MP.7) (Standards for Mathematical Practice: Commentary and Elaborations for K–5, p. 9). Students use the properties of operations to convert computations to an easier problem (a Level 3 strategy), as well as construct and critique the reasoning of others regarding the properties of operations (MP.3). Lastly, students model with mathematics with these new operations, solving one and twostep word problems using them (MP.4).
Students’ understanding of multiplication and division will further develop in Unit 4, when students study area. Students will also use their understanding of these operations in Unit 7 when they apply them in the context of measurement word problems. In subsequent years, students will depend on their conceptual understanding and fluency with these operations to apply and extend them in a variety of ways—everything from multistep multiplicative comparison words problems in 4th grade to polynomial multiplication and division in Algebra 2, and lots in between. Thus, this unit sets the seal on major work of 3rd grade as well as deeply important foundational work upon which students will rely for years to come.
Pacing: 26 instructional days (23 lessons, 2 flex days, 1 assessment day)
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The following assessments accompany Unit 3.
Have students complete the PreUnit Assessment and PreUnit Student SelfAssessment before starting the unit. Use the PreUnit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the MidUnit Assessment after lesson 16 .
Use the resources below to assess student understanding of the unit content and action plan for future units.
Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.
Read the following table that includes models used throughout the unit.
equal groups 
Example: 4 equal groups of 3 stars

array 
Example: 4 rows of 3

tape diagram 
Example: There are 4 bags with 3 plums in each bag. How many plums are there in all?

concrete or pictorial base ten blocks 
Example: Find $$2 \times 60$$ using base ten blocks.

parentheses, $${\left( \right)}$$
To see all the vocabulary for Unit 3 , view our 3rd Grade Vocabulary Glossary.
Topic A: Introduction to The Properties of Operations
Topic B: Multiplication and Division by 6 and 7
Topic C: Multiplication and Division by 8 and 9
Topic D: Multiplication and Division by Values Greater than 10
Topic E: TwoStep Word Problems and Patterns in Arithmetic
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Next
Study commutativity to find known facts of 6, 7, 8, and 9.
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