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
The scope and sequence for 3rd Grade Math was adjusted in August 2022. The scaled bar and picture graphs (3.MD.3) topic has been moved from this unit to Unit 2.
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 skip-counting (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 two-step 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 2-5 and 10, students could count all of the objects to find the product, a Level 1 strategy, and used skip-counting as their fluency developed. But, because of the increased difficulty of 6–9 facts, students will not only rely on skip-counting (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 one-digit numbers by multiples of 10 and by two-digit numbers using the associative property. Finally, students solve two-step 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 two-step 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 multi-step multiplicative comparison words problems in Grade 4 to polynomial multiplication and division in Algebra 2, and lots in between. Thus, this unit sets the seal on major work of Grade 3 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 Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the Mid-Unit Assessment after lesson 16.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
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
To see all the vocabulary for Unit 3, view our 3rd Grade Vocabulary Glossary.
Word Problems and Fluency Activities
Access daily word problem practice and our content-aligned fluency activities created to help students strengthen their application and fluency skills.
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: Two-Step 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.
Unit 2
Multiplication and Division, Part 1
Unit 4
Area