Students explore multidigit division and its applications, which include interpreting a remainder in division word problems and using division to interpret a repeating pattern.
Math
Unit 3
4th Grade
In this unit, 4th grade students explore the concept of multidigit division and its applications, such as interpreting a remainder in division word problems and using division to determine the $$n^{\mathrm{th}}$$ term in a repeating shape pattern.
Students developed a foundational understanding of division in 3rd grade, when they came to understand division in relation to equal groups, arrays, and area. They developed a variety of strategies to build towards fluency with division within 100, and they applied that knowledge to the context of one and twostep problems using the four operations. Students also came to understand the distributive property, which underpins the standard algorithm for division.
Just as at the beginning of the previous unit when students expanded their understanding of multiplication beyond 3rd grade understanding to include multiplicative comparison word problems, this unit starts off with introducing students to division problems with remainders, including interpreting them based on the context of the situation (4.OA.3). Next, students focus on extending their procedural skill with division to include up to fourdigit dividends with onedigit divisors (4.NBT.6), representing these cases with base ten blocks, the area model, partial quotients, and finally the standard algorithm, making connections between all representations as they go. The use of the area model serves to help students conceptually understand division, and as a connection to their work with area and perimeter (4.MD.3), a supporting cluster standard. Lastly, armed with a deep understanding of all four operations spanned over the last three units, students solve multistep problems involving addition, subtraction, multiplication, and division, including their new problem situations such as multiplicative comparison and interpreting remainders (4.OA.3). They also explore number and shape patterns, using the four operations to draw conclusions about them (4.OA.5).
Throughout the unit, students are engaging with the mathematical practices in various ways. For example, students are seeing and making use of structure (MP.7) as they “decompos[e] the dividend into like baseten units and find the quotient unit by unit” (NBT Progressions, p. 16). Further, "by reasoning repeatedly (MP.8) about the connection between math drawings and written numerical work, students can come to see multiplication and division algorithms as abbreviations or summaries of their reasoning about quantities” (NBT Progression, p. 14). Lastly, as students solve multistep word problems involving addition, subtraction, and multiplication, they are modeling with mathematics (MP.4).
After this unit, students will extend their conceptual understanding of multidigit division to computations with twodigit divisors in 5th Grade Math (5.NBT.6) and to fluency with the division algorithm in 6th Grade Math (6.NS.2). Every subsequent grade level depends on the understanding of multidigit division and its algorithms, making this unit an important one for students in 4th grade.
Pacing: 19 instructional days (16 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 10 .
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.
Models for up to 4digit by 1digit division  Written Numerical Work 
base ten block array (can be concrete or pictorial):

horizontally written partial quotients: 
area model with inefficient partial quotients:

partial quotients algorithm with inefficient partial quotients: 
area model with most efficient partial quotients:

partial quotients algorithm with efficient partial quotients: 

standard algorithm/long division: 
partial quotient
remainder
To see all the vocabulary for Unit 3 , view our 4th Grade Vocabulary Glossary.
Topic A: Understanding and Interpreting Remainders
Topic B: Division of up to FourDigit Whole Numbers by OneDigit Whole Numbers
Topic C: MultiStep Word Problems and Patterns
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
Solve division word problems with remainders.
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