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, 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 Grade 3, 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 Grade 3 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 Grade 5 (5.NBT.6) and to fluency with the division algorithm in Grade 6 (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 Grade 4.
Pacing: 19 instructional days (16 lessons, 2 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 20212022 school year, see our 4th Grade Scope and Sequence Recommended Adjustments.
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Resource: Progressions for the Common Core State Standards for Mathematics by Common Core Standards Writing Team
This assessment accompanies Unit 3 and should be given on the suggested assessment day or after completing the unit.
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 this course, view our 4th Grade Vocabulary Glossary.
Word Problems and Fluency Activities
Access daily word problem practice and our contentaligned fluency activities created to help students strengthen their application and fluency skills.
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.
Unit 2
MultiDigit Multiplication
Unit 4
Fraction Equivalence and Ordering