Standard

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Student Translation

"I can find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors."

Explanation

About the Math, Learning Targets, and Rigor

In fourth grade, students build on their third grade work with division within 100. Students need opportunities to develop their understandings by using problems in and out of context.

This standard calls for students to explore division through various strategies.

*See Division Strategy Sheet

After developing an understanding of using arrays to divide, students begin to use a more abstract model for division. This model connects to a recording process that will be formalized in the 5th grade.

Resources

Videos

• Teaching Video (5:18-14:00)
• Khan Academy (scroll to find 4.NBT.6, click on a skill, find videos on left side in each skill)
• Learn Zillion
  • Videos

EngageNY Lessons

• Module 3, Topic E, Lesson 14: Solve division word problems with remainders.
• Module 3, Topic E, Lesson 15: Understand and solve division problems with a remainder using the array and area models.
• Module 3, Topic E, Lesson 16: Understand and solve two-digit dividend division problems with a remainder in the ones place by using number disks.
• Module 3, Topic E, Lesson 17: Represent and solve division problems requiring decomposing a remainder in the tens.
• Module 3, Topic E, Lesson 18: Find whole number quotients and remainders.
• Module 3, Topic E, Lesson 20: Solve division problems without remainders using the area model.
• Module 3, Topic E, Lesson 21: Solve division problems with remainders using the area model.
• Module 3, Topic G, Lesson 26: Divide multiples of 10, 100, and 1,000 by single-digit numbers.
• Module 3, Topic G, Lesson 27: Represent and solve division problems with up to a three-digit dividend numerically and with number disks requiring decomposing a remainder in the hundreds place.
• Module 3, Topic G, Lesson 28: Represent and solve three-digit dividend division with divisors of 2, 3, 4, and 5 numerically.
• Module 3, Topic G, Lesson 29: Represent numerically four-digit dividend division with divisors of 2, 3, 4, and 5, decomposing a remainder up to three times.
• Module 3, Topic G, Lesson 30: Solve division problems with a zero in the dividend or with a zero in the quotient.
• Module 3, Topic G, Lesson 32: Interpret and find whole number quotients and remainders to solve one-step division word problems with larger divisors of 6, 7, 8, and 9.
• Module 3, Topic G, Lesson 33: Explain the connection of the area model of division to the long division algorithm for three- and four-digit dividends. (*Only use for students who understand area model first*)

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 4th grade at bottom, then 4.NBT.6
• Common Core Sheets

Released Assessment Questions

PARCC

4.NBT.6-1

Find whole-number quotients and remainders with three-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

• Tasks do not have a context.
• Tasks may include remainders of 0 in no more than 20% of the tasks.
• For the illustrate/explain aspect of 4.NBT.6, see 4.C.1-2 below:
  • Base explanations/reasoning on the properties of operations.
    • Students need not use technical terms such as commutative, associative, distributive, or property.
    • Tasks do not have a context.
    • Unneeded parentheses should not be used. For example, use 4 + 3 x 2 rather than 4 + (3 x 2).
• For the illustrate/explain aspect of 4.NBT.6, see 4.C.2 below:
  • Base explanations/reasoning on the relationship between multiplication and division.
    • Tasks do not have a context.

4.NBT.6-2

Find whole-number quotients and remainders with four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

• Tasks do not have a context.
• Tasks may include remainders of 0 in no more than 20% of the tasks.
• For the illustrate/explain aspect of 4.NBT.6, see 4.C.1-2 below:
  • Base explanations/reasoning on the properties of operations.
    • Students need not use technical terms such as commutative, associative, distributive, or property.
    • Tasks do not have a context.
    • Unneeded parentheses should not be used. For example, use 4 + 3 x 2 rather than 4 + (3 x 2).
• For the illustrate/explain aspect of 4.NBT.6, see 4.C.2 below:
  • Base explanations/reasoning on the relationship between multiplication and division.
    • Tasks do not have a context.

Performance Indicators: 4.NBT.6

Level 5: Exceeds Expectations

• Solves multi-step word problems using the four operations with whole numbers: in multiplying a three-or four-digit by a one-digit number or two two-digit numbers.
• Finds whole number quotients and remainders with up to four-digit dividends and one-digit divisors and interprets remainders as appropriate.
• Chooses from a variety of strategies to solve these problems and selects an appropriate context for the task.

Level 4: Meets Expectations

• Solves two-step word and other problems using the four operations with whole numbers: in multiplying a three-digit by a one-digit number or two two-digit numbers
• Finds whole number quotients and remainders with up to three-digit dividends and one-digit divisors and interprets remainders as appropriate.
• Chooses from a variety of strategies to solve these problems.

Performance Indicators: 4.C.1-1 & 4.C.2

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a complete written response based on explanations/reasoning using the:

• properties of operations

• relationship between addition and subtraction

• relationship between multiplication and division

• identification of arithmetic patterns

Response may include:

• a logical/defensible approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• an efficient and logical progression of steps with appropriate justification
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, reasonings, and approaches, utilizing mathematical connections (when appropriate). Provides a counterexample where applicable.

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a complete written response based on explanations/reasoning using the:

• properties of operations
• relationship between addition and subtraction
• relationship between multiplication and division
• identification of arithmetic patterns Response may include:
• a logical/defensible approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• a logical progression of steps
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, reasonings, and approaches, utilizing mathematical connections (when appropriate).

Integrated Standards

4.Int.4

Solve one-step word problems involving dividing a four-digit number by a one-digit number.

• The given numbers are such as to require a general strategy based on place value and the properties of operations (e.g., 2328 ÷ 8).
• Quotients are whole numbers (i.e., there are no remainders).
• Word problems shall include a variety of grade-level appropriate applications and contexts.

Critiquing & Reasoning Standards

4.C.1-2

Base explanations/reasoning on the properties of operations.

(Content Scope: Knowledge and skills articulated in 4.NBT.6)

• Students need not use technical terms such as commutative, associative, distributive, or property.
• Tasks do not have a context.
• Unneeded parentheses should not be used. For example, use 4 + 3 x 2 rather than 4 + (3 x 2).

4.C.2

Base explanations/reasoning on the relationship between multiplication and division. (Content Scope: Knowledge and skills articulated in 4.NBT.6)

• Tasks do not have a context.

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