5.NBT.6

Standard

Find whole-number quotients of whole numbers with up to four-digit dividends and two-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 Language:

"I can divide four-digit dividends by two-digit divisors."
"I can illustrate and explain a division problem using equations, arrays and/or models."

Explanation

About the Math, Learning Targets, and Rigor

This standard references various strategies for division. Division problems can include remainders. Even though this standard leads more towards computation, the connection to story contexts is critical.

Make sure students are exposed to problems where the divisor is the number of groups and where the divisor is the size of the groups. In fourth grade, students’ experiences with division were limited to dividing by one-digit divisors.

See Division Strategies

Resources

Videos

Khan Academy
Learn Zillion
Virtual Nerd

EngageNY Lessons

Extra Practice

Released Assessment Questions

PARCC

Common Core State Standards

5.NBT.6

For the illustrate/explain aspect of 5.NBT.6, see 5.C.1-1, 5.C.2-1, and 5.C.4-3
Tasks involve 3- or 4-digit dividends and one- or two-digit divisors.

Performance Indicators: 5.NBT.6

Level 5: Exceeds Expectations

Divides whole numbers up to four-digit dividends and two-digit divisors using strategies based on place value, the properties of operations and/or the relationship between multiplication and division.

Illustrates and explains the calculations by using equations, rectangular arrays, and area models.

Checks reasonableness of answers by using multiplication or estimation.

Level 4: Meets Expectations

Divides whole numbers up to four-digit dividends and one-digit divisors which are multiples of ten using strategies based on place value, the properties of operations and/or the relationship between multiplication and division

Integrated Standards

5.NBT.Int.1

Perform exact or approximate multiplications and/or divisions that are best done mentally by applying concepts of place value, rather than by applying multi-digit algorithms or written strategies.

Performance Indicators: 5.NBT.Int.1

Level 5: Exceeds Expectations

Multiplies tenths by tenths or tenths by hundredths and divides in problems involving tenths and/or hundredths using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Performs exact and approximate multiplications and divisions by mentally applying place value strategies when appropriate. Relates the strategy to a written method.

Level 4: Meets Expectations

Multiplies tenths by tenths or tenths by hundredths and divides in problems involving tenths and/or hundredths using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relates the strategy to a written method.

Critiquing/Reasoning Standards

5.C.1

Base explanations/reasoning on place value and/or understanding of operations.

(Content Scope: Knowledge and skills articulated in 5.NBT.6)

Tasks do not have a context.

5.C.2-1

Base explanations/reasoning on the relationship between multiplication and division.

(Content Scope: Knowledge and skills articulated in 5.NBT.6)

5.C.4-3

Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method.

(Content Scope: Knowledge and skills articulated in 5.NBT.6)

Performance Indicators: 5.C.1, 5.C.2-1

Level 5: Exceeds Expectations

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

properties of operations
relationship between addition and subtraction
relationship between multiplication and division

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 counter-example where applicable.

Level 4: Meets Expectations

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

properties of operations
relationship between addition and subtraction
relationship between multiplication and division

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).

Performance Indicators: 5.C.4-3

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 well-organized and complete response based on operations using concrete referents such as diagrams--including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which may include:

a logical 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, approaches, and reasoning, and providing 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 well-organized and complete response based on operations using concrete referents such as diagrams--including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which may include:

a logical 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, approaches, and reasoning.

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