5.NBT.1

Standard

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Student Language:

"I can understand and explain the value of digits."

Explanation

About the Math, Learning Targets, and Rigor

This standard calls for students to reason about the magnitude of numbers. Students should work with the idea that the tens place is ten times as much as the ones place, and the ones place is 1/10𝑡ℎ the size of the tens place. In fourth grade, students examined the relationships of the digits in numbers for whole numbers only. This standard extends this understanding to the relationship of decimal fractions.

Example:

A student thinks, “I know that in the number 5555, the 5 in the tens place (5555) represents 50 and the 5 in the hundreds place (5555) represents 500. So a 5 in the hundreds place is ten times as much as a 5 in the tens place or a 5 in the tens place is 1 10 of the value of a 5 in the hundreds place”.

Resources

Videos

Khan Academy
Learn Zillion
Virtual Nerd

EngageNY Lessons

Extra Practice

Released Assessment Questions

PARCC

Common Core State Standards

5.NBT.1

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Tasks have “thin context” or no context.
Tasks involve the decimal point in a substantial way (e.g., by involving a comparison of a tenths digit to a thousandths digit or a tenths digit to a tens digit).

Performance Indicators: 5.NBT.1

Level 5: Exceeds Expectations

In any multi-digit number, recognizes a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left and uses whole number exponents to denote powers of 10 and uses symbols to compare two powers of 10 expressed exponentially (compare 10^2 to 10^5 ).

Level 4: Meets Expectations

In any multi-digit number, recognizes a digit in one place represents 10 times as much as it represents in the place to its right or 1/10 of what it represents in the place to its left and uses whole number exponents to denote powers of 10.

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.

Tasks do not have a context.

STUDENT SAMPLE RESPONSE

5.NBT.A.Int.1

Demonstrate understanding of the place value system by combining or synthesizing knowledge and skills articulated in 5.NBT.A.

STUDENT SAMPLE RESPONSE

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.

Performance Indicators: 5.NBT.A.Int.1

Level 5: Exceeds Expectations

In any multi-digit number, recognizes a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left and uses whole number exponents to denote powers of 10 and uses symbols to compare two powers of 10 expressed exponentially (compare 10^2 to 10^5 ).

Level 4: Meets Expectations

In any multi-digit number, recognizes a digit in one place represents 10 times as much as it represents in the place to its right or 1/10 of what it represents in the place to its left and uses whole number exponents to denote powers of 10.

Critiquing/Reasoning Standards

5.C.3

Reason about the place value system itself.

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

Tasks do not involve reasoning about place value in service of some other goal (e.g., to multiply multi-digit numbers). Rather, tasks involve reasoning directly about the place value system, in ways consistent with the indicated content scope.

Performance Indicators: 5.C.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 place value system including:

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 place value system including:

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.