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
- Scroll to 5.NBT.1, click on skill, find videos on left side of each skill
- Learn Zillion
- Virtual Nerd
EngageNY Lessons
Extra Practice
- North Carolina Tasks
- Illustrative Math Tasks
- Howard County Tasks
- Click on 5th grade at bottom, then 5.NBT.1
- Common Core Sheets
PARCC
Common Core State Standards
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
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
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.