MAFS.5.NBT.1.2Archived Standard

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Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
General Information
Subject Area: Mathematics
Grade: 5
Domain-Subdomain: Number and Operations in Base Ten
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand the place value system. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    Items may contain whole number and decimal place values from millions to thousandths. Items may contain whole number exponents with bases of 10
  • Calculator :

    No

  • Context :

    No context

Sample Test Items (5)
  • Test Item #: Sample Item 5
  • Question: David multiplies and divides original numbers by powers of 10 to create new numbers.

     

    Which original numbers were multiplied by begin mathsize 12px style 10 cubed end style to create the new numbers?

     

  • Difficulty: N/A
  • Type: MS: Multiselect

Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Using Whole Number Exponents:

Students are asked to explain what 10 to the third power means and to rewrite 1,000,000 and a product of 10 using exponents.

Type: Formative Assessment

The Error:

Students are asked to analyze a problem in which a decimal number is multiplied by 10 to determine which of two answers is correct and discuss what happens when a decimal is divided by 10.

Type: Formative Assessment

Multiplying By Ten Three Times:

Students consider why a number multiplied by 10 to the third power will have three zeros in the product.

Type: Formative Assessment

How Many Zeros?:

Students are asked to determine how many zeros are in the expansion of 10 to the sixth power.

Type: Formative Assessment

Lesson Plans

Rounding Decimal Numbers - Lesson #3:

This is the final lesson in the Rounding Decimal Numbers Unit and will bring together the mathematical concepts in lesson 1 and 2. This lesson then bridges the computer science coding and mathematical thought process together as students dissect code that rounds decimal numbers as well as building their own code to make rounding an automated process.

Type: Lesson Plan

Rounding Decimal Numbers - Lesson #1:

This is lesson 1 of 3 in the Rounding Decimal Numbers unit. This lesson connects decimal place value names with exponential powers of ten. Through the inquiry based lesson, students will discover that there is a mathematical pattern they can use when performing multiplication and division using the powers of ten on a multi-digit decimal number.

Type: Lesson Plan

Rounding Decimal Numbers - Lesson #2:

This is lesson 2 of 3 in the Rounding Decimal Numbers unit. This lesson introduces Traditional Rounding method to determine an estimated value rounded to a specific place value. This lesson bridges the concepts of fractions to decimals and powers of ten as well expanded notation to rounding methods.

This lesson uses flowchart model to describe the method in which the rounding is performed. Rounded numbers are verified using a Scratch activity in this lesson.

Type: Lesson Plan

The Coasta with the Mosta:

Students will create an exciting and thrilling roller coaster model. Students will use their knowledge of forces to build a model of a roller coaster using foam insulation and a marble.

Type: Lesson Plan

What happens when you multiply by powers of 10?:

This lesson shows patterns when multiplying a whole number by powers of 10 through a hands-on conceptual approach that then leads into the procedure of multiplying numbers by a power of 10 and writing exponents using the base of 10.

This is intended to be an introductory lesson to the powers of ten in an exponent form. The concepts in this lesson will be a precursor to evaluating expressions using exponents and eventually scientific notation.

Type: Lesson Plan

X-treme Roller Coasters:

This MEA asks students to assist Ms. Joy Ride who is creating a virtual TV series about extreme roller coasters. They work together to determine which roller coaster is most extreme and should be featured in the first episode. Students are presented with research of five extreme roller coasters and they must use their math skills to convert units of measurements while learning about force and motion.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Seeking Patterns Using Base 10 and Powers of 10:

This lesson focuses on the exploration of patterns in the number of zeros of the product, when multiplying a number by powers of 10. It also uses whole-number exponents to denote powers of 10.

Patterns divided by a power of ten should be done in a subsequent lesson, once the students have the basic understanding of multiplying base ten by exponents.

Patterns using decimals should be done in a subsequent lesson, once the students have the basic understanding using whole numbers.

Type: Lesson Plan

Intro to Multiplying Decimals by 10, 100, 1000:

In this lesson, students are introduced to multiplying decimals by 10, 100, and 1000, in which students begin by creatively solving word problems. Students will analyze the number sentences used to solve the word problems, looking for and recording patterns and discovering that each place value has a value ten times as much as the place to its right, which is why each time a number is multiplied by 10, the digits move one place to the left.

Type: Lesson Plan

Original Student Tutorial

Base Ten and Exponents:

Explore base 10 and exponents in this baseball-themed, interactive tutorial. 

Type: Original Student Tutorial

Tutorials

Multiplying a Decimal by a Power of 10:

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

Type: Tutorial

Multiply and Divide Powers of 10: Zero Patterns:

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.  

Type: Tutorial

Powers of 10: Patterns:

This Khan Academy tutorial video presents the pattern, when multiplying tens, that develops when we compare the number of factors of tens with the number of zeros in the product. The vocabulary, exponent and base, are introduced.

Type: Tutorial

STEM Lessons - Model Eliciting Activity

X-treme Roller Coasters:

This MEA asks students to assist Ms. Joy Ride who is creating a virtual TV series about extreme roller coasters. They work together to determine which roller coaster is most extreme and should be featured in the first episode. Students are presented with research of five extreme roller coasters and they must use their math skills to convert units of measurements while learning about force and motion.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

MFAS Formative Assessments

How Many Zeros?:

Students are asked to determine how many zeros are in the expansion of 10 to the sixth power.

Multiplying By Ten Three Times:

Students consider why a number multiplied by 10 to the third power will have three zeros in the product.

The Error:

Students are asked to analyze a problem in which a decimal number is multiplied by 10 to determine which of two answers is correct and discuss what happens when a decimal is divided by 10.

Using Whole Number Exponents:

Students are asked to explain what 10 to the third power means and to rewrite 1,000,000 and a product of 10 using exponents.

Original Student Tutorials Mathematics - Grades K-5

Base Ten and Exponents:

Explore base 10 and exponents in this baseball-themed, interactive tutorial. 

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Base Ten and Exponents:

Explore base 10 and exponents in this baseball-themed, interactive tutorial. 

Type: Original Student Tutorial

Tutorials

Multiplying a Decimal by a Power of 10:

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

Type: Tutorial

Multiply and Divide Powers of 10: Zero Patterns:

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.  

Type: Tutorial

Powers of 10: Patterns:

This Khan Academy tutorial video presents the pattern, when multiplying tens, that develops when we compare the number of factors of tens with the number of zeros in the product. The vocabulary, exponent and base, are introduced.

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.