5.NBT.2 - About the Math, Learning Targets, and Rigor

Grade 5 Place Value and Decimals

5.NBT.2

About the Math

Full Standard

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.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

5th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.
4th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.

 

Learning Targets (I can)

  • Describe what an exponent is.
  • Express powers of 10 using exponents.
  • Explain the pattern for the number of zeros in a product and how they relate to a power of 10.
  • Explain and represent why the decimal point shifts when multiplying and dividing by powers of 10.

 

About the Math

So WHY can we just add (or subtract zeroes) when multiplying or dividing by a multiple or power of 10. When we think of 4 x 60 we are considering 4 groups of 6 tens or 4 x 6 x 10. We know that we can make use of the associative property and multiply 4 x 6. This results in 24 x 10. Therefore, we have 24 tens or 240. If we make use of the pattern, we see that we can simply multiply 4 x 6 in the original consideration (5 x 60) and just add a zero.

But does this work as well with larger numbers? Let's consider 50 x 700. We can think of this as (5 x 10) x (7 x 100). We know that we can rearrange the factors. A result of doing so is (5 x 7) x (10 x 100). From here, we can multiply with a result of 35 x 1,000 (because 10 groups of 100 is 1,000). Now, 35 x 1,000 is 35,000. (See figure B below) When you multiply by a multiple of 10 or a power of 10, explain why you can add zeros. When you multiply 50 x 500. Essential vocabulary for this standard includes: powers of 10, exponent, and decimal. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

Multiplying by a Power of 10
Figure A Figure B
4 x 60

= 4 x (6 x 10)

= (4 x 6) x 10

= 24 x 10

=240

 50 x 700

= (5 x 10) + (7 x 100)

= (5 x 7) x (10 x 100)

= 35 x 1,000

= 35,000
  • Describe what an exponent is.

An exponent identifies a quantity representing the power to which a given number or expression is to be raised.

  • Express powers of 10 using exponents.

Numbers, especially very large and very small numbers, can be represented with powers of 10.  

  • Explain the pattern for the number of zeros in a product and how they relate to a power of 10.
  • Explain and represent why the decimal point shifts when multiplying and dividing by powers of 10.

 Note that students should also have some understanding of the impact of powers of 10 and why they are used. The 1977 video "Powers of Ten" can be a nice way to introduce this standard.

 

 

Progression of Standard within Grade 5

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 
  • Describe what an exponent is.
  • Express powers of 10 using exponents.
  • Explain the pattern for the number of zeros in a product and how they relate to a power of 10.
  • Explain and represent why the decimal point shifts when multiplying and dividing by powers of 10.
  

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 4 Grade 6
  • Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (4.NBT.1)
  • Write and read decimals (4.NF.6)
  • Write/evaluate numerical expression with exponents (6.EE.1)

 

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction. 

  • Why does the product of 5 x 80 have two zeros?
  • When solving 382 x 10, Mary knows to take 382 and add a zero to make the answer 3,820. Why does this work? Use what you know about place value to explain.
  • John says if you divide 5,624 by 100, you just move the decimal point to the left two places to get the answer of 56.24. Is John right? Use your place value understanding to explain why this works.
  • The approximate height (in feet) of the Statue of Liberty can be expressed as 3 x 10 2 . Using what you know about exponents and place value, what is the height of the statue in whole numbers?
  • Jack is multiplying 64.15 x 10 so he put a zero at the end of the number to get his answer. 64.15 x 10 = 64.150. Explain why you agree or disagree with the Jack's thinking.

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 8 • Decimals

Exponents and Powers of Ten:

Multiplying and Dividing with Powers of Ten:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics 5-8 Exploring Powers of 10, Activity 10.8, Page 179 
Brain Compatible Activities for Math 4-5 9-12 "Guess-timate Estimates"

13-15 "Point and Play"

Introduction to the Process Standards

Problem Solving

 

 3-5 116-117 "Exploring Capacity"

Math In Practice

Teaching Fifth-Grade Mathematics

 5 Module 1

 

 

 

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

 

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Assessment

Learning Targets

rubric

  • Describe what an exponent is.
  • Express powers of 10 using exponents.
  • Explain the pattern for the number of zeros in a product and how they relate to a power of 10.
  • Explain and represent why the decimal point shifts when multiplying and dividing by powers of 10.

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.