MA.6.NSO.3.3

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Evaluate positive rational numbers and integers with natural number exponents.

Clarifications

Clarification 1: Within this benchmark, expectations include using natural number exponents up to 5.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Number Sense and Operations
Standard: Apply properties of operations to rewrite numbers in equivalent forms.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Base (of an exponent)
  • Expression
  • Exponents
  • Factors
  • Integers
  • Rational Number

 

Vertical Alignment

Previous Benchmarks

http://flbt5.floridaearlylearning.com/standards.html

Next Benchmarks

 

Purpose and Instructional Strategies

In grade 5, students multiplied multi-digit whole numbers and fractions. In the grade 6, students evaluate positive rational numbers and integers with natural number exponents. In grade 7, students will apply the Laws of Exponents with rational number bases and whole-number exponents. 
  • Instruction focuses on the connection to repeated multiplication.
  • Instruction allows student flexibility in their solution (MTR.2.1).
    • For example, allow for both fraction and decimal response when the base is a fraction or a decimal.
  • Instruction provides opportunities for students to continue to practice and apply multiplying fractions by fractions, decimals by decimals, and integers by integers (MTR.5.1).
  • Instruction includes the use of technology to explore and evaluate positive rational numbers and integers with natural number exponents.
  • The expectation of this benchmark is the application of exponents, not the determining of the value of and expressions with multiple operations.
    • For example, (−12)4 and (215)3 would be appropriate, but 1.2583 − 122 or (2153)(712) would not be appropriate.

 

Common Misconceptions or Errors

  • Students may multiply the base by the exponent instead of multiplying the base by itself as many times as directed by the exponent. t. Instruction includes students using expanded form to represent the multiplication.
    • For example, 1.2583 written in expanded form is (1.258)(1.258)(1.258).
  • Some students may incorrectly apply or use incorrect notation when exponents are applied to negative integers. If a negative integer has an exponent, the negative number base must be in parentheses and the exponent is on the outside of the parentheses (MTR.5.1).
    • For example, (−12)4 = (−12)(−12)(−12)(−12) is not the same as −124 = −(12)(12)(12)(12).

 

Strategies to Support Tiered Instruction

  • Instruction includes rewriting exponential expressions in expanded form to represent the multiplication before evaluating.
    • For example:
      • (14)3 = 14.14.14. = 1.1.14.4.4 = 164 
      • (−6)3 = (−6)(−6)(−6) = 36(−6) = −216 
      • 1.2583 = (1.258)(1.258)(1.258)
  • Teacher creates and posts an anchor chart with visual representations of base of an exponent, exponent, power, and factor then encourages students to utilize the anchor chart to assist in correct academic vocabulary when evaluating exponential expressions.
  • Instruction includes the use of exponent tiles to represent and evaluate numerical exponential expressions.
  • Teacher provides students with flash cards to practice and reinforce academic vocabulary.

 

Instructional Tasks

Instructional Task 1 (MTR.4.1) 
Robin determines the volume of a cube with side lengths of 3.4 cm to be 10.2 cm3. Mickey says the volume is 39.304 cm3. Which person is correct and why?

Instructional Task 2 (MTR.4.1) 
Sean told Parker that −53 = (−5)3. Parker told Sean that he is incorrect. Is Sean correct or is Parker correct? How do you know?

Instructional Task 3 (MTR.6.1)
Determine if 84 is equivalent to 48. Explain your reasoning.

 

Instructional Items

Instructional Item 1
What is the value of the expression (13)3 ?

Instructional Item 2
What is the value of the expression 25?

Instructional Item 3
What is the value of the expression 0.13?

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 - 2024, 2024 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.NSO.3.AP.3a: Identify what an exponent represents (e.g., 8³= 8 × 8 × 8).
MA.6.NSO.3.AP.3b: Solve numerical expressions involving whole-number bases and exponents (e.g.,5+Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.×6=101).

Related Resources

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

Formative Assessments

Paul’s Pennies:

Students are asked to write and evaluate a numerical expression using exponents.

Type: Formative Assessment

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

Evaluating Exponents:

Students are asked to expand and evaluate exponential expressions containing whole number exponents.

Type: Formative Assessment

Lesson Plans

Order Matters:

Students will analyze a Scratch program and compare its computerized algorithm to the mathematical order of operations, in this lesson plan.

Type: Lesson Plan

The Power of Exponents :

Students will be introduced to the power of exponents through the parable A Grain of Rice, by Demi. Students analyze the parts of an exponential expression and evaluate the expression using mental math and paper and pencil.

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

Collectively Collecting:

In this lesson, students will examine and experience collecting like terms through an analogy to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for transitioning a concrete experience to the abstract level and a card-matching activity.

Type: Lesson Plan

The "Power" of Exponents:

The students will use square tiles or cubes to explore the meaning of "squared" and "cubed" numbers. They will model squared and cubed numbers to build a strong foundation for working with exponents. The students will learn the connections between area and volume models and the related positive exponents. This is an introductory lesson.

Type: Lesson Plan

Multiplying terms that have the same base:

Students explore numerical examples involving multiplying exponential terms that have the same base. They generalize the property of exponents where, when multiplying terms with the same base, the base stays the same and the exponents are added together.

Type: Lesson Plan

Scavenger Hunt for Multiplying and Dividing Powers:

Get your students up and moving and interested in simplifying expressions with whole integer powers. After getting your students to figure out what it takes to multiply and divide powers with whole number exponents, have your students scurry about the room to find the questions and answers for scavenger hunt exercise. The lesson includes questions and answers for the hunt, directions for the hunt, printable cards for the hunt, and step by step directions on how to get your students to figure out what they need to do when multiplying and dividing powers with whole number exponents.

Type: Lesson Plan

It's Hip 2b^2 eXponent^s:

Meaning of Exponents... Students will write and simplify numerical and algebraic expressions with natural number exponents. Bases are limited to positive integers.

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

Multiplying with Common Bases:

This resource provides a Lesson Plan for teaching students how to apply the Product of Powers Property of exponents. They will be able to write equivalent exponential expressions and evaluate them when possible.

Type: Lesson Plan

Original Student Tutorial

MacCoder’s Farm Part 2: Condition Statements:

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

Tutorials

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

Patterns in Raising 1 and -1 to Different Powers:

You will discover rules to help you determine the sign of an exponential expression with a base of -1.

Type: Tutorial

Introduction to Exponents:

This video demonstrates how to evaluate expressions with whole number exponents.

Type: Tutorial

The Zero Power:

Learn why a number raised to the zero power equals 1.

Type: Tutorial

MFAS Formative Assessments

Evaluating Exponents:

Students are asked to expand and evaluate exponential expressions containing whole number exponents.

Paul’s Pennies:

Students are asked to write and evaluate a numerical expression using exponents.

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.

Computer Science Original Student Tutorials

MacCoder’s Farm Part 2: Condition Statements:

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

Click below to check out the other tutorials in the series.

Student Resources

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

Original Student Tutorial

MacCoder’s Farm Part 2: Condition Statements:

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

Tutorials

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

Patterns in Raising 1 and -1 to Different Powers:

You will discover rules to help you determine the sign of an exponential expression with a base of -1.

Type: Tutorial

Introduction to Exponents:

This video demonstrates how to evaluate expressions with whole number exponents.

Type: Tutorial

The Zero Power:

Learn why a number raised to the zero power equals 1.

Type: Tutorial

Parent Resources

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