Standard 3: Apply properties of operations to rewrite numbers in equivalent forms.

General Information
Number: MA.6.NSO.3
Title: Apply properties of operations to rewrite numbers in equivalent forms.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 6
Strand: Number Sense and Operations

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.6.NSO.3.AP.1
Use tools to find the greatest common factor and least common multiple of two whole numbers 50 or less.
MA.6.NSO.3.AP.2
Use the distributive property to express a number as the sum of two whole numbers multiplied by a common factor.
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).
MA.6.NSO.3.AP.4
4 Use a tool to show the prime factors of a composite whole number (e.g., 20 = 2 × 2 × 5).
MA.6.NSO.3.AP.5
Rewrite a positive rational number 3 or less, as a fraction, decimal or a percent.

Related Resources

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

Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Formative Assessments

Using the Distributive Property:

Students are asked to rewrite 36 + 42 in the form a(b + c) where a is the greatest common factor of 36 and 42.

Type: Formative Assessment

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

Least Common Multiples:

Students are asked to find the least common multiple of 8 and 12 and to explain how they found their answers.

Type: Formative Assessment

Greatest Common Factors:

Students are given two whole numbers less than or equal to 100 and asked to find the greatest common factor.

Type: Formative Assessment

Evaluating Exponents:

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

Type: Formative Assessment

Lesson Plans

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

Extending the Distributive Property:

In this lesson, students will build upon their arithmetic experiences with the distributive property to equate algebraic expressions through a series of questions related to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for moving the concrete learner to the abstract level and the use of matching cards.
This is an introductory lesson that only includes producing equivalent expressions such as 3(2 + x) = 6 + 3x.

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

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

Let's Understand Multiplication of Positive and Negative Numbers:

This lesson provides teachers with a way to show students why multiplying negative numbers results in a positive answer. The lesson starts with a review of decomposition, the distributive property, and finding missing addends. Then, with teacher guidance, groups of students apply these skills in a systematic way to apply properties of operations to discover the rules governing the signs of products for positive and negative factors and to multiply positive and negative numbers in mathematical and real-world problems. Finally, students independently demonstrate mastery of the lesson objectives by completing an independent practice assessment.

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

Can You Find the Relationship?:

In this lesson students will first define in their own words what the greatest common factor (GCF) and least common multiple (LCM) mean. They will take this understanding and apply it to solving GCF and LCM word problems. Students will then illustrate their understanding by creating posters based on their word problems. There are examples of different types of methods, online games, a rubric, and a power point to summarize this two-day lesson.

Type: Lesson Plan

Can you say that another way?:

Students will model how to express an addition problem using the distributive property.

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

Digesting the Distributive Property:

This lesson will show the student how to use the distributive property to express a sum of two whole numbers 1-100.

Type: Lesson Plan

You Can Never Have Too Many Shoes!:

This lesson teaches Least Common Multiples.

Type: Lesson Plan

Finding the Greatest Crush Factor:

This lesson uses a real-life approach to exploring the use of Greatest Common Factors (GCF). The students will utilize math practice standards as they analyze math solutions and explain their own solutions.

Type: Lesson Plan

Factoring out the Greatest:

This lesson teaches students how to find the GCF and LCM by factoring. This is a different method than is normally seen in textbooks. This method easily leads to solving GCF word problems and using the distributive property to express a sum of two whole numbers.

Type: Lesson Plan

Which Food Should I Feed My Cat?:

The students will convert fractions into decimals and multiply to determine the amount of food to feed their assigned cat. Using this amount, they will calculate (division of decimals) the number of servings and the price per serving of cat food. Students will work with three brands of food and enter the data into their charts. Finally, the students will analyze the data to determine the most affordable food.

Type: Lesson Plan

Predicting the decimal equivalent for a fraction - terminating or repeating?:

This lesson encourages students to make an important discovery. Will a given fraction yield a terminating or repeating decimal? Discussion includes why knowing this is important. The lesson is structured to allow exploration, discovery, and summarization.

Type: Lesson Plan

Prime Factorization - From Fingerprints to Factorprints:

This activity provides an introduction to composite numbers and prime numbers through factorization.

Type: Lesson Plan

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 Distributive Property:

Introductory lesson on the distributive property using word problems as context for area models.

Type: Lesson Plan

Original Student Tutorials

Homework Help: Least Common Multiple Part 2:

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Base Ten and Exponents:

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

Type: 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

Homework Help: Least Common Multiple Part 1:

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Problem-Solving Tasks

Adding Multiples:

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

Type: Problem-Solving Task

Bake Sale:

The purpose of this task requires students to apply the concepts of factors and common factors in a context. A version of this task could be adapted into a teaching task to help motivate the need for the concept of a common factor.

Type: Problem-Solving Task

Multiples and Common Multiples:

This problem uses the same numbers and asks similar mathematical questions as "The Florist Shop" file, but that task requires students to apply the concepts of multiples and common multiples in a context.

Type: Problem-Solving Task

The Florist Shop:

Students are asked to solve a real-world problem involving common multiples.

Type: Problem-Solving Task

Factors and Common Factors:

This problem uses the same numbers and asks essentially the same mathematical questions as "Bake Sale," but that task requires students to apply the concepts of factors and common factors in a context.

Type: Problem-Solving Task

Teaching Ideas

Communicating about Numbers-SeaWorld Classroom Activity:

Students communicate mathematical ideas and visually represent ideas by constructing charts, graphs, and scale drawings based on information cards about various marine animals.

Type: Teaching Idea

Calculating Sharks-SeaWorld Classroom Activity:

  • Given data about sharks and the amount of food they eat, students will be able to solve for the unknown in percentage problems.
  • Given information about a shark's growth, students will be able to graph coordinates and interpret a linear graph.
  • Given the conversion factor, students will be able to convert from metric to English units.

Type: Teaching Idea

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

Least Common Multiple:

This video demonstrates the prime factorization method to find the lcm (least common multiple).

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

Least Common Denominators:

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases.  Elementary teachers should note this is not a requirement for elementary standards and consider whether this video will further student knowledge or create confusion.  This chapter explains how to find the smallest possible common denominator. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.  

Type: Tutorial

Video/Audio/Animation

LCM and GCF Word Problems:

Here we have a couple of word problems searching for the least common multiple and the other for the greatest common factor. 

Type: Video/Audio/Animation

Student Resources

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

Original Student Tutorials

Homework Help: Least Common Multiple Part 2:

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Base Ten and Exponents:

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

Type: 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

Homework Help: Least Common Multiple Part 1:

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Problem-Solving Tasks

Adding Multiples:

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

Type: Problem-Solving Task

The Florist Shop:

Students are asked to solve a real-world problem involving common multiples.

Type: Problem-Solving Task

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

Least Common Multiple:

This video demonstrates the prime factorization method to find the lcm (least common multiple).

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

Least Common Denominators:

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases.  Elementary teachers should note this is not a requirement for elementary standards and consider whether this video will further student knowledge or create confusion.  This chapter explains how to find the smallest possible common denominator. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.  

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

Adding Multiples:

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

Type: Problem-Solving Task

Bake Sale:

The purpose of this task requires students to apply the concepts of factors and common factors in a context. A version of this task could be adapted into a teaching task to help motivate the need for the concept of a common factor.

Type: Problem-Solving Task

The Florist Shop:

Students are asked to solve a real-world problem involving common multiples.

Type: Problem-Solving Task