# 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.)
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+×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

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

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

## 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

## Teaching Ideas

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

## 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.