| Code |
Description |
| MA.6.NSO.3.1: | Given a mathematical or real-world context, find the greatest common factor and least common multiple of two whole numbers.Clarifications:
Clarification 1: Within this benchmark, expectations include finding greatest common factor within 1,000 and least common multiple with factors to 25.Clarification 2: Instruction includes finding the greatest common factor of the numerator and denominator of a fraction to simplify a fraction. |
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| MA.6.NSO.3.2: | Rewrite the sum of two composite whole numbers having a common factor, as a common factor multiplied by the sum of two whole numbers.Clarifications:
Clarification 1: Instruction includes using the distributive property to generate equivalent expressions. |
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| MA.6.NSO.3.3: | 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. |
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| MA.6.NSO.3.4: | Express composite whole numbers as a product of prime factors with natural number exponents. |
| MA.6.NSO.3.5: | Rewrite positive rational numbers in different but equivalent forms including fractions, terminating decimals and percentages.Clarifications:
Clarification 1: Rational numbers include decimal equivalence up to the thousandths place. |
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This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| Can you say that another way?: | Students will model how to express an addition problem using the distributive property. |
| 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. |
| 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. |
| You Can Never Have Too Many Shoes!: | This lesson teaches Least Common Multiples. |
| 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. |
| 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. |
| 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. |
| Prime Factorization - From Fingerprints to Factorprints: | This activity provides an introduction to composite numbers and prime numbers through factorization. |
| Order Matters: | Students will analyze a Scratch program and compare its computerized algorithm to the mathematical order of operations, in this lesson plan. |
| The Distributive Property: | Introductory lesson on the distributive property using word problems as context for area models. |
| Name |
Description |
| 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. |
| 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. |
| 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. |
| The Florist Shop: | Students are asked to solve a real-world problem involving common multiples. |
| 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. |
| Name |
Description |
| 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. |
| 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. |
| Least Common Multiple: | This video demonstrates the prime factorization method to find the lcm (least common multiple). |
| Introduction to Exponents: | This video demonstrates how to evaluate expressions with whole number exponents. |
| The Zero Power: | Learn why a number raised to the zero power equals 1. |
| 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. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| 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. |
| 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. |
| Least Common Multiple: | This video demonstrates the prime factorization method to find the lcm (least common multiple). |
| Introduction to Exponents: | This video demonstrates how to evaluate expressions with whole number exponents. |
| The Zero Power: | Learn why a number raised to the zero power equals 1. |
| 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. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
