Standard 1 : Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.



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General Information

Number: MA.912.NSO.1
Title: Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Number Sense and Operations

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.NSO.1.1: Extend previous understanding of the Laws of Exponents to include rational exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions involving rational exponents.
Clarifications:
Clarification 1: Instruction includes the use of technology when appropriate.

Clarification 2: Refer to the K-12 Formulas (Appendix E) for the Laws of Exponents.

Clarification 3: Instruction includes converting between expressions involving rational exponents and expressions involving radicals.

Clarification 4:Within the Mathematics for Data and Financial Literacy course, it is not the expectation to generate equivalent numerical expressions.

MA.912.NSO.1.2: Generate equivalent algebraic expressions using the properties of exponents.
MA.912.NSO.1.3: Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents.
Clarifications:
Clarification 1: Within the Algebra 2 course, radicands are limited to monomial algebraic expressions.
MA.912.NSO.1.4: Apply previous understanding of operations with rational numbers to add, subtract, multiply and divide numerical radicals.
Clarifications:
Clarification 1: Within the Algebra 1 course, expressions are limited to a single arithmetic operation involving two square roots or two cube roots.
MA.912.NSO.1.5: Add, subtract, multiply and divide algebraic expressions involving radicals.
Clarifications:
Clarification 1: Within the Algebra 2 course, radicands are limited to monomial algebraic expressions.
MA.912.NSO.1.6: Given a numerical logarithmic expression, evaluate and generate equivalent numerical expressions using the properties of logarithms or exponents.
Clarifications:
Clarification 1: Within the Mathematics for Data and Financial Literacy Honors course, problem types focus on money and business.
MA.912.NSO.1.7: Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.
Clarifications:
Clarification 1: Within the Mathematics for Data and Financial Literacy Honors course, problem types focus on money and business.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MA.912.NSO.1.AP.1: Evaluate numerical expressions involving rational exponents.
MA.912.NSO.1.AP.2: Identify equivalent algebraic expressions using properties of exponents.
MA.912.NSO.1.AP.3: Using properties of exponents, identify equivalent algebraic expressions involving radicals and rational exponents. Radicands are limited to monomial algebraic expression.
MA.912.NSO.1.AP.4: Apply previous understanding of operations with rational numbers to add and subtract numerical radicals that are in radical form.
MA.912.NSO.1.AP.5: Add and subtract algebraic expressions involving radicals. Radicands are limited to monomial algebraic expressions.
MA.912.NSO.1.AP.6: Given a numerical logarithmic expression, identify an equivalent numerical expression using the properties of logarithms or exponents.
MA.912.NSO.1.AP.7: Given an algebraic logarithmic expression, identify an equivalent algebraic expression using the properties of logarithms or exponents.


Related Resources

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

Original Student Tutorial

Name Description
The Radical Puzzle:

Learn to rewrite products involving radicals and rational exponents using properties of exponents in this interactive tutorial.

Formative Assessments

Name Description
Roots and Exponents:

Students are asked to rewrite the square root of five in exponential form and justify their choice of exponent.

Rational Exponents and Roots:

Students asked to show that two forms of an expression (exponential and radical) are equivalent.

Rational Exponents - 4:

Students are asked to rewrite expressions involving radicals and rational exponents in equivalent forms.

Rational Exponents - 2:

Students are asked to convert numerical expressions from exponential to radical form.

Rational Exponents - 3:

Students are asked to convert a product of a radical and exponential expression to a single power of two.

Rational Exponents - 1:

Students are asked to convert numerical expressions from radical to exponential form.

College Costs:

Students are asked to transform an exponential expression so that the rate of change corresponds to a different time interval.

Population Drop:

Students are asked to use the properties of exponents to show that two expressions are equivalent and compare the two functions in terms of what each reveals.

Lesson Plans

Name Description
My Geometry Classroom:

Students will learn how to find the area and perimeter of multiple polygons in the coordinate plane using the composition and decomposition methods, applying the Distance Formula and Pythagorean Theorem. Students will complete a Geometry Classroom Floor Plan group activity. Students will do a short presentation to discuss their results which leads to the realization that polygons with the same perimeter can have different areas. Students will also complete an independent practice and submit an exit ticket at the end of the lesson.

The Copernicus' Travel:

This lesson uses Inverse Trigonometric Ratios to find acute angle measures in right triangles. Students will analyze the given information and determine the best method to use when solving right triangles. The choices reviewed are Trigonometric Ratios, The Pythagorean Theorem, and Special Right Triangles.

Simply Radical!:

Students will simplify and perform operations on radical expressions. Pairs of students will work on problems at different complexity levels that lead to the same solution. The students will challenge each other to prove their solutions are correct. This activity does not address rational exponents.

Problem-Solving Tasks

Name Description
Newton's Law of Cooling:

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

Seeing Dots:

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.



Student Resources

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

Original Student Tutorial

Title Description
The Radical Puzzle:

Learn to rewrite products involving radicals and rational exponents using properties of exponents in this interactive tutorial.

Problem-Solving Tasks

Title Description
Newton's Law of Cooling:

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

Seeing Dots:

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.



Parent Resources

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

Problem-Solving Tasks

Title Description
Newton's Law of Cooling:

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

Seeing Dots:

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.