Secondary Mathematics II

Strand: NUMBER AND QUANTITY - The Real Number System (N.RN)

Extend the properties of exponents to rational exponents (Standards N.RN.1–2). Use properties of rational and irrational numbers (Standard N.RN. 3).

Standard N.RN.1

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

• Evaluating a Special Exponential Expression
The purpose of this Illustrative Mathematics task is to study the rules of exponents in the context of trying to make sense of a very interesting mathematical expression.
• Evaluating Exponential Expressions
The goal of this Illustrative Mathematics task is to use properties of exponents for whole numbers in order to explain how expressions with fractional exponents are defined.
• Extending the Definitions of Exponents, Variation 2
The goal of this task is to develop an understanding of why rational exponents are defined as they are (N-RN.1), however it also raises important issues about distinguishing between linear and exponential behavior (F-LE.1c) and it requires students to create an equation to model a context (A-CED.2)
• Fractional Exponents
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Fractional Exponents video
This video introduces and explains the concept of fractional exponents.
• Introduction to the Materials (Math 2)
Introduction to the Materials in the Mathematics Two of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
• Module 3: Solving Quadratics & Other Equations - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 3, Solving Quadratics & Other Equations. The idea that different quadratic forms are useful in graphing is extended in Module 3, Solving Quadratic and Other Equations, when students use different forms of quadratic equations to find the roots or solve quadratic equations of a single variable.
• Module 3: Solving Quadratics & Other Equations - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 3, Solving Quadratics & Other Equations. The idea that different quadratic forms are useful in graphing is extended in Module 3, Solving Quadratic and Other Equations, when students use different forms of quadratic equations to find the roots or solve quadratic equations of a single variable.
• NUMBER AND QUANTITY - The Real Number System (N.RN) - Sec Math II Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - The Real Number System (N.RN)

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.