 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).
• Calculating the square root of 2
This Illustrative Mathematics task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do.
• Checking a calculation of a decimal exponent
This Illustrative Mathematics task is primarily suited for instruction as written, though could be used for assessment in settings where varied answers can easily be checked, in particular for formative assessment. The purpose of the task is to connect properties of fractional exponents with ordering of real numbers. One can place the numbers on the number line to emphasize this.
• Classifying Rational and Irrational Numbers
This lesson unit is intended to help educators assess how well students are able to distinguish between rational and irrational numbers
• Coordinates of equilateral triangles
The purpose of this Illustrative Mathematics task is to examine angles of triangles whose vertices have specific integer coordinates.
• 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.
• Evaluating Statements about Rational and Irrational Numbers
This lesson unit is intended to help you assess how well students reason about the properties of rational and irrational numbers.
• 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.
• Kepler's Third Law of Motion
The purpose of this Illustrative Mathematics task is to solve some expressions requiring fractional exponents in an interesting modeling context.
• 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)
• Operations with Rational and Irrational Numbers
This Illustrative Mathematics task has students experiment with the operations of addition and multiplication, as they relate to the notions of rationality and irrationality.
• Rational or Irrational?
This Illustrative Mathematics task makes for a good follow-up task on rational irrational numbers after that the students have been acquainted with some of the more basic properties, asking students to reason about rational and irrational numbers (N-RN.3) in a variety of ways. In addition to eliciting several different types of reasoning, the task requires students to rewrite radical expressions in which the radicand is divisible by a perfect square (N-RN.2).
• Rules of 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.
• Rules of Exponents video
This video introduces and explains the topic.
• Sums of rational and irrational numbers
The goal of this Illustrative Mathematics task is to examine sums and products of rational and irrational numbers. 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.

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