Secondary Mathematics III

Strand: ALGEBRA - Arithmetic With Polynomials and Rational Expressions (A.APR)

Perform arithmetic operations on polynomials, extending beyond the quadratic polynomials (Standard A.APR.1). Understand the relationship between zeros and factors of polynomials (Standards A.APR.2–3). Use polynomial identities to solve problems (Standards A.APR.4–5). Rewrite rational expressions (Standards A.APR.6–7).

Standard A.APR.1

Understand that all polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

• ALGEBRA - Arithmetic With Polynomials and Rational Expressions (A.APR) - Sec Math III Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics III - Arithmetic With Polynomials and Rational Expressions (A.APR).
• Introduction to the Materials (Math 3)
Introduction to the Materials in the Mathematics Three 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: Polynomial Functions - Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 3, Polynomial Functions, begins with a task that links linear, quadratic, and cubic functions together by highlighting the rates of change of each function type and using a story context to show that a linear function is the sum of a constant, a quadratic function is the accumulation or sum of a linear function, and a cubic function is the sum of a quadratic function.
• Module 3: Polynomial Functions - Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 3, Polynomial Functions, begins with a task that links linear, quadratic, and cubic functions together by highlighting the rates of change of each function type and using a story context to show that a linear function is the sum of a constant, a quadratic function is the accumulation or sum of a linear function, and a cubic function is the sum of a quadratic function.
• Non-Negative Polynomials
The task helps foster student understanding of the analogy described in the standard -- "Understand that polynomials form a system analogous to the integers..." -- in addition to having the same arithmetic operations available, there are many other instances in which integers and polynomials share common properties.
• Powers of 11
This task might be used as either practice with polynomial arithmetic or as an introduction to the binomial theorem, providing a process for raising binomials to powers without dredging through many repetitive applications of the distributive law.
• Special Products of Polynomials video
This video introduces and explains the concept.

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.