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.5

Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers. For example, with coefficients determined by Pascal’s Triangle.

• 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.
• 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.
• Trina's Triangles
This task is a fleshing-out of the example suggested in A-APR.4 of the Common Core document, using the polynomial identity (x2+y2)2=(x2y2)2+(2xy)2 to generate Pythagorean triples.

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.