 Secondary Mathematics III

Strand: ALGEBRA - Seeing Structures in Expressions (A.SSE)

Interpret the structure of expressions. Extend to polynomial and rational expressions (Standards A.SSE.1-2). Write expressions in equivalent forms to solve problems (Standard A.SSE.4).
The purpose of this instructional task is to give students an opportunity to construct and find the value of a geometric series (A-SSE.4) in a financial literacy context. The task assumes that students have already developed the formula for a geometric series themselves; having them recognize the need for this formula (and look up if necessary) allows them to engage in MP 5, Use appropriate tools strategically. The task also provides students with an opportunity to look for and express regularity in repeated reasoning (MP 8), as the solution shows. This task also asks students to interpret the variables in the future value formula in the context of the problem (A-SSE.1).
• Adding and Subtracting Rational Expressions video
This video introduces and explains the topic.
• ALGEBRA - Seeing Structure in Expression (A.SSE) - 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 - Seeing Structure in Expression (A.SSE)
• Cantor Set
The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.
• Computations with Complex Numbers
• Course of Antibiotics
This task presents a real world application of finite geometric series. The context can lead into several interesting follow-up questions and projects. Many drugs only become effective after the amount in the body builds up to a certain level. This can be modeled very well with geometric series.
• 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.
• Multiplying and Dividing Rational Expressions video
This video introduces and explains the topic.
• Simplifying Rational Expressions
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.
• Special Products of Polynomials video
This video introduces and explains the concept.
• Triangle Series
The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation. 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.