Secondary Mathematics III

Strand: ALGEBRA - Creating Equations (A.CED)

Create equations that describe numbers or relationships, using all available types of functions to create such equations (Standards A.CED.1-4).

Standard A.CED.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

• ALGEBRA - Creating Equations (A.CED) - 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 - Creating Equations (A.CED).
• Clea on an Escalator
This task has students create equations to model a physical scenario, and then reason with those equations to come up with a solution.
• Global Positioning System I
This question examines the algebraic equations for three different spheres. The intersections of each pair of spheres are then studied, both using the equations and thinking about the geometry of the spheres.
• How Much Folate?
This task a could be used as an introduction to writing and graphing linear inequalities. Part (a) includes significant scaffolding to support the introduction of the ideas. Part (b) demonstrates that, in some situations, writing down all possible combinations is not feasible.
• Inscribing and Circumscribing Right Triangles
This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems.
• 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.
• Module 4: Rational Expressions and Functions - Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 4, Rational Expressions and Functions, students work with the fractions that are ratios of polynomials, rational expressions and functions.
• Module 4: Rational Expressions and Functions - Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 4, Rational Expressions and Functions, students work with the fractions that are ratios of polynomials, rational expressions and functions.
• Optimization Problems: Boomerangs
This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the constraints and variables mathematically, select appropriate mathematical methods to use, explore the effects of systematically varying the constraints, and interpret and evaluate the data generated and identify the optimum case, checking it for confirmation.
• Regular Tessellations of the plane
This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.
• Silver Rectangle
This task provides a geometric context for working with ratios and algebraic equations. Students will create and then solve an algebraic equation describing a remarkable shape, the silver rectangle.
• Throwing a Ball
Although this task is quite straightforward, it has a couple of aspects designed to encourage students to attend to the structure of the equation and the meaning of the variables in it.
• Uranium 238
The goal of this task is to represent an exponential relationship by an equation and identify, using knowledge of the context and the structure of the equation, possible graphs for the equation.

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.