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Mathematics - Secondary Curriculum Secondary Mathematics III
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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.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, maximizing the volume of a box for a given surface area while drawing attention to the practical domain.

  • 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).
  • Bernardo and Sylvia Play a Game
    This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.
  • Dimes and Quarters
    This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system.
  • Fishing Adventures 3
    This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.
  • Growing coffee
    This task is designed to make students think about the meaning of the quantities presented in the context and choose which ones are appropriate for the two different constraints presented. In particular, note that the purpose of the task is to have students generate the constraint equations for each part (though the problem statements avoid using this particular terminology), and not to have students solve said equations.
  • 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.
  • 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.
  • Writing constraints
    The purpose of this task is to give students practice writing a constraint equation for a given context.

UEN logo - 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.