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There Has to Be a System for This Sweet Problem

Web-based Content

There Has to Be a System for This Sweet Problem

Grade Levels

10th Grade, 11th Grade, 12th Grade, 9th Grade

Course, Subject

Algebra I, Algebra II
Related Academic Standards
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  • Big Ideas
    Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
    Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
    Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
  • Concepts
    Algebraic properties and processes
    Algebraic properties, processes and representations
    Analysis of one and two variable (univariate and bivariate) data
    Exponential functions and equations
    Functions and multiple representations
    Linear relationships: Equation and inequalities in one and two variables
    Linear system of equations and inequalities
    Polynomial functions and equations
    Quadratic functions and equations
  • Competencies
    Extend algebraic properties and processes to quadratic, exponential, and polynomial expressions and equations and to matrices, and apply them to solve real world problems.
    Represent a polynomial function in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated polynomial equation to each representation.
    Represent a quadratic function in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated quadratic equation to each representation.
    Represent exponential functions in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the growth/decay rate of the associated exponential equation to each representation.
    Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation.
    Use algebraic properties and processes in mathematical situations and apply them to solve real world problems.
    Write, solve, and interpret systems of two linear equations and inequalities using graphing and algebraic techniques.
    Write, solve, graph, and interpret linear equations and inequalities to model relationships between quantities.

Description

We are confronted with problems on a regular basis. Some of these are easy to solve, while others leave us puzzled. In this lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution.

Web-based Resource

Content Provider

Illuminations

 

Illuminations is a project designed by the National Council of Teachers of Mathematics (NCTM) and supported by the Verizon Foundation.  Illuminations works to serve you by increasing access to quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers.

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