Topic: Problemsolving 
Thinking and Reasoning 
 Standard 2. Understands and applies basic principles of logic and reasoning 
  Level IV (Grade 912) 
   Benchmark 10.  Understands that logic may be of limited help in finding solutions to problems if the general rules upon which conclusions are based do not always hold true; most often, we have to deal with probabilities rather than certainties 
    Knowledge/skill statements 
     1.  Understands that logic may be of limited help in finding solutions to problems if the general rules upon which conclusions are based do not always hold true 
     2.  Knows that most often in problemsolving one has to deal with probabilities rather than certainties 
 Standard 5. Applies basic troubleshooting and problemsolving techniques 
  Level I (Grade K2) 
   Benchmark 1.  Identifies simple problems and possible solutions (e.g., ways to make something work better) 
    Knowledge/skill statements 
     1.  Identifies simple problems 
     2.  Identifies possible solutions 
  Level II (Grade 35) 
   Benchmark 1.  Identifies issues and problems in the school or community that one might help solve 
    Knowledge/skill statements 
     1.  Identifies school issues that one might help solve 
     2.  Identifies school problems that one might help solve 
     3.  Identifies community issues that one might help solve 
     4.  Identifies community problems that one might help solve 
   Benchmark 2.  Analyzes the problems that have confronted people in the past in terms of the major goals and obstacles to those goals 
    Knowledge/skill statements 
     1.  Analyzes the problems that have confronted people in the past in terms of the major goals 
     2.  Analyzes the problems that have confronted people in the past in terms of the obstacles to the goals 
  Level III (Grade 68) 
   Benchmark 1.  Generates alternative courses of action and compares the possible consequences of each alternative 
    Knowledge/skill statements 
     1.  Generates alternative courses of action 
     2.  Compares the possible consequences of each alternative 
   Benchmark 2.  Selects the most appropriate strategy or alternative for solving a problem 
    Knowledge/skill statements 
     1.  Knows that one strategy or alternative for solving a problem may be more appropriate than others 
  Level IV (Grade 912) 
   Benchmark 5.  Engages in problem finding and framing for personal situations and situations in the community 
    Knowledge/skill statements 
     1.  Engages in problem finding for personal situations 
     2.  Engages in problem framing for personal situations 
     3.  Engages in problem finding situations in the community 
     4.  Engages in problem framing situations in the community 
   Benchmark 6.  Represents a problem accurately in terms of resources, constraints, and objectives 
    Knowledge/skill statements 
     1.  Represents a problem accurately in terms of resources 
     2.  Represents a problem accurately in terms of constraints 
     3.  Represents a problem accurately in terms of objectives 
   Benchmark 7.  Evaluates the effectiveness of problemsolving techniques 
    Knowledge/skill statements 
     1.  Knows criteria to judge the effectiveness of problemsolving techniques 
   Benchmark 8.  Reframes problems when alternative solutions are exhausted 
    Knowledge/skill statements 
     1.  Tries all alternative strategies to solve a problem 
   Benchmark 9.  Examines different options for solving problems of historical importance and determines why specific courses of action were taken 
    Knowledge/skill statements 
     1.  Examines different options for solving problems of historical importance 
     2.  Determines why specific courses of action were taken for problems of historical importance 
   Benchmark 10.  Evaluates the feasibility of various solutions to problems; recommends and defends a solution 
    Knowledge/skill statements 
     1.  Evaluates the feasibility of various solutions to problems 
     2.  Recommends a solution to a problem 
   Benchmark 11.  Understands causes and critical issues of problems (e.g., personal, social, ethical considerations) 
    Knowledge/skill statements 
     1.  Understands causes of problems 
     2.  Understands critical issues of problems such as personal considerations 
     3.  Understands critical issues of problems such as social considerations 
Business Education 
 Standard 12.
Uses common international standards of measurement to solve business problems

  Level IV (Grade 912) 
   Benchmark 3.  Solves realworld problems involving two and threedimensional measures (e.g., maximizing shelf space, designing floor displays) 
    Knowledge/skill statements 
     1.  Solves realworld problems involving twodimensional measures 
     2.  Solves realworld problems involving threedimensional measures 
     3.  Solves realworld problems such as maximizing shelf space 
     4.  Solves realworld problems such as designing floor displays 
 Standard 13. Analyzes and interprets data using common statistical procedures, charts, and graphs 
  Level IV (Grade 912) 
   Benchmark 1.  Uses statistical concepts to analyze data, evaluate results, and draw conclusions (e.g., data found in financial reports) 
    Knowledge/skill statements 
     1.  Uses statistical concepts to analyze data 
     2.  Uses statistical concepts to evaluate results 
     3.  Uses statistical concepts to draw conclusions 
     4.  Uses statistical concepts to analyze data found in financial reports 
 Standard 14. Uses basic mathematical operations to solve business problems 
  Level IV (Grade 912) 
   Benchmark 12.  Uses recurrence relations (i.e., formulas expressing each term as a function of one or more of the previous terms, such as the Fibonacci sequence or the compound interest equation) to model and to solve realworld problems (e.g., home mortgages, annuities) 
    Knowledge/skill statements 
     1.  Uses recurrence relations to model realworld problems 
     2.  Uses recurrence relations to solve realworld problems 
     3.  Uses formulas expressing each term as a function of one or more of the previous terms in order to model and to solve realworld problems 
     4.  Uses the Fibonacci sequence to model and to solve realworld problems 
     5.  Uses the compound interest equation to model and solve realworld problems 
     6.  Uses recurrence relations to model and to solve problems such as home mortgages 
     7.  Uses recurrence relations to model and to solve problems such as annuities 
Engineering Education 
 Standard 17. Understands elements of production planning 
  Level IV (Grade 912) 
   Benchmark 7.  Proposes alternative solutions to manufacturing problems (e.g., recommend changes to a product or process)

    Knowledge/skill statements 
     1.  Proposes alternative solutions to manufacturing problems such as recommend changes to a product 
     2.  Proposes alternative solutions to manufacturing problems such as recommend changes to a process 
Mathematics 
 Standard 1. Uses a variety of strategies in the problemsolving process 
  Level I (Grade K2) 
   Benchmark 4.  Makes organized lists or tables of information necessary for solving a problem 
    Knowledge/skill statements 
     1.  Constructs table to solve a numerical problem 
     2.  Makes organized lists to solve a numerical problem 
     3.  Makes a chart to solve a numerical problem 