### Standard 1: Mathematics as Problem Solving

In grades 5-8, the mathematics curriculum should include numerous experiences with problem solving as a method of inquiry and application so that students can:
• Use problem solving approaches to investigate and understand mathematical content
Benchmarks 12A (Habits of Mind: Values and Attitudes)
Keep records of their investigations and observations and not change the records later.

• Formulate problems from situations within and outside mathematics
Benchmarks 1B (The Nature of Science: Scientific Inquiry)
Scientists’ explanations about what happens in the world come partly from what they observe, partly from what they think. Sometimes scientists have different explanations for the same set of observations. That usually leads to their making more observations to resolve the differences.

• Develop and apply a variety of strategies to solve problems, with emphasis on multi-step and non-routine problems
Benchmarks 2A (The Nature of Mathematics: Patterns and Relationships)
Usually there is no right way to solve a mathematical problem; different methods have different advantages and disadvantages.

Benchmarks 1B (The Nature of Science: Scientific Inquiry)
Scientific investigations may take many different forms, including observing what things are like or what is happening somewhere, collecting specimens for analysis, and doing experiments. Investigations can focus on physical, biological, and social questions.

• Verify and interpret results with respect to the original problem situation
Benchmarks 1B (The Nature of Science: Scientific Inquiry)
If more than one variable changes at the same time in an experiment, the outcome of the experiment may not be clearly attributable to any one of the variables. It may not always be possible to prevent outside variables from influencing the outcome of an investigation (or even to identify all of the variables), but collaboration among investigators can often lead to research design that are able to deal with such situations.

Benchmarks 1B (The Nature of Science: Scientific Inquiry)
What people expect to observe often affects what they actually do observe. Strong beliefs about what should happen in particular circumstances can prevent them from detecting other results. Scientists know about this danger and take steps to try and avoid it when designing investigations and examining data. One safeguard is to have different investigators conduct independent studies of the same question.

• Generalize solutions and strategies to new problem situations
• Benchmarks 3B (The Nature of Technology: Design and Systems)