NSES Content Standard A  Science as Inquiry: Abilities necessary to do scientific inquiry Grades 5-8, page 145 Think critically and logically to make the relationships between evidence and explanations. Thinking critically about evidence includes deciding what evidence should be used and accounting for anomalous data. Specifically, students should be able to review data from a simple experiment, summarize the data, and form a logical argument about the cause-effect relationships in the experiment. Students should begin to state some explanations in terms of the relationship between two or more variables.

Benchmark 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 designs that are able to deal with such situations.

Benchmark 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 to objectivity 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 questions.

Benchmark 1B The Nature of Science: Scientific Inquiry
Hypotheses are widely used in science for choosing what data to pay attention to and what additional data to seek, and for guiding the interpretation of the data (both new and previously available).

Benchmark 9B The Mathematical World: Symbolic Relationships
Mathematical statements can be used to describe how one quantity changes when another changes. Rates of change can be computed from differences in magnitudes and vice versa.

Benchmark 9B The Mathematical World: Symbolic Relationships
Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease indefinitely, increase or decrease in steps, or do something different from any of these.

Benchmark 9E The Mathematical World: Reasoning
Some aspects of reasoning have fairly rigid rules for what makes sense; other aspects don't. If people have rules that always hold, and good information about a particular situation, then logic can help them to figure out what is true about it. This kind of reasoning requires care in the use of key words such as if, and, not, or, all, and some. Reasoning by similarities can suggest ideas but can't prove them one way or the other.

Benchmark 9E The Mathematical World: Reasoning
Sometimes people invent a general rule to explain how something works by summarizing observations. But people tend to overgeneralize, imagining general rules on the basis of only a few observations.

Benchmark 9E The Mathematical World: Reasoning
People are using incorrect logic when they make a statement such as "If A is true, then B is true; but A isn't true, therefore B isn't true either."

Benchmark 9E The Mathematical World: Reasoning
A single example can never prove that something is always true, but sometimes a single example can prove that something is not always true.

Benchmark 12B Habits of Mind: Computation and Estimation