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Problem SolvingProblem Solving
A Scientific ProcessA Scientific Process
A Scientific Process… A Scientific Process…
Is Based on Observed FactsIs Based on Observed Facts
Has Repeatable ResultsHas Repeatable Results
Produces Verifiable OutcomesProduces Verifiable Outcomes
Is Carried Out in a Standard, Systematic Is Carried Out in a Standard, Systematic WayWay
Scientific MethodScientific Method
The Standard, Systematic Way to Carry The Standard, Systematic Way to Carry Out a Scientific ProcessOut a Scientific ProcessHypothesis (Untested Idea)Hypothesis (Untested Idea)Experiment (Test to Check Validity of Experiment (Test to Check Validity of
Hypothesis)Hypothesis)Theory (Valid Explanation of Observations)Theory (Valid Explanation of Observations)
Model – Simplified Theory with AssumptionsModel – Simplified Theory with Assumptions
Law (Summary of Key Experimental Law (Summary of Key Experimental Observations)Observations)
The Scientific MethodThe Scientific Method
Experiment
TheoryLaw
Hypothesis
Scientific Problem SolvingScientific Problem Solving
HypothesisHypothesis
ExperimentExperiment
Theory/LawTheory/Law
Understand Problem ConceptsUnderstand Problem Concepts
Propose Solution Based on Propose Solution Based on Applicable RelationshipsApplicable Relationships
Try Proposal (ie – Do the Try Proposal (ie – Do the Math!)Math!)
Check Results – Do they Make Check Results – Do they Make Sense?Sense?
Document/Summarize ResultsDocument/Summarize Results
It’s All About MeasurementsIt’s All About Measurements
Measurement – 3 PartsMeasurement – 3 PartsA Number or Value; MagnitudeA Number or Value; MagnitudeA Unit: Provides the Standard ScaleA Unit: Provides the Standard Scale
One of the Standard Scale – Known and ConstantOne of the Standard Scale – Known and Constant
Eg, pound, gram, liter, newtonEg, pound, gram, liter, newton
What is Being Measured – Sometimes Very What is Being Measured – Sometimes Very ImportantImportant
Examples of MeasurementsExamples of Measurements
3.98 calories of heat3.98 calories of heat
5.67 newtons force of bowling ball striking 5.67 newtons force of bowling ball striking pinspins
10.0 liters of water10.0 liters of water
57 km/hour auto speed57 km/hour auto speed
7.65 gallons gasoline7.65 gallons gasoline
Not MeasurementsNot MeasurementsObjects CountedObjects CountedDefinitions – eg. Exactly 2.54 cm = 1 inchDefinitions – eg. Exactly 2.54 cm = 1 inchWhy Not?Why Not?Counted Items and Definitions are not Counted Items and Definitions are not
debatabledebatableThey are “perfect”They are “perfect”No “perfect” measurements; always error; No “perfect” measurements; always error;
never exact never exact
A Very Useful TechniqueA Very Useful Technique
Dimensional Analysis (aka “Factor Dimensional Analysis (aka “Factor Labeling”)Labeling”)Converting a Measurement from One Unit to Converting a Measurement from One Unit to
AnotherAnother““Cutting to the Chase” of a Proportion Cutting to the Chase” of a Proportion
ProblemProblemm Unit 1 x Unit 2/Unit 1 = n Unit 2m Unit 1 x Unit 2/Unit 1 = n Unit 2Problem to Try – How many pounds is 583 Problem to Try – How many pounds is 583
grams?grams?